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FOCUS Editorial Board: Rob Bradley; J.Kevin Colligan; Sharon Cutler Ross; JoeGallian; Jackie Giles; Maeve McCarthy; ColmMulcahy; Peter Renz; Annie Selden;Hortensia Soto-Johnson; Ravi Vakil.
Letters to the editor should be addressed toFernando Gouvêa, Colby College, Dept. ofMathematics, Waterville, ME 04901, or byemail to [email protected].
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Inside
4 Elvis: Optimizing My OpportunitiesBy Tim Pennings
5 Alder Awards Will Recognize Talented Beginning Teachers
6 One Day as Washington LobbyistsBy Jason L. Haun, Kelly A. Peck, and Richard B. Thompson
8 MAA Tour of Greece
10 Mathematics and ArtBy Alexander Bogomolny
12 Manjul Bhargava Receives Hasse Prize at MathFest
13 MAA Writing Prizes Announced at MathFest
14 2003 Award Winners for Distinguished Teaching
16 The Mathematical Olympiad Summer Program Brings TogetherTalented High School StudentsBy Steven R. Dunbar
17 A Problem-Solving DynastyBy Steve Olson
18 NSF Beat
19 MAA Election Results Are In
20 Short Takes
28 What’s the Best Textbook?—Elementary Number TheoryBy Fernando Q. Gouvêa
August/September 2003Volume 23 Issue 6
On the cover: Elvis working on his math paper. Photo courtesy of Tim Pennings.
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The first Abel Prize in Mathematicswas awarded to French mathematicianJean-Pierre Serre. At a formal ceremonyon June 3, King Harald of Norway pre-sented the award, honoring Serre “forplaying a key role in shaping the mod-ern form of many parts of mathemat-ics, including topology, algebraic geom-etry, and number theory.” The awardsceremony was part of a week full of spe-cial events related to mathematics.Events included the laying of a wreathat the monument in honor of NielsHenrik Abel, the Abel Lecture by Serre(“Prime Numbers, Equations and Modu-lar Forms”), and the Abel symposium,which included lectures by several math-ematicians, including Barry Mazur andPeter Sarnak. A “Math Carnival” was heldat the Universitetsplassen, in CentralOslo, with the participation of many chil-dren aged 10 to 12. Serre was present tohand out prizes to the winners of math-ematical competitions.
Jean-Pierre Serre, who is Emeritus Pro-fessor at the Collège de France, in Paris,is noted both for his mathematics andfor his expository skills. He has madefundamental contributions to topology,number theory, and algebraic geometry.He has also written many books and isfamous for the clarity and penetrationof his writing.
Jean-Pierre Serre Is First Abel Laureate
By Fernando Q. Gouvêa
Most good college and university li-braries own many volumes of collectedpapers by various mathematicians, butfew of these volumes ever make it intoprivate book collections. Buying what isusually an expensive set of books issomething one only does if the works inquestion are so useful that one knowsthey will be opened and read again andagain. Thus, it is an indication of howvaluable Serre’s work is to note that allfour volumes of his collected works areon my shelves—the only living math-ematician whose collected works I havefelt I absolutely needed to buy. Next tothem are a volume of summaries of semi-nars, a volume of correspondence, andat least eight other books, several ofwhich I have studied in detail.
Serre’s work focuses mostly on three ar-eas: topology, algebraic geometry, andnumber theory. In all three fields, he hashad a formative impact, changing thevery shape of the subject. Some of hispapers are cited so often that they areknown by nicknames: for example,
The Abel Prize, which was establishedin January 2002 and is awarded annu-ally to recognize outstanding achieve-ment in mathematics, carries a cashaward of 6 million Norwegian kroner,which comes out to about $800,000. Theprize is named for Niels Henrik Abel,who lived in Norway in the early 19thcentury and is recognized as one of themost brilliant mathematicians of histime. The Abel Prize is administered bythe Norwegian Academy of Science andLetters, which has appointed an AbelCommittee consisting of five mathema-
ticians to review the nominated candi-dates and submit a recommendation fora worthy Abel laureate.
For more about the Abel Prize and aboutJean-Pierre Serre, visit the Abel Prizewebsite at http://www.abelprisen.no/index_english.html. Among other things,the site includes a well-written exposi-tory account of Serre’s work.
of his work was recognized by the AMSa few years ago, when it awarded him aSteele prize for exposition.
In addition to his work at the Collège deFrance, Serre was a frequent visitor toAmerican universities. He spent a semes-ter at Harvard while I was a graduate stu-
dent there. Itwas then com-mon knowl-edge amongthe graduatestudents thatSerre’s pres-ence had apositive effecton the depart-ment: hiscourses wereexciting, hisping-pong was top-notch, and the wineat the Friday afternoon wine-and-cheeseparties was noticeably better.
Asked by a French news magazinewhether being a great mathematicianrequired genius, Serre replied that it wasabove all a question of taste: a taste formathematics itself, and good taste inchoosing the right mathematical prob-lems. In fact, the first Abel Laureate hasboth taste and genius.
About Jean-Pierre Serre
GAGA (“Geométrie Algébrique etGeométrie Analytique”), FAC(“Faisceaux Algébriques Coherents”),and “Serre’s Duke paper” (“Sur lesreprésentations modulaires de degré 2 deGal(Q/Q),” published in the Duke Math-ematical Journal). The last is particularlyfamous; in it, Serre formulated a far-reaching conjecture connecting modu-lar forms and Galois representations, asmall part of which was the core of Wiles’proof of Fermat’s Last Theorem. Serrecalls it his paper pour optimistes.
In addition to his research work, Serrehas written many books, some at an ad-vanced level, others more accessible. Hiswriting is famous for being clean, effi-cient, and easy to understand. This side
Jean-Pierre Serre receiving the Abel Prize fromKing Harald of Norway.
Jean-Pierre Serre
Photos courtesy of: The Abel Prize website:http://www.abelprisen.no/presse/
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Hi. I’m Elvis. I got my name becauseas a nursing puppy I gyrated my backlegs in a motion similar to my namesake,the King of Rock and Roll. As withPresley, I love the spotlight, from pos-ing for a camera to diving into an eagercrowd of high school students.
I knew that I was destined for fame, butwhen I went to live with mathematicsprofessor, Tim Pennings, two years ago,I could see that my opportunities werelimited. Nice guy, but not star quality, ifyou know what I mean. Then one fineday playing fetch at the beach, I had aninspiration: Show him that I have an in-stinctual knack for calculus by choosingthe quickest path to the ball. (I havetrouble with symbolic manipulation, butmax-min problems come naturally tome.) It took him a few weeks to catchon, but when he did we researched andwrote the paper and I knew that I wason my way to the top.
With my smile gracing the front coverof the May issue of The College Math-ematics Journal, what would come next?Well, first several local papers wrote sto-ries, including two with headlines andfront page pictures. Then The ChicagoTribune and The Baltimore Sun followedsuit. ABCNEWS.com called for an inter-view and ran me as their top story, justahead of the Microsoft-AOL merger.(And Bill Gates thought that HE was topdog!)
The BBC found out about me and calledfor a live on-the-air interview, as did ourown country’s NPR radio. Finally, we hadan offer to go to Los Angeles for a spoton an NBC daytime talk show in August.(I was all for it, but my co-author wouldrather go camping.) All together we gavenine interviews and appeared in 28 newsstories of various types.
All of this press led to some fine lettersfrom dog lovers including one from a sin-cere elderly woman who described herRottweiler’s ability to solve algebraic for-mulas and do square roots. As for my-self, I’ll stick to calculus, and look for-
Elvis: Optimizing My Opportunities
As told to Tim Pennings
ward to us giving our talk in various highschools and colleges next fall. Those stu-dents are just suckers for my handsomeface.
Tim Pennings is an Associate Professor ofMathematics at Hope College in Holland,Michigan. His research, done col-laboratively with undergraduate students,is in dynamical systems and modeling. Healso directs the Hope College NSF-REUMathematics Summer Research Program.Other reasons for living include ultimatefrisbee, racquetball, nature photography,choral music, folk song guitar gigs, andplaying with Elvis at the beach.
Don Albers, the MAA’s Associate Executive Di-rector, John dePillis, author of 777 Mathemati-cal Conversation Starters, and Lisette dePillismet Jay Leno after the Tonight Show aired onApril 21, 2003. Leno likes mathematics andAlbers and dePillis talked with him about Elvisand getting more math on the Tonight Show.Photo courtesy of The Tonight Show.
Elvis relaxing at home in between interviews and persona l appearances.Photo courtesy of Tim Pennings.
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Before his recent death, Henry Alderendowed a new MAA teaching award, tobe known as the Henry L. Alder Awardfor Distinguished Teaching by BeginningCollege or University Mathematics Fac-ulty. The awards “are to be made to col-lege or university faculty who have taughtfull time in a mathematical science in theUnited States or Canada for at least twobut not more than seven years since re-ceiving their Ph.D. and whose teachinghas been extraordinarily successful. Theireffectiveness in teaching undergraduatemathematics must be documented andshown to have influence beyond theirown classroom.”
Nominations for the first Alder Awardsshould be sent to Martha Siegel at theDepartment of Mathematics, TowsonUniversity, 8000 York Rd., Towson, MD21252-0001 by December 15, 2003. Con-tact Linda Sons, chair of the AlderAwards Committee, with any other ques-tions. Sons can be reached at the Depart-ment of Mathematical Sciences, North-ern Illinois University, DeKalb, IL 60115,by phone at 815-753-6760, or by emailat [email protected].
Alder Award Description
In January 2003 the MAA established theHenry L. Alder Award for DistinguishedTeaching by a Beginning College or Uni-versity Mathematics Faculty Member tohonor beginning college or universityfaculty whose teaching has been extra or-dinarily successful and whose effective-ness in teaching undergraduate math-ematics is shown to have influence be-yond their own classrooms. An awardeemust have taught full time in a math-ematical science in the United States orCanada for at least two, but not morethan seven, years since receiving thePh.D. Each year at most three college oruniversity teachers are to be honoredwith this national award and are to re-ceive $1,000 and a certificate of recogni-tion from the MAA. Award recipients willbe expected to make a presentation atone of the national meetings of the MAA.
Nominations for the award may be madeby any member of the MAA or by anysection of the MAA.
Alder Award Eligibility and Guidelinesfor Nomination
Eligibility
Nominees must:
Hold the Ph.D. degree
Be college or university teachers whohave taught full time in a mathematicalscience in the United States or Canadafor at least two, but not more than seven,years since receiving the Ph.D.
Hold membership in the MathematicalAssociation of America
Guidelines for nomination
Nominees for the award may be made byany member of the MAA or by any sec-tion of the MAA
Nominees should:
Be recognized as extraordinarily success-ful in their teaching
Have effectiveness in teaching under-graduate mathematics that can be docu-mented
Have had influence in their teaching be-yond their own classrooms
Interpretive notes
In determining eligibility, we do notcount time spent in a postdoctoral posi-tion where nearly all the nominee’s timewas spent on research, and the nomineedid very little or no teaching (e.g. threesemester courses a year or less).
Teaching is intended to include class-room instruction as well as activitiesoutside the classroom, such as workingwith student groups, preparing students
for mathematical competitions, directingundergraduate students in research inmathematics, directing students in thepreparation of honors theses, preparingteaching materials used by others, etc.
Nominations must be submitted accord-ing to the Nomination Form. Instruc-tions for that form should be followedprecisely to assure uniformity in the se-lection process.
The Nomination Form and a Nomina-tion Packet that provides evidence docu-menting extraordinary success in teach-ing should be submitted to the Secretaryof the MAA by December 15 of the aca-demic year in which the nomination isto be considered. Directions for thenomination packet should be followedwith precision to assure uniformity in theselection process. Nomination forms andfurther information can be found onlineat http://www.maa.org/news/062703alder.html.
Alder Awards Will Recognize Talented Beginning Teachers
Henry Alder
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One Day as Washington Lobbyists
By Jason L. Haun, Kelly A. Peck and Richard B. Thompson
Thompson, Kolbe, Haun, & Peck
This year the MAA sponsored theUniversity of Arizona’s Mathemat-ics for Business Decisions project ona tour of congressional offices andat the CNSF Exhibition and Recep-tion. On June 17, 2003 we spent afascinating day as Washington lob-byists for the mathematical commu-nity for both research and educa-tion. Those of us participatingfound it to be a surprisingly reward-ing day. More than lobbying, wewere sharing very important infor-mation with members of Congress.And yes, seeing how governmentworks was fascinating. Our prepa-ration for promoting National Sci-ence Foundation funding and ourobservations from Washington mayoffer some insights into the mechan-ics of gaining support for math-ematics.
The Coalition for National ScienceFunding (CNSF) is an alliance ofuniversities and major professionalsocieties from many areas of science,mathematics, and engineering. Itspurpose is to encourage funding forthe National Science Foundation. Amajor part of this endeavor is anannual exhibition and reception formembers of Congress and their staff.Each coalition member may presenta project that has received NSF sup-port. Each year the MAA sponsors aproject that highlights funding forundergraduate mathematics educa-tion and provides additional sup-port for the reception.
This year the MAA chose us and theMathematics for Business Decisionscourse to be their exhibitors. Thecourse was developed by myself, Ri-chard Thompson, of the Universityof Arizona Department of Math,along with my colleague ChrisLamoureux of the University of Ari-zona Department of Finance. JasonHaun and Kelly Peck are studentswho have been through the course.Each was very excited to be invited
to join me on this trip to Washington,D.C.
Mathematics for Business Decisions is atwo-semester sequence of mathematicscourses for undergraduate business ma-jors that has been developed at the Uni-versity of Arizona, with partial supportfrom the NSF. It is now published anddistributed by the MAA as self-containedelectronic texts. The MAA chose this
project for its innovation in both con-tent and delivery and its ready appeal tothe public.
In Washington, we were escorted by TinaStraley, Executive Director of the MAA,on half-hour visits to the offices of fivecongressmen from the Arizona delega-tion. In the evening the MAA’s Associ-ate Executive Director, Don Albers,helped us set up a display booth at anexhibition and reception in the RayburnOffice Building. It was one of 30 pre-
sentations that were viewed by over 270attendees from House, Senate, and WhiteHouse offices. The MAA exhibit at-tracted one of the most important guests
to the exhibit: Congressman JimKolbe (R, Tucson), who is amember of the House Appro-priations Committee. Represen-tative Kolbe came especially tomeet with us, as he had promisedhe would.
As a mathematician and co-au-thor of Mathematics for BusinessDecisions, I prepared materialsfor our exhibit and invited twoof our students, Kelly Peck andJason Haun, to join me on the
trip.
We wanted our exhibit to make a goodimpression. The MAA supported traveland the distribution of CD’s and colorbrochures, and The University of Ari-zona supported the production of a 4′ x6′ laminated color display poster. TheMAA rented a 37″ plasma video moni-tor as part of their exhibit space. In theintense competition for Washington dol-lars, a low quality presentation is per-
ceived as reflecting the value of thecause that it promotes. People werenotably impressed with the profes-sional appearance of our materials.
Congressmen and their staffers re-ally do care about young peopleand students. Comments by Jasonand Kelly held people’s attentionduring both the office visits and atthe exhibition. A copy of a courseproject report by Kelly commandedmore interest than did some of ourdescriptive material. In fact, ouronly copy of the report went home
with Representative Kolbe since we didnot really want to ask him to give it back.The follow-up e-mails that I have re-ceived all mention the outstanding qual-ity of our students. It is, of course, pos-sible that this favorable impression isrelated to the fact that I managed to in-vite two outstanding, articulate youngpeople!
Our scheduled office visits all had thesame format. Tina Straley would thankthe congressman for past NSF support
Albers, Straley, Thompson, Haun, & Peck
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Haun, Thompson, & Ehlers
and ask for continued support, es-pecially for the effort to doubleNSF’s budget over a five-year pe-riod. She explained that The Univer-sity of Arizona project that the MAAwas presenting represented one typeof work that had received funding.She suggested that Congress mightnot be as familiar with funding forundergraduate education as it iswith research dollars. I would thengive a brief explanation of the e-texts, and ask the students for theirreactions to the program.
On most occasions when I discuss ourproject I am talking to other mathema-ticians who share my background in, andappreciation of, mathematics. In short,I am usually preaching to the choir. Pub-lic officials cannot be assumed to shareour views of mathematics.
My approach to congressmen was basedon the assumptions that they care aboutstudents in their home districts, that theywant a work force which is competitivein the world market, and that they seetechnology as a key to the future. Re-flecting these, I mentioned that Math-ematics for Business Decisions is builtaround the topics, project structure,teamwork, and computer skills that areactually used in business. I was carefulto work in the name of a local commu-nity college or university in therepresentative’s home district and to notethat students who can use mathematicseffectively will be the ones who createjobs and expand the local tax base. Theseideas resonated well with most of thecongressmen, eliciting some very percep-tive responses.
Several representatives mentioned thespecific courses (ranging from AlgebraII to Calculus) where mathematics haddisconnected from the real world andstopped having meaning to them. Ourprogram’s continual contact with stu-dents’ goals and interests was seen ashighly desirable. In some cases, congress-men actually suggested ideas, such asextending our program to areas otherthan business and implementing ourapproach in high schools, for further ex-ploration. They recognized that a majoreffort would be required and that muchinstructor preparation would be neces-
sary to implement the agenda. Theseideas brought us back to the need forcontinued NSF support and funding.
Our display at the evening exhibitiondrew attention from quite a few people,leading to discussions of NSF fundingand of our project. We had a nice visitwith Congressman Vernon Ehlers (R,Grand Rapids). He is a member of theHouse Committee on Science who alsoholds a Ph.D. in physics. RepresentativeEhlers has been a strong supporter of theNational Science Foundation.
Jason Haun: One needs to make contactwith several congressional offices in or-der to be heard. I constantly encounterideas and complaints from peoplearound me. However, in most cases theirwords are never heard by Congress. Dueto this incredible opportunity offered byProfessor Thompson and the Math-ematical Association of America I wasable to be heard and show my supportfor something in which I truly believe,“the future of education.” Education isconstantly changing and it is our duty,as citizens, to make sure that thesechanges propel the system in the rightdirection. Laws go through the govern-mental structure. However, “officials” actas liaisons to voice the views of citizenswithin their communities. It is the citi-zens’ ultimate duty to make sure thattheir words are heard. In the world to-day, this may mean building a team ofpeople who share common beliefs andthen going to Washington.
This is only the beginning. The next steplies in making a direct connection withthe person to whom you are speaking.He or she must begin to feel and believein the same way that you do. Once this
connection is made, change and in-novation can take place. I want tothank everyone at the MAA as wellas everyone who has worked with theMathematics for Business Decisionsprogram.
Kelly Peck: It is not every day thatyou get an invitation to go to Wash-ington, D.C. with an agenda that in-cludes meeting personally with Ari-zona Congressmen. Yet, here I am, a20-year-old college student who isable to say that I have “been there,done that.” The whole experience
went by in a flash, but I walked away fromit with some treasured memories.
Having virtually no knowledge of politi-cal procedures, I was quite surprised tosee how things ran at the congressionaloffices. When speaking with congress-men, whose days are packed, you imme-diately learn how to get your point acrossas concisely as possible. I had to learn tocondense two semester’s worth of Math-ematics for Business Decisions into a fewminutes, and hope that I could maintainthe representative’s attention. It was defi-nitely a learning experience, to say theleast.
The beautiful Washington cityscape alsoleft a lasting impression. I was awed bythe grand historic buildings and theirclassical features. Perhaps even moreimpressive was the fact that the entire cityis surrounded by, and engulfed in, lus-cious greenery—something considered aluxury by Arizonans.
In addition to the experience and thescenery, I will forever remember thepeople. Tina Straley, Don Albers, and theother MAA members I met were ex-tremely friendly and accommodating.They became familiar faces in an unfa-miliar place. Unfortunately, the tripwent by way too fast. Upon leavingWashington, there was one thing I knewfor certain: I would be back.
Photographs by Sharon L. Thompson. In-formation on the CNSF can be found athttp://www.cnsfweb.org. Information onMathematics for Business Decisions can befound at http://www.maa.org and http://bus iness .math .a r izona .edu/MBD/mbd.html.
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Thirty members (and guests) of theMAA traveled to Greece in late May toparticipate in the first MAA Study Tourabroad. There was a wide variety of par-ticipants, from high school teachers toretired professors, including two formerpresidents of the MAA as well as the cur-rent and former executive directors. Allagreed that the trip met, and even ex-ceeded, their expectations. Five of themagreed to write brief comments for FO-CUS about their experiences.
From Joel and Linda HaackUniversity of Northern Iowa,Cedar Falls, IA:
There were quite a few reasons that wewere eager to participate on the MAAStudy Tour of Greece. First, of course,as I have been teaching the history ofmathematics for parts of the past 15years, I was very eager to see Athens,Delphi, Miletus, and Samos. Second,there are a few places in the world thatmy wife Linda and I have always wantedto see. Greece has been one of those, eversince learning about it in our ancient his-tory class way back in ninth grade. Fi-nally, this trip provided us the perfectoccasion to celebrate our thirtieth wed-ding anniversary.
The focus on mathematics and the spon-sorship by the MAA set this trip apartfrom other tours we’ve taken. The pre-travel readings and videos increased my
interest in Epidauros and the EupalinosTunnel. The mathematical presentationsthat were arranged at various sites inGreece were a pleasure. We were treatedas mathematical ambassadors from theUSA at several receptions, and in fact wedid carry out those responsibilitiesthroughout our trip. Talking with col-leagues from Greece was enlightening.Because of the special interests of ourgroup, the aegis of the MAA, the hardwork of those putting the trip together,and some serendipity, we had the chanceto visit the Academy of Athens and threeGreek universities, see and hear themodel of the ancient Greek harmonium,attend a special museum exhibit entitled“Is There a Solution for Everything? AJourney to the World of Greek Math-ematics,” receive guided tours of sites inAthens and on Samos by archaeologistsfrom the region, and visit Miletus. Allthose on the trip were pleasant and re-sponsible, creating an atmosphere ofgeneral good will that was a delight. And,the fellow travelers included previousacquaintances and new friends that wecan expect to see again in the future.
One of the special treats for me on thistrip was the chance to see and experiencesites that would not normally be includedin a tour of Greece, in particular the an-cient harmonium, the visit to Miletus,and the time spent on Samos. (Paren-thetically, a word about Miletus: its in-clusion on our trip was one of the rea-
sons I was excited to participate. Thechance to see where Thales walked andcreated what are regarded as the firstproofs in mathematics, the creation ofthe theoretical mathematics that weclaim as ours, was an opportunity thatI’d likely have on no other tour. Thankyou for including it!)
Finally, an insight from Linda: this tripwas of such great interest to even thenon-mathematicians because so much ofthe focus was on mathematics and itsrelation to other disciplines: architecture,art, music, philosophy, mythology, his-tory, astronomy, etc.
MAA Tour of Greece
Victor Katz and Lisa Kolbe, tour organiz-ers, at the Acropolis.
Temple at DelphiThe Academy of Athens
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From Julius BarbanelUnion College,Schenectady, NY:
Over the past few years, Ihave become quite fasci-nated with ancient Greekmathematics. When I heardabout the MAA trip toGreece, I knew this was forme. It was a great trip, com-bining lectures on ancientGreek mathematics andtravel to some marveloussites.
My favorite three lectureswere on ancient Greek as-tronomy, the mathematicsof Plato’s Academy, and theMethod of Archimedes. TheGreek mathematicians thatwe met were very welcom-ing and kind. They allseemed delighted to host agroup of visiting mathema-ticians from the UnitedStates.
We saw some marveloussites. Some of the highpoints for me were: Delphi,where the ancient oracle used to dispenseher wisdom; Olympia, site of the origi-nal Olympic Games; and the ancient cityof Mycenae, the oldest site of all, homeof the civilization about which Homerwrote in the Iliad.
Greece is a beautiful country. I’ll alwaysremember the gorgeous mountains, thebeautiful sea, the vibrant people, and, ofcourse, the great food. I wish I could doit all over again. What a joy this was!
From Genevieve KnightCoppin State University,Baltimore, MD:
My trip to Greece was one of the mostrewarding activities that I have experi-enced in both my personal and profes-sional life. The planners carefully ar-ranged an exceptional mix of mathemat-ics, Greek history, mythology, entertain-ment, culture, food, and the list could goon.
The tours across Greece and lectures atthe university level were excellent. I feltcomfortable participating in the formaland informal discussions. The guidesand bus drivers were knowledgeableabout all aspects of Greek life and cul-ture. And I feel that my presence en-riched the impression that our Greek col-leagues had of American mathemati-cians.
Special thanks to a host of MAA friendswho assisted those of us who needed anextra arm. That’s what friends are for!
The MAA should organize other similaractivities for the membership. Readinga book or surfing the Internet providesinformation, but walking among the re-mains of ancient Greece is a once-in-a-lifetime experience!
Tour participants at the Statue of Pythagoras in Pythagoreion,Samos.
From Marcia SwardExecutive Director Emeritus,MAA, Rockville, MD:
When I tell my non-math-ematical friends that I went ona “mathematical tour ofGreece,” they invariably lookpuzzled, seeing no connectionbetween mathematics andGreece. But mathematiciansknow immediately about thedeep roots that modern math-ematics has in ancient Greeceand are curious about what welearned. Some of our learningcame from lectures by Greekmathematicians and astrono-mers, some through dialoguewith them. One particularspecial occasion was a visit tothe Academy of Athens.
But the deepest insights camefrom just being in places whereancient Greeks lived and wor-shiped. A picture may beworth a thousand words, butactually being there is worth athousand pictures. Althoughthe ancient temples, fortresses,towns, and homes lie in ruins,it is still possible to imagine
traveling back in time and seeing themas they must have been so long ago. Atthe archaeological sites we visited, wewere surrounded by the ancient Greeks’records of commerce, their tributes towinning athletes, and the many tales ofthe lives and loves of the gods and god-desses, all meticulously carved in stone.We were awed by the engineering featsrequired to construct elaborate templesand fortresses, and most particularly bythe immense stone arches, still firmly inplace after thousands of years.
Day after day, for fourteen days, we weretreated to a bounteous feast of ideas andimages. Meal after meal we were alsotreated to the delights of Greek cuisine.And sharing all this with friends and col-leagues made those two weeks even morespecial. This was definitely a trip to re-member.
Photographs courtesy of: Julius BarbanelLisa Kolbe, and Liz Teles.
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Mathematics and Art
By Alexander Bogomolny
Who will wish to paint you, when noone wishes to see you? Gotthold EphraimLessing Laocoön, Everyman’s Library,1970, p. 10
Mathematics and Art was the theme ofthis year’s Mathematics AwarenessMonth. I believe that the theme selectionwas unfortunate on several counts. First,we tend to forget that in common lan-guage words may have meanings differ-ent from their conventional meanings inmathematics. As an example:
Mother: Would you like to have a cookieor ice cream for dessert?
Kiddie: But, Mommy, I want a cookieand ice cream.
Regardless of which connective is used,these two treats are perceived as indi-vidual, independent desserts. A similarimpression is left by the combinationMathematics and Art. For additional ex-amples, let’s have a look at past MAMthemes. There is never doubt as to whatmathematics is not.
Mathematics and Decision Making(1996). Democracy is a human inven-tion. Vote counting and power indices aremathematics. He who loves numbercounting is bound to be a mathemati-cian. Democracy is one thing. The im-possibility to satisfy everyone’s politicalpreferences is a proven mathematicaltruth.
Mathematics and the Internet (1997).First engineers invented the ethernet,then the internet. Computer scientiststhen came up with the web and eventu-ally a browser. Mathematicians made theinternet secure with very, very big primenumbers.
Mathematics and Imaging (1998). Well,getting an image is imaging. Multi-reso-lution image compression is mathemat-ics. Just think of the abstraction of anexpanding hierarchy of vector spaces andtheir wavelet bases. Incomprehensibleabstractions is what mathematicians are
good at. But even very abstract math-ematical ideas may have practical appli-cations.
Mathematics and Biology (1999). Evenwithout a definition everything is veryclear: epidemics is in the domain of bi-ology, epidemics modelling is in the pur-view of mathematics as is the solutionof the resulting equations. This is whatmathematicians do after all—solve equa-tions. Biology is biology. Mathematics issomething else.
Mathematics and Art (2003). There areplenty of connections. But by juxtaposi-tion or by inductive reasoning, if you will,art is art, whereas mathematics is some-thing else.
I am sure that the message that math-ematics is not art was not the intendedpurpose of the MAM/2003. No, of coursenot. Mathematics is multifaceted, and itsartistic nature is hard to deny. In theirwell-known book, Kasner and Newmanwrote:
Mathematics is an activity governed bythe same rules imposed upon the sym-phonies of Beethoven, the paintings ofDa Vinci, and the poetry of Homer.
In the Middle Ages and during the Re-naissance, mathematics constituted amajor part of the Liberal Arts. This is whymath departments usually belong to Lib-eral Arts colleges. To be sure, mathemat-ics has changed fundamentally since. Butit became more of an art, not less.
Therefore I feel apprehensive that theintention of the theme Mathematics andArt might have been misconstrued. In-deed, I think it is highly probable that itwas. “Sculpture and Art” or “Music andArt” look and sound incongruous, right?Why doesn’t “Mathematics and Art”? Iwould be more comfortable with the cap-tion “Mathematics and the Visual Arts”that was probably the intention to startwith. However, I would remain appre-
hensive even if the latter were selected asthe MAM theme.
Why? Because art is an active pursuit ofbeauty. The concept of beauty, however,and the expressive means of achieving it,differ between various arts. G. E. Lessing,whose Laocoön: An Essay on the Limits ofPainting and Poetry is considered the ori-gin of modern esthetics, alluded in pass-ing to the difference between paintingand sculpture, the most congenial of anytwo arts:
The mere wide opening of the mouth—apart from the fact that the otherparts of the face are thereby violentlyand unpleasantly distorted—is a blotin painting and a fault in sculpturewhich has the most untoward effectpossible.
The Mandelbrot set is beautiful even if itis the monochromatic blot in the middleof the colorful depiction of equipoten-tial lines. Just to think of the infinite in-tricacy of the whirl patterns produced bya mere quadratic formula takes one’sbreath away. Add to that the fact that theset serves as an index into the variety ofJulia sets which, in turn, are classifiedaccording to the location of a single pa-rameter inside the Mandelbrot set.
Certainly, the now common colorful pic-tures of the Mandelbrot set have greatvisual appeal. But then it is so mucheasier to substitute one for the other: “Ah,this is beautiful; and there’s mathemat-ics behind all that! Hence mathematicsis beautiful!” I believe such misrepresen-tations are popular and I deplore the dis-service they might be doing to math-ematics education. Here’s an episodefrom my personal experience.
The incident occurred several years ago,when my older son took Geometry I injunior high. The boy was given an assign-ment. The basic idea was to take two linesegments and divide them both into anequal number of subintervals. The divi-sion points then had to be connected to
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form a pretty web of straight lines. It wasleft to the student’s imagination to com-bine the webs into more intricate pat-terns. The assignment did not follow, norwas it preceded by, any discussion ofmathematical relevance. Division of aline segment into a number of equalparts with straightedge and compass —no. The standard ruler with tick markswas sufficient to complete the assign-ment. The idea of an envelope of a fam-ily of lines had not been mentioned ei-ther. The assignment lacked any math-ematical content whatsoever. I suggestedthat he program QuickBasic to automati-cally generate various patterns. My soninsisted that programming was strictlyand specifically forbidden. The assign-ment had to be completed by hand.
After a couple of unsuccessful attemptsto engage the teacher, I was granted ameeting with the principal. In the school,the web patterns were proudly decorat-ing all the available wall space. Therewere lace masterpieces by girls and in-tricate woodwork by boys—all for thesake of extra credit. The assignment ap-peared to be a yearly milestone for Ge-ometry I.
The principal readily admitted the shal-lowness of this exercise. The district mathsupervisor who was also present re-mained unmoved. After a short exchangeI left utterly disappointed. What a wasteof time! And zero knowledge acquisition.As far as I know, the assignment is stillbeing offered as a mathematical attrac-tion.
I am not building a critical edifice basedon a single personal experience. There isdefinitely an unfortunate trend in math-ematics education that seeks to endearmathematics to students with no attemptat transferring any significant mathemat-ics. D. Hofstadter asks this question:
Why does mathematics today have tobe ‘relevant’ and ‘fun’, have to prove itsworth by chewing gum like a sports star,acting sexy like a movie star, spoutingcutesy sound-bytes like a with-it jour-nalist, displaying itself as eye candy likea top model—but, heaven forbid, notby exploring unsuspected symmetriesand subtle patterns purely for their own
sake, like a scientist (let alone a math-ematician!)?
A common argument leaves me cold.We are often attracted to a book by itscover and may even purchase a bookwithout first tasting a page or two. Yes,we may. But would it not be a disappoint-ment to uncover at home a constructionset where we thought to find a book? Andwhat about shoes? Do we buy shoes solelyby appearance?
True, it often pays to introduce math-ematics gently with story telling or col-orful illustrations. The best teachers dothat all the time. I could not possibly havean issue with that. So what is it about?
This sound byte, which is the themeMathematics and Art, draws a line be-tween mathematics and art. It pulls thetwo apart more than it invokes any pos-sible connections. And the fact is that thefirst impression, however false, is oftenhard to get rid of. The theme, taken byitself, suggests at best that mathematicshas found yet another application, nowin art. Big deal! Most artists hate math-ematics just like anyone else. Who do wewant to cheat? Besides, since the appli-cability of mathematics is talked aboutall the year round, would it not makemore sense to emphasize its (specificallymathematical) beauty at least once a year,during this special event—MathematicsAwareness Month?
Perhaps it’s fitting to relay a story toldby Raymond Smullyan in one of hisbooks. A friend invited him for dinner.He told Smullyan that his teenage sonwas crazy about Smullyan’s logic puzzlebooks and could not wait to meet him.The friend warned Smullyan not to men-tion that he is a mathematician and thatlogic is a part of mathematics because theyoung fellow hated mathematics.
Branko Grünbaum wondered:
... it is very likely that Escher did notwish to learn any of the mathematicswe think might have helped him, andthat we are much richer for it.
No one knows better than mathemati-cians themselves where the real beautyof mathematics lies. I believe it wouldenrich both mathematics education andpublic awareness of mathematical beautywere it pursued regularly and consis-tently. The other arts could take care ofthemselves.
The first paragraph makes an allusion toD. Schattschneider’s note in the March2003 issue of FOCUS. Other references canbe found in Alex’s MAA Online April col-umn. This note is in fact a mutilated (butalso somewhat improved) version of thelatter.
Alex Bogomolny is a former Associate Pro-fessor of Mathematics at the University ofIowa. One of the greatest pleasures he en-joys nowadays is watching his 4-and 23-year old sons play together. Alex also spendsmuch time working on his website, Inter-active Mathematics Miscellany andPuzzles (http://www.cut-the-knot.org),that has been recently recognized with the2003 Sci/Tech Web Award from the edi-tors of Scientific American.
IASE 2004 Roundtable
The International Association for Sta-tistics Education (IASE) will hold a“Roundtable” at Lund University in Swe-den on June 28 to July 3, 2004. LundUniversity is close to the ICME-10 loca-tion, so this will act as a kind of “satelliteconference.” The Roundtable will bringtogether a small number of experts, rep-resenting as many different countries aspossible, to discuss Curricular Develop-ment in Statistics Education. Papers pre-sented and discussed during the confer-ence will be published in a proceedingsvolume that will present a global over-view of Statistics Education. For moreinformation, contact Gail Burrill [email protected] or visit http://h o b b e s . l i t e . m s u . e d u /~IASE_2004_Roundtable.
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At the August 2003 MathFest in Boul-der Manjul Bhargava received the MAA’sHasse Prize for exposition. It has beenquite a year for Manjul. In November2002 he was the only mathematicianamong Popular Science’s “Brilliant 10”,the publication’s first annual celebrationof ten scientists who are shaking up theirfields. (The article is available online athttp://www.popsci.com/science/article/0,12543,364881,00.html) In January2003 he was selected to be one of theAMS/MAA one hour invited speakers atthe January 2004 Joint Meetings in Phoe-nix. Then came offers of tenured Associ-ate Professorships from the top IvyLeague schools. Shortly thereafter, theseoffers were increased to full professor-ships. It is believed that the two yearsfrom thesis to full professorship offers isthe shortest period ever for an Ivy Leagueschool. In June he accepted the profes-sorship from Princeton and also was ap-pointed to the editorial board of theJournal of Number Theory.
Awards are not new to the 29-year-oldBhargava, who is the son of a chemistfather and mathematician mother, MiraBhargava, a professor at Hofstra Univer-sity. In high school Manjul was the win-ner of the First Annual New York StateScience Talent Search. As an undergradu-ate at Harvard he won the Hoopes Prizefor his outstanding senior thesis and(three times!) the Derek Bok Award forExcellence in Teaching. He was selectedto lead the commencement of the 1600Harvard graduates of the class of 1996.
Also in 1996 Bhargava received the AMS-MAA-SIAM Frank and Brennie MorganPrize for Outstanding Research in Math-ematics by an Undergraduate Student forwork he began at the Duluth REU andexpanded on in his senior thesis. A yearbefore he obtained his Ph.D. fromPrinceton on a Hertz Fellowship, Manjulwas also appointed as the first Clay Math-ematics Institute Long-Term Prize Fel-low and a Visiting Fellow at PrincetonUniversity. This past year he was a visit-ing professor at Harvard.
Manjul’s research interests include alge-braic number theory, combinatorics, andrepresentation theory. The paper forwhich he won the Hasse Prize, “The fac-torial function and generalizations,” pub-lished in the American MathematicalMonthly (November 2000), explains hisnew generalization of the factorial func-tion and its connections with some clas-sical problems in number theory, ringtheory, and combinatorics. His work onthe factorial function unifies and gener-alizes the results of about 20 previouspapers, many by well-known mathema-ticians.
One of Bhargava’s recent accomplish-ments has to do with the so-called “Fif-teen Theorem”, which was originallyproved by Conway and Schneeberger in1993. It states that if a positive definitequadratic form whose associated sym-metric matrix has integer values repre-sents all positive integers up to 15, thenit is “universal,” that is, it represents allpositive integers. Bhargava not only sim-
plified the Conway-Schneeberger proof,but also generalized the result in severalbeautiful ways. Another of Bhargava’sachievements, which was the basis for histhesis, is a generalization of Gauss’s 1801law of composition of binary forms.Manjul showed that Gauss’s compositionis only one of at least 14 such composi-tion laws.
Andrew Wiles, Manjul’s Ph.D. advisor, isquoted in the Popular Science article assaying Bhargava’s thesis was one of thestrongest he’s seen in 20 years. Alsoquoted in the article is Princeton profes-sor Peter Sarnak: “We are watching himvery closely. He is going to be a super-star. He’s amazingly mature mathemati-cally. He is changing the subject in a fun-damental way.”
In addition to doing mathematics,Manjul is also an accomplished tablaplayer, and performs extensively in theNew York and Boston areas. He also en-joys nature hiking, running, tennis, andspending time with friends.
Manjul Bhargava Receives Hasse Prize at MathFest
By Joseph Gallian
Manjul Bhargava lecturing on the Fifteen Theorem.
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August/September 2003
MAA Writing Prizes Announced at MathFest 2003
Carl B. Allendoerfer Awards
Ezra Brown“The Many Names of (7, 3, 1),”Mathematics Magazine,April 2002, pp. 83-94.
Dan Kalman“Doubly Recursive MultivariateAutomatic Differentiation,”Mathematics Magazine,June 2002, pp. 187-202.
The Carl B. Allendoerfer Awards, estab-lished in 1976, are made to authors ofexpository articles published in Math-ematics Magazine. The Awards are namedfor Carl B. Allendoerfer, a distinguishedmathematician at the University ofWashington and President of the Math-ematical Association of America, 1959-60.
Trevor Evans Awards
Laura Taalman and Eugenie Hunsicker“Simplicity is not Simple,”Math Horizons, September, 2002.
Philip D. Straffin, Jr.“The Instability ofDemocratic Decisions,”Math Horizons, April 2002.
The Trevor Evans Awards, established bythe Board of Governors in 1992 and firstawarded in 1996, are made to authors ofexpository articles accessible toundergraduates that are published inMath Horizons. The Awards are namedfor Trevor Evans, a distinguishedmathematician, teacher, and writer atEmory University.
Lester R. Ford Awards
Leonard Gillman“Two Classical Surprises Concerningthe Axiom of Choice and theContinuum Hypothesis,”The American MathematicalMonthly, June-July 2002, pp. 544-553.
Warren P. Johnson“The Curious History of Faà duBruno’s Formula,” The AmericanMathematical Monthly, March 2002,pp. 217-234.
Sam Northshield“Associativity of the Secant Method,”The American Mathematical Monthly,March 2002, pp. 246-257.
Eleanor Robson“Words and Pictures: New Light onPlimpton 322,” The AmericanMathematical Monthly,February 2002, pp. 105-120.
Sérgio B. Volchan“What Is a Random Sequence?,” TheAmerican Mathematical Monthly,January 2002, pp. 46-63.
The Lester R. Ford Awards, establishedin 1964, are made to authors of exposi-tory articles published in The AmericanMathematical Monthly. The Awards arenamed for Lester R. Ford, Sr., a distin-guished mathematician, editor of TheAmerican Mathematical Monthly, 1942-46, and President of the MathematicalAssociation of America, 1947-48.
Merten M. Hasse Prize
Manjul Bhargava“The Factorial Function andGeneralizations,” The AmericanMathematical Monthly,November 2000, pp. 783-799.
In 1986 an anonymous donor gave theMathematical Association of Americafunds sufficient to support a prize hon-oring inspiring and dedicated teachers.The price is named after Merten M.Hasse, who was a former teacher of thedonor, and who exemplified the quali-ties of a fine teacher. The Merten M.Hasse Prize is given for a noteworthy ex-pository paper appearing in an Associa-tion publication, at least one of whoseauthors is a younger mathematician. Theprize is designed to be an encouragementto younger mathematicians to take upthe challenge of exposition and commu-nication.
George Pólya Awards
David L. Finn“Can A Bicycle Create a UnicycleTrack?,” College Mathematics Journal,September 2002, pp. 283-292.
Dan Kalman“An Undetermined Linear System forGPS,” College Mathematics Journal,November 2002, pp. 384-390.
The George Pólya Awards, established in1976, are made to authors of expositoryarticles published in the College Math-ematics Journal. The Awards are namedfor George Pólya, a distinguished math-ematician, well-known author, and pro-fessor at Stanford University.
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FOCUS August/September 2003
2003 Award Winners for
NORTH CENTRAL
Tom SibleySt. John’s University
Mark FinkelsteinUniversity of California, Irvine
SOUTHERN CALIFORNIA
Judy L. WalkerUniversity of Nebraska-Lincoln
NEBRASKA-SE SD
Hugh KingColorado School of Mines
ROCKY MOUNTAIN
Steven A. BleilerPortland State University
PACIFIC NORTHWEST
Peter TannenbaumCalifornia State University,
Fresno
NORTHERN CALIFORNIA
Gregory B. PasstySouthwest Texas State University
TEXAS
KANSAS
Frank S. BrennemanTabor College
Alexander F KleinerDrake University
IOWA
Janet M. McShaneNorthern Arizona University
SOUTHWESTERN
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August/September 2003
Rebecca BergBowie State University
MD-DC-VA
KENTUCKY
Ted J. SuffridgeUniversity of Kentucky
Tom IngramUniversity of Missouri-Rolla
MISSOURI
Sue GoodmanUniversity of North Carolina
at Chapel Hill
SOUTHEASTERN
Olympia NicodemiSUNY Geneseo
SEAWAY
Steve GreenfieldRutgers, the State University
of New Jersey
NEW JERSEY
INDIANA
Johnny E. BrownPurdue University
NORTHEASTERN
Emma PreviatoBoston University
Thomas P. DenceAshland University
OHIO
Not pictured:Florida Section: Athanassios KartsatosMichigan Section: Steven Kahn
Distinguished Teaching
The following sections did not makeawards this year: Allegheny Mountain,EPADEL, Illinois, Intermountain,Louisiana-Mississippi, Metro New York,Oklahoma-Arkansas, and Wisconsin.
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FOCUS August/September 2003
In late June and earlyJuly, 30 of the besthigh school math-ematics students inthe nation grappledwith challengingmathematical prob-lem solving at the an-nual MathematicalOlympiad SummerProgram (MOSP)held on the campusof the University ofNebraska-Lincoln inLincoln, NE. TheMOSP is sponsoredby the MathematicalAssociation ofAmerica through theAmerican Mathemat-ics Competitions pro-gram. This extraordi-nary group of youngmathematicians spent8 to 9 hours each dayin classes and study sessions learningproblem solving techniques and solvingOlympiad-caliber problems in both teamand individual contests. All of the stu-dents were top scorers from the 32ndUSA Mathematical Olympiad (USAMO)exam in May. Each USAMO participanthad already survived two challengingpreliminary examinations: the AmericanMathematics Competition held in Feb-ruary 2003 and the American Invita-tional Mathematics Exam held in Marchand April.
Among the participants at the MOSPwere the top twelve named as theUSAMO Winners. They are BorisAlexeev of Cedar Shoals High School inAthens GA, Jae Min Bae of the Academyfor Advancement of Science and Tech-nology in Hackensack NJ, Daniel Kaneof Madison West High School in Madi-son WI, Anders Kaseorg of the Char-lotte Home Educators Association inCharlotte NC, Mark Lipson of Lexing-ton High School in Lexington MA,Tiankai Liu of Phillips Exeter Academy
in Exeter, NH, Po-Ling Loh of JamesMadison Memorial High School inMadison WI, Po-Ru Loh of James Madi-son Memorial High School in MadisonWI, Aaron Pixton of Vestal Senior HighSchool in Vestal NY, Kwok Fung Tang ofPhillips Exeter Academy in Exeter, NH,Tony Zhang of Phillips Exeter Academyin Exeter, NH and Yan Zhang of ThomasJefferson High School of Science andTechnology in Alexandria,VA. The win-ners were celebrated on June 22-23 witha reception at the MAA Headquarters inWashington D.C., a tour of the NationalScience Foundation, a reception at theNational Academy of Sciences with a talkby Dr. Peter Winkler of Bell Labs (Lu-cent Technologies), and a gala dinnerwith the mathematical sciences commu-nity in the U.S. Department of State Dip-lomatic Reception Rooms.
After taking yet another rigorous two-day Team Selection Contest six studentswere named as the USA team for the 44thInternational Mathematical Olympiad tobe in Tokyo, Japan, on July 11-19. The
IMO attracts 500 of themost talented mathemat-ics students from morethan 80 countries. TheUSA team consists ofDaniel Kane, AndersKaseorg, Mark Lipson,Po-Ru Loh, AaronPixton, and Yan Zhang.Zuming Feng of PhillipsExeter Academy is theHead Coach and GregoryGalperin of Eastern Illi-nois University is the As-sistant Coach.
MOSP, which covers thesubjects which appear onthe USA and Interna-tional MathematicalOlympiads, is deep andsophisticated. It includesnumber theory, advancedEuclidean geometry, po-lynomial theory, in-
equalities, invariants, combinatorics,and counting methods. Students prac-ticed their skills frequently with home-work sets and contests which weregraded and discussed daily. A typicalproblem is Problem 2 from the 2003USAMO: A convex polygon P is dis-sected into smaller convex polygons bydrawing all of its diagonals. The lengthsof all sides and all diagonals of the poly-gon P are rational numbers. Prove thatthe lengths of all sides of all polygons inthe dissection are also rational numbers.
The 12 USAMO Winners, along withtheir hometowns and schools, the Hon-orable Mentions, and the questions onthe USAMO as well as the answers canall be found at www.unl.edu/amc/. Morepictures and information about theAmerican Mathematics Competitions,the USAMO, the IMO and the MOSP arealso available on the website.
By Steven R. Dunbar
Clockwise from lower left seated individual: Jae Min Bae, Tiankai Liu, BorisAlexeev, Daniel Kane, Mark Lipson, Aaron Pixton, Anders Kaseorg, Ron Gra-ham, MAA President, Tony Zhang, Yan Zhang, Zwok Fung Tang, Po-Ling Loh,Po-Ru Loh, and Tina Straley, MAA Executive Director. Photo by Robert A.Strawn.
The Mathematical Olympiad Summer Program Brings Together Talented
High School Students
On MOSP, see also the advertisement onpage 22 of this issue. Steven R. Dunbar isthe Director of the American MathematicsCompetitions.
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August/September 2003
A Problem-Solving Dynasty
By Steve Olson
Tennis stars Venus and SerenaWilliams may be better known,but the three children of Wei-Yin and Theresa Loh are no lessaccomplished.
Po-Shen Loh, a senior at theCalifornia Institute of Technol-ogy, Po-Ru, a Caltech freshman,and their sister Po-Ling, a jun-ior at James Madison MemorialHigh School in Madison, Wis-consin, are the most decoratedset of siblings in the history ofU.S. competitive mathematics.All three have scored at the high-est levels of national competi-tions, and the two older boys arethe first set of siblings ever toqualify for U.S. InternationalMathematical Olympiad teams. “Theirachievement is unprecedented,” says TituAndreescu, who formerly served as di-rector of the MAA’s American Math-ematics Competitions and leader of theU.S. IMO team.
As is the case with many mathematicallytalented U.S. students, the Lohs learnedabout competitive mathematics throughMathcounts, the middle school problem-solving program. “In the sixth grade, ateacher called Po-Shen and said that heshould take the selection test for theschool team,” says Wei-Yin, a professorof statistics at the University of Wiscon-sin. “We had no idea what to expect. Wejust thought it was a local event.”
The following year, Po-Shen did so wellat the local and state levels of Mathcountsthat he was one of four people selectedto the Wisconsin state team. He went toWashington to compete at the nationallevel against 227 other middle schoolersand finished in the top 30. “I wasshocked,” says Po-Shen, “I thought forsure that I would be in the lower half.”
The following year, in eighth grade, Po-Shen placed third in the nation inMathcounts. According to his father,“That got the attention of his brother, Po-Ru,” who was then in the fifth grade.
(The Lohs have observed a Chinese tra-dition of giving their children the samename; one meaning of “po,” in Chinese,is “breadth.”) “Everybody told Po-Ru hehad to do better than his brother, and Ithought there was no way he could dothat,” says Loh, but he was wrong. In theseventh grade, Po-Ru finished second inthe nation in Mathcounts, and he fin-ished first in the eighth grade.
“That got the eye of his sister, Po-Ling,”says Loh. Two years younger than Po-Ru, Po-Ling was not sure at first that sheliked competitive mathematics. “It’s tra-ditionally been more of a boys’ subject,”she says. But in the seventh grade she,too, advanced to the national level inMathcounts, where she did even betterthan her eldest brother had done. Thefollowing year, in the eighth grade, shewas second in the nation. No other girlhas ever done as well in the nationalMathcounts competition.
When Po-Shen began high school, “wethought that was the end of the compe-titions,” says Wei-Yin. But then the Lohsdiscovered the American MathematicsCompetitions (AMC) examinationssponsored by the MAA. Beginning hisfreshman year, Po-Shen took the Ameri-can High School Mathematics Examina-
tion (which has since beensplit into the AMC 10 andAMC 12). In his junior yearhe did so well that he quali-fied first for the American In-vitational Mathematics Ex-amination and then for theUnited States of AmericaMathematical Olympiad(USAMO). He finishedamong the top 12 in the na-tion on the USAMO, earninga trip to Washington, D.C., tobe honored at a black tie din-ner at the State Department.And he qualified for the U.S.International MathematicalOlympiad team that year,where as one of six teammembers he earned a bronze
medal at the 1999 Olympiad in Roma-nia.
The next year Po-Shen and Po-Ru, thena freshman, finished among the top 12on the USAMO — the first time two sib-lings ever had achieved that feat. Po-Shen opted to do a fellowship at Caltechthat summer, but Po-Ru was on theOlympiad team that went to Korea in2000, where he earned a silver medal. Po-Ru also was on the Olympiad teams thatcompeted in Scotland in 2002 and Japanin 2003, earning gold medals both times.And in 2003, the second set of siblingsever to finish together in the top 12 onthe USAMO came to the State Depart-ment dinner in Washington, when Po-Ru was joined by his sister Po-Ling.
With such accomplished children, Wei-Yin and Theresa Loh often are asked fortheir secret. But they say that the creditbelongs entirely to their children. “Wehaven’t done anything special withthem,” says Wei-Yin. “They got eachother interested in it.”
Steve Olson is the author of “MappingHuman History: Genes, Race, and OurCommon Origins” and the forthcoming“Brainstorms: Six Kids Vie for Glory atthe World’s Toughest Math Competition.”
Po-Ru Loh, MAA President Ron Graham, and Po-Ling Loh atthe USAMO Award Ceremony at the US Department ofState.Photo by Robert A. Strawn.
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FOCUS August/September 2003
The NSF has announced a new pro-gram to complement the VIGRE (Verti-cal Integration of Research and Educa-tion) initiative that is already underway.VIGRE will become part of a three-pronged effort to increase the number ofU.S. citizens, nationals, and permanentresidents who are well prepared and pur-sue careers in the mathematical sciences.The new program, Enhancing the Math-ematical Sciences in the 21st Century(EMSW21), is comprised of VIGRE, Re-search Training Groups in the Math-ematical Sciences (RTG), and Mentoringthrough Critical Transition Points in theMathematical Sciences (MCTP). A broadstroke description of each componentfollows. A complete description may befound at the NSF website. All three com-ponents have the same proposal dead-line: 16 September 2003.
VIGRE
VIGRE projects must be designed to pro-mote interaction among undergraduates,graduate students, postdoctoral associ-ates, and faculty members in a depart-ment (or departments). A team approachbased on broad support by faculty shouldintegrate research and education forgraduate students and involve under-graduates in learning by discovery. A newfeature of the revised VIGRE program isthe possibility of support for interna-tional research and education activities.All VIGRE proposals are required to in-clude an extensive curriculum reviewsupported by five years of data.
Goals for graduate students in a VIGREproject include significant teaching ex-perience, involvement with research ac-tivities involving the full range of par-ticipants, broad and deep graduate edu-cation, and the development of strongcommunication skills. In contrast to tra-ditional graduate support, VIGRE par-ticipants should have significant time forcourse work, research, and other activi-ties as well as at least one year of super-vised teaching.
Undergraduates in a VIGRE project willgain research experience through activi-ties such as faculty-directed projects, in-ternships, or participation in interdisci-plinary research. Mentoring of these stu-dents should aim to stimulate furtherinterest in the mathematical sciences andto develop enhanced mathematical com-munication skills.
A VIGRE project is intended to offerpostdoctoral associates opportunitiesoutside the usual mathematical scienceseducation and training through interdis-ciplinary research experiences, externalinternships, and participation in researchinstitute programs. A critical element ismentoring as it is for the undergraduateand graduate students. For thepostdoctoral associates, mentors shouldhelp develop successful researchers, com-municators, and mentors.
The NSF anticipates making up to sevenVIGRE awards based on a budget of$10,000,000. Grants will be $400,000 to$1,000,000 per year for three years withthe possibility of an extension for twomore years. A VIGRE proposal shoulddescribe a five-year plan.
RTG
A Research Training Group will be agroup of researchers focused on a majorresearch theme. Members may comefrom different departments or institu-tions, but the research and educationactivities must be based in the math-ematical sciences and in a mathematicalsciences department. Support requestsfor advanced undergraduates, graduatestudents, postdoctoral investigators, andvisitors may be included in a RTG pro-posal. A significant collective mentoringcomponent is required to help ensurethat all participants benefit from new orenhanced research-based training andeducation. Funding of $4,000,000 willsupport up to nine RTG awards. A pro-gram may receive up to $500,000 per yearfor one to five years.
MCTP
The Mentoring through Critical Transi-tion Points program solicits proposalsthat deal with any of the following orsimilar career transitions: from under-graduate to graduate school; from coursework to original research; from gradu-ate school to a postdoctoral appoint-ment, to a teaching position at an un-dergraduate institution, or to a positionin industry. Proposers should describeplans for addressing the issues related toa specific transition point or set of points,for the recruitment of participants withparticular attention to those fromunderrepresented groups, and for care-ful mentoring of the participants. TheNSF hopes to make awards of up to$500,000 per year for one to five years tofund six MCTP projects.
NSF Beat
September 2003
By Sharon Cutler Ross
NSF to Fund “Science
of Learning” Centers
The National Science Foundation plansto fund several Science of Learning Cen-ters that focus on studying how peoplelearn and transform the knowledge intopractical ways of improving teaching.The Centers are to be interdisciplinaryand are expected to develop “appropri-ate partnerships with academia, indus-try, all levels of education, and other pub-lic and private entities.” For more infor-mation, see http://www.nsf.gov/home/crssprgm/slc/summary.htm.
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August/September 2003
Carl C. Co-wen of PurdueUniversity willbe the MAA’snext President.He will serve asPresident-Electin 2004 andbegin a two-year term asPresident inJanuary 2005, when he will succeedRonald Graham. That year will alsomark the MAA’s 90th anniversary.
Barbara T. Faires of Westminster College(New Wilmington, PA) was elected theAssociation’s next First Vice-Presidentfor the term 2004-2005.
And for the position of Second Vice-President, Jean Bee Chan of SonomaState University (Rohnert Park, CA) wonthe two-year term 2004-2005.
Professor Cowen is at present the MAA’sFirst Vice-President. He is former Headof the Mathematics Department ofPurdue University, and is coauthor ofComposition Operators on Spaces ofAnalytic Functions (1995).
He won the Haimo Award forDistinguished Teaching in l997 and hasover the past decade served theAssociation as a representative andconsultant to numerous committees,councils, and boards, and been a memberof the Joint Advisory Board for FOCUSand MAA Online.
“I will work within the MAA and withother organizations to connect ourstudents with the phenomenalopportunities in the mathematicalsciences,” he said, “and to build bettermathematical futures for us all.”
Barbara T. Faires, a 2002 AlleghenyMountain Section Teaching Award
winner, is a long-standing member of theMAA who has served as Chair of theCommittee on Sections and on a host ofcommittees, including Audit and Budget,Finance, Executive, Strategic Planning,Gung Hu Award, and others. She iscurrently the Chair of the CoordinatingCouncil on Awards.
One im-portant goalof the MAA “isto expandmembershipto include alarger per-centage ofthose in-terested inundergraduatemathematicse du c a t i on ,”said Professor Faires. “I will work toensure continued success of ProjectNExT and other such projects fromwhich future leaders will come.”
Jean Bee Chan served on the MAA Boardof Governors (l999-2002) and as Vice-Chair of the Northern California Section(l996-97). She has also served on theAssociation’s Membership Committee,Development Committee, andCommittee on Undergraduate StudentActivities and Chapters.
Prof. Chanstated “I willdevote myenergy to in-crease publicappreciationof math-ematics, workfor studentp r o g r a m s ,and generatef i n a n c i a lsupport forthe MAA.”
MAA Election Results Are In: Carl Cowen Will
Become the Association’s 51st President
Barbara T. Faires
Former FOCUS Editor
Keith Devlin Wins
Italian Literature Prize
Keith Devlin
Jean Bee Chan
Carl C. Cowen
MAA Onlinecolumnist KeithDevlin has beenawarded theItalian PeanoPrize for 2002.The prize isawarded to theauthor of a bookof “readablemathemat ic s”published in Italian during the year ofattribution, and is the only award in Italydedicated to this subject. Devlin waschosen to receive the award for his booksThe Math Gene and The Language ofMathematics, both of which have beenreviewed in the Read This! section ofMAA Online.
Previous winners are Apostolos Doxiadisof Greece and Alaine Connes of France.Other authors whose books wereconsidered for the 2002 prize includedAmir Aczel, Freeman Dyson, MicheleEmmer, Stephen Hawking, RogerPenrose, Charles Seife, and Ian Stewart.
Devlin will travel to Turin in the fall tobe awarded the prize and to give aninvited public lecture.
Distance Learning
Program Sought
Community College mathematics profes-sor is seeking a doctoral program in math-ematics that would offer some courses viadistance learning. His plans are to com-plete the degree (on location) during atwo/three year leave of absence from fulltime employment.
Contact Information:
S. KaczkowskiS.U.N.Y. Orange115 South StreetMiddletown, NY 10940Email: [email protected]
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FOCUS August/September 2003
MAA Online on the Radio
We understand that Michael Krazny,in a program called Forum that can beheard on KQED (the NPR station in theSan Francisco area) recently recom-mended that viewers visit MAA Online’sRead This! section. He also recom-mended John dePillis’s book, 777 Math-ematical Conversation Starters. We are, ofcourse, in full agreement with both ofKrazny’s recommendations.
This Just In
Patricia A. McKillip’s new book, In theForests of Serre, was recently offered bythe Science Fiction Book Club with theblurb “Whoever walks the forests of Serremay never find his way home.” We arereliably informed, however, that the bookis not about being lost in the mathemati-cal work of the recent Abel laureate. Hismany papers, after all, are more likemountaintops than they are like forests.
Commemorations
This year marks the 400th anniversary ofthe death of French mathematicianFrançois Viète (1540-1603), who madecontributions to algebra and otherbranches of mathematics. It is also thecentenary of the birth of AndreiNikolaevich Kolmogorov, famous amongother things for proposing a mathemati-cal foundation for the theory of prob-ability. Both anniversaries will be markedby conferences and other special events.Also worthy of note is the 25th anniver-sary of TEX, celebrated this July at theTUG (TEX Users Group) meeting in Ha-waii.
AMS Centennial Fellowships
The AMS announced that it has awardedCentennial Fellowships to two outstand-ing research mathematicians: Henry H.Kim of the University of Toronto, whoworks on the theory of automorphicforms and L-functions, and John E.Meier of Lafayette College, who works on
geometric group theory. Meier, who is amember of the Association, is one of thefew Centennial Fellows to work at a smallcollege.
Kaplan Plans Move Into TeacherEducation
Kaplan Inc. is the latest institution toopen a school of education, hiringHarold O. Levy, the former New YorkCity schools chancellor, to run its school,which will target working adults whowant to switch careers. When he waschancellor in New York, Levy developeda Teaching Fellows program that cateredto those who sought to change careers.Levy envisions “a full-service school ofeducation” that would award associate,bachelor’s and master’s degrees. Kaplanwill seek accreditation for the schoolfrom the North Central Association ofColleges and Schools.
National Research Council SuggestsStates Fund Educational Research
A report by the National Research Coun-cil calls upon states to band together andinvest in educational research. The NRCreport proposes the creation of a “stra-tegic education research partnership”that would bring together scientists andpartnerships to conduct research inschool and district settings. The report,“Strategic Education Research Partner-ship,” can be viewed online at http://books.nap.edu/books/0309088798/html/index.html.
RAND Report Released
The RAND Corporation has released areport entitled Mathematical Proficiencyfor All Students. Prepared by a panel ofmathematicians and mathematics edu-cators chaired by Deborah L. Ball, thereport concludes that the many attemptsto create the conditions for all studentsto attain a reasonable level of mathemati-cal proficiency suffer from an inadequateempirical research base. It, therefore, pro-poses a wide-ranging research program
in mathematics education aimed at fig-uring out what actually will help attainthe goal of proficiency for all. The reportcan be ordered in book form or viewedonline at http://www.rand.org/publica-tions/MR/MR1643/.
MAA Member George Andrews Electedto National Academy of Sciences
The National Academy of Sciences an-nounced the election of 72 new mem-bers and 18 foreign associates from 11countries in recognition of their distin-guished and continuing achievements inoriginal research. Six of the new mem-bers are mathematicians, statisticians, orcomputer scientists and one—GeorgeAndrews —is also a member of the MAA.Election to membership in the Academyis considered one of the highest honorsthat can be accorded a scientist or engi-neer.
The new members in the mathematicalsciences are: George E. Andrews of Penn-sylvania State University, James O. Bergerof Duke University, Yakov Eliashberg ofStanford University, Solomon W.Golomb of the University of SouthernCalifornia, Karl Hess of the University ofIllinois, and Haim Brezis of theUniversitè Pierre et Marie Curie, electedas a foreign associate.
Sources. Krazny: Jerry Alexanderson,Frank Farris. Forests of Serre: SFBC flyer.Commemorations: email communica-tions, http://tug.org. Centennial Fellow-ships: email communication, Chronicleof Higher Education, AMS website.Kaplan: Chronicle of Higher Education,http://www.kaplan.com/about/f1b.html.NRC: Education Week, 09 April 2003,National Academy of Sciences website.RAND report: Education Week, 30 April2003, RAND website. New NAS mem-bers: NAS website.
Short Takes
Compiled by Fernando Q. Gouvêa
FOCUS
21
August/September 2003
Proposals are now being solicited bythe American Institute of Mathematics(AIM) Research Conference Center(ARCC), for small, focused workshopsto be held between summer 2004 andsummer 2005. These workshops aresponsored by AIM and the NationalScience Foundation, which jointly fundARCC. It is anticipated that there willbe eighteen focused workshops in 2004-2005, at AIM in Palo Alto, California.Each workshop will last approximatelyone week and involve up to 32 partici-pants, allowing for close collaborationbetween scholars. All participants re-ceive full funding to attend.
Whereas fifty years ago mathematicalcollaboration was relatively rare, todayapproximately half of all mathematicalpapers are written by multiple authors.ARCC helps to develop and supportsuch collaborations by holding small,focused research workshops that allowentire groups of attendees to devotetheir efforts toward accomplishing a
specific mathematical goal. Special atten-tion is paid to facilitating collaborationsthat include women, underrepresentedminorities, and researchers at primarilyundergraduate institutions. To aid in col-laboration before and after the work-shops, each workshop has an accessiblewebsite which includes open problemsand progress updates.
Proposals will be accepted until Novem-ber 1, 2003. Typically one to two pagesin length, proposals should describe thespecific mathematical goal comprisingthe focus of the workshop. Also includedshould be an outline of how this goalwould be accomplished during the week,as well as anticipated workshop out-comes. Proposals will be judged for theirscientific merit and timeliness, as wellupon their appropriateness for a small,intensive workshop format. The overallquality of the workshop plan and thelikelihood that the proposed goals wouldbe achieved are also considered. A list ofexpected participants is required as part
American Institute of Mathematics Research Conference Center
Call for Proposals
of the proposal. The inclusion of women,members of underrepresented ethnic/racial groups, junior researchers, and re-searchers from primarily undergraduateinstitutions is a plus.
AIM is a nonprofit mathematics institutebased in Palo Alto, California, and hasbeen in existence since 1994. AIM wasfounded by Silicon Valley businessmenJohn Fry and Steve Sorenson, to supportresearch mathematics. John Fry receivedan undergraduate degree in mathemat-ics at Santa Clara University, and was in-spired by his professor and former MAApresident, Gerald Alexanderson, who ischair of the board of trustees of AIM.AIM also sponsors conferences, smallfocused research groups, REUs, publicmath lectures, and math activities forlocal high school students.
See http://www.aimath.org/ARCC/ formore information.
An NSF-funded project to develop sta-tistical indicators to help college math-ematics departments to monitor thequality of their lower division (first twoyears) undergraduate mathematics pro-grams was announced in a prior issue ofFOCUS (August/September, 2001). Theproject, carried out under the directionof a national advisory panel, collecteddata from the mathematics departmentson three campuses: a community college;a comprehensive state university, and aresearch university. A final report sum-
marizing the major findings is nowavailable online or on CD at the website,http://www.mste.uiuc.edu.
The final report also provides back-ground for the project. Student outcomesand assessment, by John A. Dossey andAlan H. Schoenfeld, is a comprehensivepaper, that outlines strategies, togetherwith abundant sample assessmentitems, for monitoring student achieve-ment in mathematics. Also included isa collection of abstracts of over 100 re-
Final Report on Project to Assist Mathematics Departments to Monitor
Their Undergraduate Programs
search articles on teaching and learningundergraduate mathematics. The docu-ments are provided in a database that issearchable by topic, statistical indicator,author, and title. For further informationcontact Kenneth J. Travers [email protected].
22
FOCUS August/September 2003
The Tenth International Congress on
Mathematical Education (ICME-10)
The MAA seeks a mathematician to beAcademic Director of the MathematicalOlympiad Summer Program June-July,2004 in Lincoln, NE and Leader of theUS delegation to the International Math-ematical Olympiad in Athens, GreeceJuly 6-18, 2004. Must be excellent math-ematical problem solver, have excellentteaching skills and be able to work withexceptionally talented high schools stu-dents, and be able to represent the USAand the MAA. Experience with AMCand Olympiad style math competitionsis desired. The position is renewable forsucceeding summer programs in 2005and 2006. Please send letter of applica-tion and resume by November 1, 2003,to Prof. Steve Dunbar, MAA AmericanMathematics Competitions, 1740 VineStreet, Lincoln, NE. Please direct yourinquiries about the position to Profes-sor Dunbar at 1-402-472-6206 [email protected].
MAA American
Mathematics
Competitions
Program Seeks
MOSP-IMO Leader
Under the auspices of ICMI (Interna-tional Commission on Mathematical In-struction) the 10th International Con-gress on Mathematical Education,ICME-10, will be held in Copenhagen,Denmark, July 4-11, 2004. The aim ofthe ICME congresses is to:
• Show what is happening in math-ematics education worldwide, interms of research as well as teachingpractices
• Exchange information on the prob-lems of mathematics educationaround the world
• Learn and benefit from recent ad-vances in mathematics as a discipline
ICME-10 hopes to attract between threeand four thousand researchers in math-ematics education, mathematics educa-tors, including teachers, and others work-ing within the educational system, fromaround 100 countries. Applications toattend can be found at the ICME-10website at http://www.icme-10.dk. Travelgrants are available through NCTM. Formore information and grant applica-tions, visit the NCTM website at http://www.nctm.org/icme10/.
MAA Awards
Total Awards 22Female Awardees 3Male Awardees 19
Percentage of Female Participation: 14%
Board of Governors
Total Board Members 51Female Board Members 17Male Board Members 34
Percentage of Female Board Members:33%
Nominees to the Board of Governors
This list includes nominees for sectiongovernors elected in 2002 as well asnominees for other governor slots in-cluded in Board agendas.
Total Nominees 26Female Nominees 5Male Nominees 21
Percentage of Female Nominees: 19%
Committee Chairs
This list includes chairs of committees,including joint committees, representa-tives, and editors.
Total Chairs 96Female Chairs 31Male Chairs 65
Percentage of Female Chairs: 32%
Speakers at National Meetings
This list includes MAA Invited Addresses,Minicourses and Short Course Instruc-tors, and Organizers of Contributed Pa-per Sessions.
Total Speakers 110Female Speakers 44Male Speakers 66
Percentage of Female Participation: 40%
Data on Gender For 2002
Below is the information collected for the year 2002.
The MAA makes it easy to changeyour address. Please inform theMAA Service Center about yourchange of address by using the elec-tronic combined membership list atMAA Online (www.maa.org) or call(800) 331-1622, fax (301) 206-9789,email: [email protected], or mailto the MAA, PO Box 90973, Wash-ington, DC 20090.
Have You Moved?
FOCUS
23
August/September 2003
Career BrochureOrder Form
The new MAA career brochure We Do Math! highlights eleven profiles from 101Careers in Mathematics. These vignettes describe a variety of non-academic careersfor which a background in the mathematical sciences is useful. Each of the jobspresented shows real people in real jobs.
The eight-panel brochure is 4’’ by 9’’ (folded) and can be mailed in a standardenvelope or distributed in the classroom or at career fairs or recruiting events.
When students want to know how a mathematics degree can benefit them, beprepared to answer with We Do Math!
A Special OfferYour school logo and/or contact information can be printed on the brochureSchools ordering brochures in time have the option of including the school logo and/or contact information on the front of thebrochure. PRE-ORDERS + LOGO (black or one-color version only) must be received by MAA headquarters by September 12,2003.
I want to order brochureswithout my school logo on thefront.
Yes! I want to preorderbrochures with my school logoand/or contact information onthe brochure.
Copies of We Do Math! are available in bulk in multiples of 1000. Ifyou add your institutional information on the brochure, there is aone-time set up fee of $150.00.
Quantity:____________ at $175/1000 = __________
Setup: $150.00
Total: __________
We're looking for more career profiles. If you would like to contribute profiles featuring your students forpossible use in future brochures, please contact us.
24
FOCUS August/September 2003
I. Bernard Cohen, the thesis director formany of the first generation of profes-sionally trained American historians ofmathematics and the first American toreceive a Ph.D. in the History of Sciencein the United States, died at his home inWaltham, Massachusetts on June 20. Bestknown to the mathematical communityas America’s most prominent Newtonianscholar, Cohen was the author of manybooks, including his monumental criti-cal edition (1972) and the definitivemodern translation (1999, with LatinistAnne Whitman) of Newton’s Principia.Also notable are The Newtonian Revolu-tion (1980), analyzing Newton’s math-ematical physics, and Newton: Text, Back-ground, Commentaries (1995), a compre-hensive collection of primary sourcesand recent scholarship, co-edited withRichard S. Westfall.
Educated at Harvard, Cohen received hisB.S. in Mathematics in 1937, and hisPh.D. in the History of Science in 1947.He taught history of science at Harvardfrom 1946 until 1984, and later taught atBrandeis and at Boston College. Al-though the history of mathematics wasnot Cohen’s primary field, his knowledgeof it was amazing, and it was he who in-troduced many future historians ofmathematics to topics as diverse as alge-bra in Islamic civilization, the statisticalrevolution of the nineteenth century, andKepler’s anticipations of the integral cal-culus. Among his Ph.D. students atHarvard were the historians of math-ematics Uta Merzbach, Victor Hilts,Bruce Collier, Joseph Dauben, KennethManning, Lorraine Daston, JoanLivingston Richards, and the presentwriter. Other notable historians of math-ematics, including Wilbur Knorr, tookCohen’s courses while at Harvard.
Cohen was a wonderful mentor. He andhis wife often had graduate students overto their home, bringing students togetherwith visiting scholars. He made it seemas though this was the natural way totreat graduate students. He alwaysworked to help young—and older—
scholars, whoever and wherever theymight be, independently of their conven-tional academic stature. Without fanfareor ideology, he was a champion of equaltreatment for women at a time when itwas far from universal at Harvard.
He taught his students, many of whomwere trained in the sciences, how to thinklike historians. One of his maxims was“Remember that scientists of the pastwere just as intelligent as we are, so that,if we had lived when they did, whatpuzzled them would puzzle us too.” An-other maxim, a call to ethical scholarshipand the excitement of research, was“Truth is more interesting than fiction.”Above all, Cohen had an unerring abil-ity to pick out what was important andto discourage what was lazy, superficial,or trivial—and to do this in a way thatempowered, rather than discouraged. Hewas always delighted when somebodycould teach him something new. “That’svery interesting!” was one of his charac-teristic responses. He understood theexigencies of academic life thoroughlyand got them across to his students. I amfond of quoting what he said when I wastrying to finish my dissertation by thedeadline: “Don’t get it perfect; get itdone.”
Generations of Harvard students wereintroduced to the physical sciencesthrough Cohen’s general-educationcourses. His lectures were intellectuallyand physically dramatic: The model train
exhibiting the inertial motion of projec-tiles and the stroboscopic photographsof parabolic motion remained in stu-dents’ minds many years later. I have avivid memory of Cohen demonstratingCopernicus’s three motions of the earthby walking around a table and twirling awell-aimed yardstick.
Arising from his courses was his wonder-ful little book, historically sophisticatedbut also highly readable, The Birth of aNew Physics (1960, updated 1985), whichclearly and succinctly describes the his-tory of physics and astronomy fromAristotle through Copernicus, Tycho,Galileo, and Kepler, culminating in theachievements of Newton. Yet another ofhis books, Revolution in Science (1985),covering developments from Renaissanceastronomy and anatomy to Einstein andContinental Drift, won the 1986 Pfizeraward of the History of Science Society.His interest in the history of computersresulted in another book, Howard Aiken:Portrait of a Computing Pioneer (1999).Among his many articles on subjects ofinterest to mathematicians, I would es-pecially highlight three in the ScientificAmerican: on Florence Nightingale as astatistician, on Newton’s discovery ofgravity, and an interview with AlbertEinstein shortly before the latter’s death.The manuscript of Cohen’s last book,The Triumph of Numbers, a history ofnumbers and their impact on society andculture, was mailed to the publisher oneweek before he died.
Cohen leaves his wife of nineteen years,Susan Johnson, a daughter, Dr. FrancesCohen, and granddaughter AngelicaKoch of New York, and two stepsons,David Johnson of St. Louis and BenjaminJohnson of New York. A memorial ser-vice is being planned for November 19,2003; see http://www.fas.harvard.edu/~hsdept/ for information. His manygraduate students, colleagues, andfriends will miss him beyond what wordscan convey.
I. Bernard Cohen (1914–2003)
By Judith V. Grabiner
I. Bernard Cohen
FOCUS
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August/September 2003
Etta Z. Falconer passed away on Sep-tember 19, 2002. She had retired in May2002 as Fuller E. Callaway Professor ofMathematics at Spelman College whereshe spent 37 years on the faculty. Falconerwas a transforming force at the Collegewhile holding positions as Chair of theMathematics Department, Chair of theDivision of Natural Sciences and Math-ematics, Associate Provost for SciencePrograms and Policy, Senior Advisor tothe President and Acting Provost. In theseand her many roles beyond SpelmanCollege, she committed herself to excel-lence and left a rich legacy that foreverplaces her at the national forefront in ef-forts to increase the presence of minori-ties and women in mathematics and sci-ence.
Etta was one of two daughters born toWalter A. Zuber and Zadie L. Montgom-ery in Tupelo, Mississippi. At age 15, sheentered Fisk University where she earnedthe B.A. degree in mathematics in 1953.A year later she would earn the M.S. de-gree in mathematics from the Universityof Wisconsin and begin a teaching careerat Okolona Junior College (MS). She re-turned to graduate school at Emory Uni-versity where she earned the Ph.D. de-gree in 1969 with a dissertation entitledQuasigroup Identities Invariant UnderIsotopy, written under advisor TrevorEvans. Prior to that time, there werefewer than 15 African-American womenin the U.S. who had earned the doctor-ate in mathematics.
Falconer’s research in algebra and sub-sequent publications were highly re-garded, yet she chose to devote her ex-ceptional creativity to the design ofhighly effective academic structures thatwould increase access to education inscience and mathematics for generationsof black women. It was her greater vi-sion to increase the diversity of the U.S.scientific community. Under Falconer’sleadership, the College added majors anddepartments in Computer Science andPhysics and a concentration in Environ-mental Science, and worked with theNational Aeronautics and Space Admin-istration to launch the Women in Scienceand Engineering Program, an initiativethat has contributed scores of extremelytalented women to the scientific commu-nity over the past decade. In addition, shewas an inspiring mentor for hundreds ofstudents, faculty and staff, including thiswriter.
Several honors and awards indicate theextent of Etta’s impact, the breadth of herservice and the depth of her commitmentto the advancement of students in math-ematics and science. Recognitions in-clude the Giants in Science Award fromthe Quality Education for MinoritiesNetwork; an honorary doctorate degreefrom the University of Wisconsin atMadison; a Lifetime Mentor Award fromthe American Association for the Ad-vancement of Science; a DistinguishedService Award and a Lifetime Achieve-ment Award from the National Associa-
Etta Zuber Falconer (1933-2002)By Sylvia T. Bozeman
tion ofMathema-ticians; andthe LouiseHay Awardfor Contri-butions toMathemat-ics Educa-tion fromthe Asso-ciation forWomen in Mathematics. In April 2002,Spelman College gave recognition to themagnitude and importance of Etta’s con-tributions when it opened a state-of-the-art science center that bears the Falconername.
Falconer’s impact on the development ofminorities in science is profoundly re-flected in her own family. She, with herloving husband Dolan, nurtured the de-velopment of their children: Dolan, Jr., anuclear engineer; Alice, a pediatrician;and Walter, an urologist. Following inEtta’s footsteps is granddaughter, Shelby,a sophomore at Spelman College.
We will miss Etta Falconer—miss herwise counsel, her warm and gentle spirit,and her strong voice of advocacy in thescientific community.
Sylvia T. Bozeman is Professor of Math-ematics at Spelman College.
Etta Z. Falconer
On May 26-30, 2003 a culturally diverse group of math-ematics professors participated in an MAA PREP Work-shop entitled “Integrating Technology into MathematicsInstruction.” The focus was on the use of technology inprecalculus and calculus classes. Prof. Jacqueline BrannonGiles was the program director and Professors Wade Ellis,Queen Hamilton, and William Hawkins were workshoppresenters. HCC Central College’s Academic Dean, Dr.Cheryl Peters served as an administrative consultant toassure that the interface between the workshop activitiesand the HCC system was smooth. The workshop wasfunded by the National Science Foundation and adminis-tered by the Mathematical Association of America.
PREP Workshop–Integrating
Technology into Math Instruction
26
FOCUS August/September 2003
In Memoriam
Barbara Beechler died on March 18, 2003. She was an active member of the Association andserved as a governor of the Southern California section. She was an MAA member for 53years.
James Crawford died on May 8. He had been an MAA member for 42 years and was honoredwith an MAA teaching award by the EPADEL Section in 1998.
Robert James, co-author of one of the first dictionaries of mathematics, first published in1942. He was an MAA member for 51 years.
Geraldine D. Smith, editor and author of many mathematics textbooks, was 100 years oldwhen she died in June. She was an MAA member for 49 years.
FOCUS will print short death notices of MAA members. Please send names, dates, and one ortwo biographical sentences to the editor at [email protected].
Harold Scott McDonald Coxeter, notedgeometer and author of many books,passed away on March 31 at the age of96. Known as Donald to family andfriends, Coxeter was educated at the Uni-versity of Cambridge and came to theUniversity of Toronto in 1936. There, hewas active as both teacher and researcheruntil his death.
Coxeter made important contributionsto geometry and related areas, focusingespecially on group theory and discretegroups, graph theory, projective geom-etry, the theory of polytopes, and non-Euclidean geometries. As happens tomany creative and influential mathema-ticians, Coxeter’s name has been attachedto several mathematical objects, includ-ing Coxeter groups and the Coxetergraph. He wrote more than 200 math-
ematical papers on many different sub-jects.
But while Coxeter’s research was impor-tant and creative, his talents as an exposi-tor may have been even greater. His ex-pository books are classics to whichthose who love the subject find them-selves returning over and over. Two ofthose books were published by the MAA:Non-Euclidean Geometry and GeometryRevisited (the latter co-authored with S.L. Greitzer). His most famous book isprobably Introduction to Geometry, writ-ten in 1969 and still in print from Wiley.
In addition to mathematics, Coxetercherished music and the arts, and wasparticularly interested in connectionsbetween mathematics and the arts. Hewas intimately involved in studying M.
C. Escher’swork. Coxeterwas a Fellowof the RoyalSociety of Ca-nada (1947),Fellow of theRoyal Society,L o n d o n(1950), andCompanionof the Orderof Canada(1997). He also received several honor-ary degrees.
Coxeter is survived by his daughter Su-san Thomas and his son Edgar. He willbe missed by all of the mathematics com-munity.
H.S.M. Coxeter (1907-2003)
H.S.M. Coxeter
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August/September 2003
I am writing to comment on the article,“The Four As: Accountability, Accredi-tation, Assessment, and Articulation” byPeter Ewell and Lynn Arthur Steen, whichappeared in the May/June, 2003, issue ofFOCUS.
In evaluating the issues raised in this ar-ticle it is of fundamental importance foryour readers to be aware of some con-troversial aspects of the “No Child LeftBehind” legislation (NCLB) that werenot fully explicated by your writers. Ibecame aware of these aspects onlythrough my work as a member of a localboard of education, and I suspect thatrelatively few of your readers are famil-iar with them.
Earlier this month I attended a meetingorganized by a senior member of con-gress that was attended by several dozenlocal school officials and a handful ofstate legislators as well as some high-ranking state education officials. The dis-cussion made it clear that many within
Letter to the Editor
the K-12 community see NCLB not as alegitimate effort to improve the qualityof education but rather as part of a sys-tematic effort to undermine support forpublic education in this country.
It is tempting to dismiss this concern asparanoia. To be sure, people in publiceducation are prone to be suspicious ofan administration whose secretary ofeducation has publicly declared that heconsiders parochial schools superior topublic schools.
Nevertheless, the educators raise sometelling points. For example, results (theproportion and number of ‘failing’schools and districts, based ultimately onthe raw scores of individual students onvarious exams) are to be reported uni-formly nationwide, even though the levelof rigor on the actual exams varies widelyfrom one state to the next. Another ex-ample is the shortage of new funding forthis major initiative that will require sig-nificant resources. Whether or not one
embraces the suspicions, the concernscannot be dismissed out of hand. Mo-tives aside, it is important to think care-fully about consequences. This was justunderscored by recent news reports thatstates such as Texas are now scramblingto weaken their standards in order tocope with the provisions of NCLB.
From this perspective, the remark that“[m]any feel that higher education’s turnis next” is rather ominous. The math-ematics community needs to pay closeattention.
Daniel FrohardtWayne State University
The authors reply:
This remark was intended to be ominous.Professor Frohardt’s concerns are wellfounded, as is his urging that the math-ematics community become better ac-quainted with the implications of NCLB.
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FOCUS August/September 2003
The “best textbook” is, of course, not awell-defined concept. The phrase imme-diately brings questions to mind: Best forwhat purpose? Who is the professor?Who are the students?
At Colby, the introductory numbertheory course is offered in alternate yearsand attracts a wide range of students.Because it has few pre-requisites, pro-spective mathematics majors can take itin order to find out what this math thingis all about. The class usually includesseveral such students, plus mathematicsmajors and a few computer science ma-jors. Some students are very experiencedat reading and writing proofs, others arevery much beginners at this game.
My goals for the course reflect this var-ied audience. I want to give students ataste of the fascination of the subject, tohave them realize how easy it is to spotnumber-theoretical patterns and howdifficult it is to predict whether the pat-terns, once found, will be easy or hard toprove. I emphasize numerical experi-mentation, but I also emphasize the im-portance of finding proofs.
What kind of textbook is helpful for sucha course? There are actually manychoices. One could choose a text that isuseful as a reference, a place for studentsto look for formal proofs of statementshandled informally in class. I have madethis choice in courses for more advancedstudents, but for this course I feel such abook would be too hard to handle. Mostof my students don’t have enough expe-rience of the typical terseness of formalmathematics books.
A second possibility would be to choosea textbook that emphasizes the compu-tational side of the course, using the com-puter either to create an interactive class-room or as a source for interesting prob-lems. For an interactive and exploratorycourse, I would probably choose Discov-ering Number Theory, by Jeff Holt andJohn Jones (Freeman, 2001), which wasreviewed in MAA Online (see http://www.maa.org/reviews/dnt.html). A more
advanced course with a computationalemphasis could be based on A Course inComputational Number Theory, by DavidBressoud and Stan Wagon (Key CollegePublishing, 2000), also reviewed in MAAOnline (http://www.maa.org/reviews/bresswagon.html).
In the end, though, I prefer a more tra-ditional teaching style, and I don’t reallywant to make my course too dependenton the computer. Many of the studentswho take the course would be happy touse a program like Mathematica, butmany others have little experience withcomputers and would prefer not to haveto deal with such a large and complicatedcomputer program. I do encourage themto use computational aids (at least a cal-culator, but preferably something thatcan do infinite-precision integer arith-metic, such as a TI-89 or the GP-PARI pro-gram). I try to leave enough room forpersonal choice and variation.
Two other important factors need to beconsidered. The first is whether one isgoing to expect students to read theirtextbook. I usually want them to do that,and I hope they will get something outof their reading. That puts severe con-straints on the choice of textbook. A fewof my personal favorites, such as H.Davenport’s The Higher Arithmetic andDaniel E. Flath’s Introduction to NumberTheory, turn out not to work very wellwith students. Davenport, for example,is a penetrating and readable book, buthe rarely delimits his proofs and theo-rems in a formal way. For students whoare just starting out, this makes the bookvery difficult to read and understand: itis already hard enough for them to un-derstand proofs; asking them to figureout where the proof starts and ends with-out clear textual markers is asking toomuch.
The second crucial factor is whether thebook is “open” or “closed.” What I meanis this: Does the book hint at the gloriesand mysteries of number theory, or doesit simply try to do a good job of present-ing the subject without pointing to fur-ther questions? I can see arguments for
both approaches. A “closed” book cangive students a satisfying feeling of hav-ing mastered something, for example. ButI have always preferred an “open” stylethat constantly hints at deeper questions.In number theory, this is particularly cru-cial in the treatment of quadratic reci-procity, perhaps the biggest theorem inthe elementary course. The quadraticreciprocity theorem can be presented insuch a way that the student gets no hintof why it is important (the most com-monly used proof is not helpful). I wantthe author to work at opening up hori-zons, and particularly so when it comesto the really deep results.
In the end, my choice is A Friendly Intro-duction to Number Theory, by Joseph H.Silverman, a book that works hard to beapproachable. Its one fault is the fact thatit doesn’t include a proof of quadraticreciprocity. But I can supply that.Silverman does a great job of exactlythose things I care about: his book isreadable; it makes students aware of therole of both experimentation and proof;it includes many pointers to deeper ques-tions and even to open questions. Eventhe jokes are the sort that I would make!
No matter how much I may like a book,the real test happens with real studentsin a real classroom. My impression is thatSilverman’s book does what I want it todo. Students can read the book and useit as a complement to what happens inclass. (I tell students early on that it is notmy plan to transcribe the textbook on theblackboard!) I don’t come anywhere nearto covering all the material in the book,but that is to be expected.
The reader might object that I cannotpossibly have looked at all the numbertheory textbooks on offer. The readerwould be right. Life is too short. It’sperfectly possible that I’ve completelymissed some wonderful book. Perhapsone of my readers will let me know aboutit.
What’s the Best Textbook is the overalltitle for a series of articles discussing text-books for mathematics courses. If you’d liketo contribute an article (even one contest-ing the conclusions of this article), pleasecontact the editor at [email protected].
What’s the Best Textbook?—Elementary
Number Theory
By Fernando Q. Gouvêa
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