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HISTORY OF MATHEMATICIAN
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BIOGRAPHYThough his exploits in the field of geometry,
science, and physics are widely famous, not
much is known about his personal life, as all
records have been lost. He was so much in
love with geometry and his inventions that
the last words he uttered were "Do not
disturb my circles."
He was killed in the Second Punic War by a
Roman soldier against the wishes of General
Marcellus. Plutarch writes that Archimedeswas contemplating a mathematical diagram
at the time of his death. His tomb was
engraved with the figure of a sphere andcylinder as per his wish.
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INVENTIONS
In the field of mathematics, Archimedes produced severaltheorems that became widely known throughout the world.He is credited with producing some of the principles ofcalculus long before Newton and Leibniz. He worked outways of squaring the circle and computing areas of severalcurved regions. His interest in mechanics is credited with
influencing his mathematical reasoning, which he used indevising new mathematical theorems. He proved that thesurface area and volume of a sphere are two-thirds that of itscircumscribing cylinder.
He is credited with the invention of Archimedes screw or screwpump, which is a device used to raise the level of water froma lower area to a higher elevation. He is known for theformulation of Archimedes' principle, a hydrostatic principlestating that an object in any liquid is buoyed by force equalto the weight of fluid it displaces. Legend has it that hediscovered the principle of buoyancy while taking bath and
following the discovery, he ran naked shouting "Eureka,Eureka," meaning I have found it.
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Using the method of exhaustion, he was able toaddress irrational numbers, such as square rootsand Pi. He showed how to calculate areas andtangents. His mastery of applied mathematics
reflects from his work on the Archimedes screw.
From his invention of war machines, such asparabolic mirrors, Archimedes claw and death rayand complex lever systems, shows that he playedan important role in guarding Syracuse against the
siege laid by Romans. Though he could not saveSyracuse from being captured by General MarcusClaudius Marcellus and his Roman forces in 212B.C., his war machines might have delayed thecapture. Archimedes himself was killed when thecity was captured by the Romans.
Undoubtedly, Archimedes was one of the mostbrilliant minds of all times. His contributions in thefield of geometry, science, and physics trulyreflect his genius. He wrote many treatises, butonly a few would survive the Middle Ages. Still his
work and fame live on.
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BACKGROUND
Charles Babbage was born in London, England December 26,
1791. Babbage suffered from many childhood illnesses,
which forced his family to send him to a clergy operated
school for special care.
Babbage had the advantage of a wealthy father that wished to
further his education. A stint at the Academy at Forty Hills
in Middlesex began the process and created the interest in
Mathematics. Babbage showed considerable talent inMathematics, but his disdain for the Classics meant that
more schooling and tutoring at home would be required
before Babbage would be ready for entry to Cambridge.
Babbage enjoyed reading many of the major works in
math and showed a solid understanding of what theories
and ideas had validity. As an undergraduate, Babbage
setup a society to critique the works of the Frenchmathematician, Lacroix, on the subject of differential and
integral calculus. Finding Lacroix's work a masterpiece and
showing the good sense to admit so, Babbage was asked to
setup a Analytical Society that was composed of
Cambridge undergraduates.
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CONTRIBUTIONS
Written Works:
A Comparative View of the Various Institutions for the
Assurance of Lives (1826)
Table of Logarithms of the Natural Numbers from 1 to 108,
000 (1827)
Reflections on the Decline of Science in England (1830)On the Economy of Machinery and Manufactures (1832)
Ninth Bridgewater Treatise (1837)
Passages from the Life of a Philosopher (1864)
Famous Quote:
"The whole of the developments and operations of analysis
are now capable of being executed by machinery. ... Assoon as an Analytical Engine exists, it will necessarily
guide the future course of science."
---Excerpt from the Life of a Philosopher
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Ren Descartes was born on March 31, 1596 in a village in Touraine,
France, which is now called La Haye-Descartes. His mother died shortly
after he was born (thirteen months). About 1606, Ren entered the
Jesuit college of La Fleche, in which a relative of his, Father Charlet, atheologian would watch out for him. Because of his delicate health,
Descartes was allowed to spend mornings in bed, meditating, reading,
and writing -a habit he maintained for most of his life.
He left La Fleche, because he was more confused about knowledge, and
he did not get his thirst for knowledge fulfilled. He then studied at theUniversity of Poitiers in 1615-16, earning a bachelor's degree and a
licentiate in law there.
At the age of twenty-two he left Paris and join the army of Prince Maurice
of Nassau. In the next year he was transferred to the army of
Maximailian. Duke ofB
avaria.B
ut in the night of November 10, 1619,he had a series of three dreams, that he interpreted as a message from
God tell him to devote his life to the rational quest for certain truth.
After ending his voluntary military service he went back to Paris.
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The social life in Paris was too distracting, so he moved to Holland in
1628. He lived in Holland until 1649. During this time, he avoided
reading any scholastic texts.
He wrote a couple of works in Holland, but when he heard of the
Inquisition condemning Galileo to death for his thoughts, as well as,
other thinkers, he decided to suppress his works.
In late 1604, Descartes' daughter, though he was never married, and father
died.
Descartes' philosophy became famous during the last decade of his life.
Descartes was later accused of heresy at the University of Leyden and
wrote a letter of self-defense to its trustees in 1647. He feared that he
might be arrested and killed, like Galileo, but that never happened.
In around 1648, Queen Christina of Sweden invited him to come to her
court to instruct her in philosophy. Despite his cautious reluctance,Descartes accepted her invitation. She sent an admiral with a warship
to carry him to Sweden, and Descartes left for Stockholm in September
of 1649. This was the costliest mistake of his life.
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German mathematician who is sometimes called the "prince ofmathematics." He was a prodigious child, at the age of threeinforming his father of an arithmetical error in a complicatedpayroll calculation and stating the correct answer. In school,when his teacher gave the problem of summing the integers
from 1 to 100 (an arithmetic series ) to his students to keepthem busy, Gauss immediately wrote down the correctanswer 5050 on his slate. At age 19, Gauss demonstrated amethod for constructing a heptadecagon using onlya straightedge and compass which had eluded the Greeks.(The explicit construction of the heptadecagon wasaccomplished around 1800 by Erchinger.) Gauss also showedthat only regular polygons of a certain number of sides
could be in that manner (a heptagon, for example, couldnot be constructed.) Gauss proved the fundamental theoremof algebra, which states that every polynomial has a rootof the form a+bi. In fact, he gave four different proofs, thefirst of which appeared in his dissertation. In 1801, he provedthe fundamental theorem of arithmetic, which states thatevery natural number can be represented asthe product ofprimes in only one way. At age 24, Gauss
published one of the most brilliant achievements inmathematics, Disquisitiones Arithmeticae (1801). In it, Gausssystematized the study ofnumber theory (properties ofthe integers ). Gauss proved that every number is the sum ofat most threetriangular numbers and developedthe algebra ofcongruences.
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n 1801, Gauss developed the method ofleast squares fitting, 10 yearsbeforeLegendre, but did not publish it. The method enabled him to calculatethe orbit of the asteroid Ceres, which had been discovered byPiazzi from
only three observations. However, after his independentdiscovery,Legendre accused Gauss of plagiarism. Gauss published hismonumental treatise on celestial mechanics Theoria Motus in 1806. He becameinterested in the compass through surveying and developed the magnetometerand, withWilhelm Weber measured the intensity of magnetic forces.WithWeber, he also built the first successful telegraph. Gauss is reported to
have said "There have been only three epoch-makingmathematicians:Archimedes, Newton and Eisenstein" (Boyer 1968, p. 553). Mosthistorians are puzzled by the inclusion of Eisenstein in the same class as theother two. There is also a story that in 1807 he was interrupted in the middle ofa problem and told that his wife was dying. He is purported to have said, "Tellher to wait a moment 'til I'm through" (Asimov 1972, p. 280). Gauss arrived atimportant results on the parallel postulate, but failed to publish them. Creditfor the discovery ofnon-Euclidean geometry therefore went toJanosBolyai andLobachevsky. However, he did publish his seminal workon differential geometry in Disquisitiones circa superticiescurvas. The Gaussian curvature (or "second" curvature) is named for him. Healso discovered the Cauchy integral theorem
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G. W. Leibniz was one of the most important thinkers of his time. Hiscontributions to such diverse fields as philosophy, linguistics, and history areundeniable. And yet although he became acquainted quite late in his life with themathematical achieveme nts of his generation, it will always be his innovations inthis field that put him to the forefront of the enlightened thinkers of his era.These achievements are especially remarkable considering that Leibniz often
treated the subject as a corollary to his studies in other fields, notably logic,
philosophy, and even law. It was precisely for this reason that Leibniz had somuch success in the field, in that he was unhampered by much of the dogma thatmight have hindered its progress. Leibniz viewed the subject through his ownlens, interpreting the mathematical issues differently from his colleagues. Perhapsit was the distance from which he viewed the field that allowed Leibniz to besuch an innovator in the rapidly changing subject. He gathered and pr ocessed asmuch contem-porary mathematics as possible, reassessed it, and through his
innovative system of notation, repackaged it as a superior product. It wasLeibniz's algebraic symbolism that freed the subject from much of its rigid verbalstructure, allowing it to develop at an even faster rate. Leibniz's modernmathematical notation probably represents his greatest single contribution tomathematics. G.W. Leibniz is generally considered, along with Isaac Newton, as acofounder of the differential and integral Calculus.
INTRODUCTION
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Mathematicians had developed algebraic methods for finding areas and volumes of a great variety
geometric figures. This marks one of the greatest developments in m athematics since the Greeks be
using limits to approximate areas and then find the value of p. It was Cavalieri (1598-1647) who fir
introduced the concept of "indivisible magnitudes" in his Geometry of Indivisibles to study areas un
curves of the form:
y = xn (n(1)
At roughly the same time Descartes published his La Giomitrie, in which he showed, somewhat obs
how to use Viite's algebra to describe curves and obtain an algebraic analysis of geometric problems
319-331] The work of these two mathematici ans would have an especially great influence on the
development of Leibniz's new calculus. [4, X]
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Newton, Sir Isaac (1642-1727), Englishnatural philosopher, generally regardedas the most original and influentialtheorist in the history of science. Inaddition to his invention of theinfinitesimal calculus and a new theoryof light and color, Newtontransformed the structure of physicalscience with his three laws of motion
and the law of universal gravitation. Asthe keystone of the scientificrevolution of the 17th century,Newton's work combined thecontributions of Copernicus, Kepler,Galileo, Descartes, and others into a
new and powerful synthesis. Threecenturies later the resulting structure- classical mechanics - continues to bea useful but no less elegant monumentto his genius.
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Life & Character - Isaac Newton was born prematurely on Christmas day
1642 (4 January 1643, New Style) in Woolsthorpe, a hamlet near
Grantham in Lincolnshire. The posthumous son of an illiterate yeoman
(also named Isaac), the fatherless infant was small enough at birth to fit'into a quartpot.' When he was barely three years old Newton's
mother, Hanna (Ayscough), placed her first born with his grandmother
in order to remarry and raise a second family with Barnabas Smith, a
wealthy rector from nearby North Witham. Much has been made of
Newton's posthumous birth, his prolonged separation from his mother,and his unrivaled hatred of his stepfather. Until Hanna returned to
Woolsthorpe in 1653 after the death of her second husband, Newton
was denied his mother's attention, a possible clue to his complex
character. Newton's childhood was anything but happy, and
throughout his life he verged on emotional collapse, occasionally
falling into violent and vindictive attacks against friend and foe alike.
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Mathematics - The origin of Newton's interest in mathematics can be traced to his
undergraduate days at Cambridge. Here Newton became acquainted with a number of
contemporary works, including an edition of Descartes Gomtrie, John Wallis' Arithmetica
infinitorum, and other works by prominent mathematicians. But between 1664 and his return
to Cambridge after the plague, Newton made fundamental contributions to analytic
geometry, algebra, and calculus. Specifically, he discovered the binomial theorem, newmethods for expansion of infinite series, and his 'direct and inverse method of fluxions.' As the
term implies, fluxional calculus is a method for treating changing or flowing quantities. Hence,
a 'fluxion' represents the rate of change of a 'fluent'--a continuously changing or flowing
quantity, such as distance, area, or length. In essence, fluxions were the first words in a new
language of physics.
Scientific Achievements
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Pythagoras of Samos was an Ionian
(Greek) philosopher and founder of the
religious movement called
Pythagoreanism. He is often revered as
a great mathematician, mystic andscientist; however some have
questioned the scope of his
contributions to mathematics or natural
philosophy. We do know that
Pythagoras and his students believed
that everything was related tomathematics and that numbers were
the ultimate reality and, throughmathematics, everything could be
predicted and measured in rhythmic
patterns or cycles. The Pythagoreans
were musicians as well asmathematicians. Pythagoras wanted to
improve the music of his day, which hebelieved was not harmonious enough
and was too hectic.