Years Ago David E. Rowe, Editor

Inventing Traditionin 16th- and 17th-CenturyMathematicalSciences: Abrahamas Teacherof Arithmetic andAstronomyVOLKER R. REMMERT

Years Ago features essays by historians and

mathematicians that take us back in time. Whether

addressing special topics or general trends, individual

mathematicians or ‘‘schools’’ (as in schools of fish), the

idea is always the same: to shed new light on the

mathematics of the past. Submissions are welcome.

� Submissions should be uploaded to http://tmin.edmgr.com

or sent directly to David E. Rowe,

e-mail: rowe@mathematik.uni-mainz.de

IIn the history of science, the period between thepublication of Nicolaus Copernicus’s famous De

revolutionibus orbium coelestium (1543) and IsaacNewton’s epoch-making Philosophiae naturalis principia

mathematica (1687) is known as the Scientific Revolution.Indeed, this period was full of spectacular speculations andpragmatic inventions that accompanied stunning develop-ments in the mathematical sciences ranging from thecalculus and logarithms to telescopes and microscopes,air pumps and barometers, and the conception of aninfinite universe. The mathematical sciences proper wereconceived of as a field of knowledge comprised of twopure parts—arithmetic and geometry (scientiae mathema-

ticae purae)—together with many mixed parts (scientiaemathematicae mixtae), which often had a clear practicalbent, ranging from the traditional disciplines of astronomyand music to architecture, fortification, geography, hy-drology, navigation, and so forth.

Looking back, this period seems to reflect a sense ofglamour, and it has sometimes been seen as a kind ofGolden Age. However, as is so often the case, all thatglitters is not gold, and the practitioners of the mathema-tical sciences were well aware of a variety of means forpromoting their work. Indeed, this was an age whenmathematicians constantly had to argue for the relevance oftheir work and research.1 Yet the context for such argu-ments during the Scientific Revolution was very differentfrom what it is today. Bacon’s famous motto that ‘‘knowl-edge is power’’ may sound convincing to us, but in fact theLondon Royal Society had no means to finance scientificresearch. Nor was novelty alone the type of argument thatwas likely to persuade those royal patrons of the arts andsciences who were most likely to promote such work.Within this context, those who sought such support werelikely to appeal to arguments that might exalt the reputa-tion of a monarch and his court, where interest in the oldwas often at least as important as any new invention,however spectacular.

Thus a typical strategy for those who sought to legit-imize the mathematical sciences was to make use ofreferences to the past, in particular classical antiquity. Thistype of argument, highlighting the long-accepted role ofmathematics in the ancient world, was part of a process thatcan best be understood as the invention of traditions for themathematical sciences.2 Had not Atlas been the first

1Regarding this, see, e.g., Annette Imhausen/Volker R. Remmert: The Oration on the Dignity and the Usefulness of the Mathematical Sciences of Martinus Hortensius

(Amsterdam, 1634): Text, Translation and Commentary, in: History of Universities 21(2006), 71-150.2Regarding this context, see Robert Goulding: Defending Hypatia. Ramus, Saville, and the Renaissance Rediscovery of Mathematical History, Dordrecht, et al. 2010;

Volker R. Remmert: Picturing the Scientific Revolution: Title Engravings in Early Modern Scientific Publications, Philadelphia 2011; Spelda, Daniel: The Search for

Antediluvian Astronomy: Sixteenth- and Seventeenth-Century Astronomers’ Conceptions of the Origins of Science, in: Journal for the History of Astronomy 44(2013),

337-362.

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astronomer and Hercules his first disciple?3 What aboutArchimedes, the eminent mathematician and engineer,who had, according to legend, single-handedly defendedSyracuse against the Romans?4 And what about Abraham,the biblical patriarch and ‘‘planter of mathematics inEgypt’’?5 The role of the first two, and in particular ofArchimedes, in this triple-A strategy has been closelystudied by historians of science, but Abraham has only justbegun to make his way back into the story. In fact, lookingbeyond the mathematical sciences one might even add afourth A: Adam, the first gardener, who towers as afounding father over many a discipline, such as alchemyand botany.6 However, in what follows I will concentrateon Abraham and his importance for the invention of tra-dition as a means of bolstering the mathematical sciences inthe 16th and 17th centuries.

The conception of Abraham as the first astronomer isbased on Genesis 15, where it is reported that Abraham,well advanced in age, had his doubts that he would everhave children. In verse 5 we read: ‘‘He [God] tookAbraham outside and said, ‘Look up into the sky, andcount the stars if you can. So many shall your descendantsbe.’’’ Through the centuries this passage led to the notionthat Abraham had been ‘‘a man wise and skilful in as-tronomy,’’ as the Jesuit exegete Benito Pereira put it in hiscommentary on Genesis in 1590 (viro sapienti & astrolo-

giae perito).7

This tradition of seeing Abraham as the founder of as-tronomy originates with the Hellenistic Jewish philosopherPhilo of Alexandria (ca. 20 BCE to 50 CE). In his biography ofAbraham (On Abraham 71), Philo mentioned thatAbraham, who had learned astronomy from the Babyloni-ans, was later urged by God to ‘‘dismiss the rangers of theheavens and the science of Chaldea [i.e., astronomy], anddepart for a short time from the greatest of cities, this world,to the lesser.’’ By doing so, he was told that he would ‘‘bebetter able to apprehend the overseer of the All.’’8 How-ever, the ensuing events, during which he droppedastronomy after migrating to Egypt, did not imply thatAbraham had lost his astronomical expertise. Indeed welearn from the Judean Antiquities (I, 167f) of the scholarFlavius Josephus (ca. 37/38-100), whose works werewidely read in the Renaissance, that Abraham continued toteach the subject: ‘‘having been admired by them [the

Egyptians] as an extremely intelligent man and gifted notonly in understanding but also in persuading by his wordswith regard to whatever he would undertake to teach, hepleased them with arithmetic and transmitted to them thelore concerning astronomy. For before the arrival ofAbraham the Egyptians were ignorant of these. For thesematters reached Egypt from the Babylonians, whence theycame also to the Greeks.’’9

This view of the history of astronomy and arithmetic wasvery prominent in the 16th and 17th centuries; in his 1574inaugural lecture in Copenhagen, the illustrious astronomerTycho Brahe celebrated Abraham as the first astronomer.There he also referred to the origins of astronomy inantediluvian times based on another well-known storyfrom Flavius’s Judean Antiquities (I, 69f), where he writesthat Adam and his son Seth had ‘‘discovered the sciencewith regard to the heavenly bodies and their orderly ar-rangement. And in order that humanity might not lose theirdiscoveries or perish before they came to be known, Adamhaving predicted that there would be an extermination ofthe universe, at one time by a violent fire and at anothertime by a force with an abundance of water, they made twopillars, one of brick and the other of stones and inscribedtheir findings on both […].’’10

During the Middle Ages, specific disciplines wereascribed to the two pillars: geometry and astronomy,which were often illustrated in manuscripts (Fig. 1). Again,this had an important impact on early modern storiesabout the origins of geometry and astronomy. For instance,the French humanist and avid propagator of the mathe-matical sciences, Pierre de la Ramee (Petrus Ramus),bestowed a place of honour on both Adam and Abrahamin recounting the history of astronomy, arithmetic, andgeometry.11 A century later, the chemist Robert Boyle alsosympathized with the view that Seth had saved astro-nomical knowledge, whereas Abraham had introducedastronomy among the Egyptians.12 This list of early mod-ern textual references to Abraham and Adam/Seth asbiblical fathers of arithmetic, astronomy, and geometrycould easily be extended, but these allusions to the mythicpast were just as prominent in the world of imagery. Iwould like to illustrate this by way of three examples.

In 1565 the Dutch engraver Cornelis Cort (1533-1578), inline with contemporaneous fashion, produced a cycle of

3Cf. Remmert: Picturing the Scientific Revolution, chapter 5: The Visual Legitimization of Astronomy during the 16th and 17th Centuries: Atlas, Hercules and Tycho’s

Nose.4Cf. Mary Jaeger: Archimedes and the Roman Imagination, Ann Arbor 2008.5Cf. Nicholas Popper: ‘‘Abraham, Planter of Mathematics’’: Histories of Mathematics and Astrology in Early Modern Europe, in: Journal of the History of Ideas 67(2006),

87-106.6Cf. Raphael Patai: The Jewish Alchemists. A History and Source Book, Princeton 1994, 18f.7Benito Pereira: Commentariorum et disputationum in Genesim, 2 vols., Ingolstadt 1590, vol. I, 290.8Philo: On Abraham, in: Philo with an English translation by F. H. Colson, 10 vols. (Loeb Classical Library), London/Cambridge (Mass.), 1929-1962, vol. VI, 1-135, on 41.9Flavius Josephus: Translation and Commentary. Edited by Steve Mason. Volume III: Judean Antiquities 1-4. Translation and Commentary by Louis H. Feldman,

Leiden/Boston/Cologne 2000, 63f. Slightly adapted translation.10Ibid., 24f.11Pierre de la Ramee: Scholarum mathematicarum libri unus et triginta, Basle 1569, 2f.12Robert Boyle: Of the Usefulness of Natural Philosophy, in: Works, 6 vols., London 1772, vol. II, 5-201, on 10.

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Figure 1. Chronica regia coloniensis: Adam and Seth with the two columns representing geometry and astronomy, second half of

the 12th century (Herzog August Bibliothek Wolfenbuttel Cod. Guelf. 74.3 Aug. 2�).

Figure 2. Cornelis Cort: Arithmetic, 1565 (Exhibition catalogue: Cornelis Cort. Accomplished plate-cutter from Hoorn in Holland,

edited by Manfred Sellink, Museum Boymans-van Beunigen, Rotterdam 1994, 129).

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the seven liberal arts (following the design of Frans Floris[1517-1570]). His representation of arithmetic includes anobvious reference to Abraham as founder and teacher ofarithmetic (Fig. 2). One might conjecture that the beardedold man in the middle of the scene represents Abraham,because his stylus is reminiscent of a shepherd’s or a pa-triarch’s crook. This interpretation, however, gains furtherplausibility when we take note of the two books in theforeground lying in front of the table—works written byAbraham and Pythagoras.

Astronomy takes center stage in a painting by AntonioZanchi (1631-1722), well known for his works in the Scuoladi San Rocco in Venice (in particular the Plague of Venice

from 1666). The painting is mentioned as Abraham teaches

astronomy to the Egyptians in 1697 (‘‘un’ Abraamo, cheinsegna l’Astrologia agli Egittij’’) (Fig. 3).13 Attentive spec-tators surround Abraham, who is on the left withmathematical instruments and papers at his feet as hemeasures a celestial globe—thus teaching, in a certainmanner, astronomy to the Egyptians.

A more hidden reference to Abraham and Adam/Sethcan be found on the intricate astronomical clock built forLandgrave William IV of Hesse-Kassel (1532-1592), the‘‘Ptolemy of Kassel,’’ in 1590/1591. William IV’s courtmathematician and clockmaker, Jost Burgi, a multitalentedSwiss craftsman who also happens to have been theco-inventor of logarithms, constructed this device. Thisclock is rather small, based on a square of ca. 6 inches andbarely 4.5 inches high (Fig. 4). Historian of science KarstenGaulke has analysed the iconography.14 Each of the foursides illustrates two episodes from the history of geometryand astronomy, and they span a period from ancient times

to the 16th century. These four panels depict, respectively,three patriarchs and Thales (Fig. 5); Euclid andArchimedes; Hipparchus and Ptolemy; and the medievalpatron of astronomy, King Alfonso of Castile, and Coper-nicus. Although it is obvious that Hipparchus and Ptolemy,and King Alfonso and Copernicus, stand for a tradition inastronomy, whereas Thales, Euclid, and Archimedes standfor the tradition in geometry, and that both traditions reachback to Greek antiquity, the interpretation of the threepatriarchs and the two columns is not immediately obvious.There is a consensus of opinion that this image showsAbraham instructing the Egyptians in astronomy. However,I suggest that two different but overlapping stories aboutthe origins of astronomy and geometry are depicted here.Thus the central place of the three patriarchs who wereknown to be experts in astronomy and mathematics issuggested: we see Abraham, the instructor of the Egyptians,whereas Adam and Seth stand for their pillars representingastronomical and geometrical knowledge. The essentialpoint is that the reference to the origins of the mathematicalsciences in ancient times is twofold: to Greek antiquity aswell as to the Old Testament. What more could one wish

Figure 3. Antonio Zanchi: Abramo insegna l’astrologia agli

Egizi (Pietro Zampetti: Antonio Zanchi, Bergamo 1988, 448).

Figure 4. Jost Burgi: Equation clock, 1591 (Karsten Gaulke:

Perfect in Every Sense: Scientific Iconography on an Equation

Clock by Jost Burgi and the Self-Understanding of the

Astronomers at the Kassel Court in the Late 1580s, in: Nuncius.

Journal of the Material and Visual History of Science 30 [2015],

37-74, on 39).

13Pietro Zampetti: Antonio Zanchi, Bergamo 1988, 562.14Karsten Gaulke: Perfect in Every Sense: Scientific Iconography on an Equation Clock by Jost Burgi and the Self-Understanding of the Astronomers at the Kassel

Court in the Late 1580s, in: Nuncius. Journal of the Material and Visual History of Science 30(2015), 37-74.

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for in order to to argue for the relevance and nobility of themathematical sciences?

Interdisciplinary Centre for Science and Technology Studies

Bergische Universitat Wuppertal

Gaußstraße 20

D-42097 Wuppertal

Germany

e-mail: remmert@uni-wuppertal.de

Figure 5. Jost Burgi: Equation clock, 1591, detail: Patriarchs

(Karsten Gaulke: Perfect in Every Sense: Scientific Iconography

on an Equation Clock by Jost Burgi and the Self-Understand-

ing of the Astronomers at the Kassel Court in the Late 1580s, in:

Nuncius. Journal of the Material and Visual History of Science

30 [2015], 37-74, on 50).

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The Mathematical Intelligencer ISSN 0343-6993Volume 37Number 3 Math Intelligencer (2015) 37:55-59DOI 10.1007/s00283-015-9562-9

Inventing Tradition in 16th- and 17th-Century Mathematical Sciences: Abrahamas Teacher of Arithmetic and Astronomy

Volker R. Remmert