Abraham, Planter of Mathematics: Histories of Mathematics and Astrology in Early Modern Europe

"Abraham, Planter of Mathematics": Histories of Mathematicsand Astrology in Early Modern Europe

Nicholas Popper

Journal of the History of Ideas, Volume 67, Number 1, January 2006,pp. 87-106 (Article)

Published by University of Pennsylvania PressDOI: 10.1353/jhi.2006.0010

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‘‘Abraham, Planter of Mathematics’’:Histories of Mathematics and Astrology in

Early Modern Europe

Nicholas Popper

Francis Bacon’s 1605 Advancement of Learning proposed to dedicateeJames I a massive reorganization of the institutions, goals, and methods ofgenerating and transmitting knowledge. The numerous defects crippling thecontemporary educational regime, Bacon claimed, should be addressed bystrengthening emphasis on philosophy and natural knowledge. To that end,university positions were to be created devoted to ‘‘Artes and Sciences atlarge,’’ rather than to the professions. High salaries would render lecturers‘‘able and sufficient,’’ undistracted from their task. Most famously, he ar-gued that teaching of the ‘‘operatiue studie of many Scyences’’ should in-volve sophisticated technical education. The study of natural philosophydemanded not only books, but globes, astrolabes, and other ‘‘instrumen-tals.’’ Most significantly, yielding reliable and meaningful knowledge fromexperiential gleanings required a rigorous system of deductive reasoning.

The legacy of this colossal proposal has earned Bacon honored statusas devisor of the scientific method.1 But Bacon’s educational reform extend-

I would like to thank Lauren Kassell, Robert Goulding, James Byrne, Darrel Rutkin, AmyHaley, Anthony Grafton, Simon Schaffer, and Walter Stephens for their invaluable com-ments, suggestions and improvements. The paper was given in a slightly different formfrom the 2004 History of Science Society Meeting version at the 2004 Thomas HarriotSeminar, and I thank the participants of both for useful questions and suggestions.1 Francis Bacon, The tvvoo bookes of Francis Bacon. Of the proficience and aduancementof learning, diuine and humane (London, 1605), Aa.1.r-Aa.4.v. The history of science

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ed beyond the methods of producing and transmitting knowledge. To facili-tate more efficient ‘‘vse and administration’’ of the knowledge produced byhis system, he also demanded a searching examination of the history oflearning. This history would provide a mirror enabling his contemporariesto deploy the fruits of his method, by considering how learning in the pasthad been used successfully or ill-advisedly. Producing this history was theambition of the Advancement, for he explained: ‘‘no man hath propoundedto himselfe the generall state of learning to bee described and representedfrom age to age, as many have done the works of Nature, & the State civileand Ecclesiastical.’’ He continued:

And yet I am not ignorant that in divers particular sciences, as ofthe Iurisconsults, the Mathematicians, the Rhetoricians, the Phi-losophers, there are set down some smal memorials of theSchooles, Authors, and Bookes: and so likewise some barren rela-tions touching the Invention of Arts, or usages. But a iust story oflearning, containing the Antiquities and Originalls of Knowl-edges, & their Sects; their Inventions, their Traditions; their diverseAdministrations and Managings; their Flourishings, their Opposi-tions, Decayes, Depressions, Oblivions, Removes, with the causes,and occasions of them, and all other events concerning learning,throughout the ages of the world; I may truly affirme to bewanting.2

Bacon thus positioned himself not only as a Father of Modern Science, butalso a Father of the History of Science.

Following Bacon’s suggestion, I will examine the ‘‘small memorials’’of the history of mathematics—and particularly the mathematical art ofastrology—in the sixteenth and seventeenth centuries. My conclusion, how-ever, will not bear out Bacon’s claims. Despite his frustration, Bacon wasonly one of many early modern scholars appraising the role of mathematicswithin history. And he devoted less energy than others to mapping its ori-gins and tracing its transmissions between communities. In fact, Bacon’s1605 proposal for a history of mathematics was already out-of-date. Dis-

literature on Bacon is immense. In this context see Paolo Rossi, Francis Bacon: FromMagic to Science, trans. Sasha Rabinovitch (Chicago: University of Chicago Press, 1968);and Wilhelm Schmidt-Biggemann, Topica universalis: eine Modellgeschichte humanist-ischer und barocker Wissenschaft (Hamburg: Meiner, 1983), 212–25.2 Bacon, Bb.3.v.

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Popper ✦ Histories of Science in Early Modern Europe

cussions of the history of mathematics had been rife on the continent andin England throughout the previous century.3

The evidence that Renaissance scholars inherited was sprawling andinconclusive. Several genealogies for mathematics could be found withinclassical Greek, Latin, and patristic references. One lineage claimed mathe-matics began in ancient Assyria, where the priestly caste, the Chaldeans,practiced a form of mathematics that seemed a corrupt admixture of phi-losophy, medicine, and religion, and relied heavily on observation of theheavens. Other scholars traced the origins to Egypt, claiming that the fielddeveloped to survey lands frequently flooded by the Nile. The real problemfor ancient, late antique, and medieval scholars had not been the origins ofmathematics, but what exactly mathematics were. For some, the term strict-ly referred to the quadrivium: geometry, arithmetic, astronomy, and music.But for others, mathematics’ origins amongst the Egyptians or Chaldeansinextricably linked it to forms of astrological divination, augury, and necro-mancy that were unsavory to both Latin and Christian traditions. Mathe-matici were included alongside ghastly lists of Magi, Brahmins, Aruspices,Genethliaci, and other diabolic practitioners of idolatrous magic. Thesemight or might not be distinguished from mathematici such as Pythagorasand Euclid, who were considered philosophers, or from useful practitionerssuch as Archimedes. The term itself was a source of unending confusion. Amathematician in Aristotle’s time, as later generations acknowledged, didgeometry and arithmetic; but, by late antiquity, Augustine and Jeromecould complain that nativity-readers were vulgarly called mathematici. Thisconfusion and distrust spread in turn to later historical understandings of

3 There are few studies devoted to the histories early modern scholars composed for vari-ous sciences. By far the most important is Nicholas Jardine’s Birth of History and Philoso-phy of Science: Kepler’s A Defence of Tycho against Ursus, with Essays on its Provenanceand Significance (Cambridge: Cambridge University Press, 1984). Jardine focuses onKepler, who was more central to the Scientific Revolution than any of the individuals inthis article. Kepler’s history was distinct in its discussion of, and commitment to, a historyof technical advancement. But to attribute the origins of the history of science to hiswork, as Jardine does, requires an understanding of the discipline as fundamentally com-mitted to a progressive narrative. See also Peter Dear, Discipline and Experience: TheMathematical Way in the Scientific Revolution (Chicago: University of Chicago Press,1995), 93–123; Anthony Grafton, ‘‘From Apotheosis to Analysis: Some Late RenaissanceHistories of Classical Astronomy,’’ in History and the Disciplines: The Reclassification ofKnowledge in Early Modern Europe, ed. Donald R. Kelley (Rochester, N.Y.: Universityof Rochester Press, 1997), 261–76. D.P. Walker’s, The Ancient Theology: Studies inChristian Platonism from the Fifteenth to the Eighteenth Century (London: Duckworth,1972) is the classic work on the power of genealogies of knowledge in early modernEurope.

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mathematics, and justifies considering the Renaissance histories of magic,mathematics, astrology, and astronomy, as deeply interwoven.4

Renaissance scholars devoted serious attention to delineating the vari-ous kinds of mathematics. To help distinguish the licit from illicit, the ques-tion of origins was given a new priority in the years leading up to 1500.The debate originated with Pico della Mirandola’s considerations of theorthodoxy of astrology, that most controversial of mathematical arts.Against the backdrop of a late Quattrocentro Italy bursting with astrologi-cal prediction, Pico set the grounds for debate in two considerations of thehistory of magic.5 The first, his Apologia, defended a rigorously narrowrange of pious magic. This tract answered the papal condemnation oftwelve of his famous 900 theses.6 In defense, he wrote, ‘‘I put forward magi-cal theorems, in which I show Magic to be twofold. One side is supportedby the work and authority of demons, and consists of things, by my faith,execrable and portentous; the other is nothing other, when it is well ex-plored, than the absolute consummation of natural philosophy.’’7 Pico wenton to claim that natural magic was necessary for faith, since it alone al-lowed one to distinguish miracles from simple extraordinary events. Picodid not, however, offer much support for modern practitioners of the magi-cal arts. With few caveats, he defended the thesis that, ‘‘All the magic,

4 For classical and late antique attitudes towards the disciplines under consideration here,see esp. Fritz Graf, Magic in the Ancient World, trans. Franklin Philip (Cambridge: Har-vard University Press, 1997), esp. 20–60. See also Jan N. Bremmer, ‘‘The Birth of theTerm ‘Magic’ ’’ in The Metamorphosis of Magic from Late Antiquity to the Early ModernPeriod, ed. Jan N. Bremmer and Jan R. Veenstra (Leuven: Peeters, 2002) 1–11 and PeterBrown, The Making of Late Antiquity (Cambridge: Harvard University Press, 1978),19–26.5 The classic studies of this context are Paola Zambelli (ed.), ‘‘Astrologi hallucinati’’: Starsand the End of the World in Luther’s Time (Berlin: W. de Gruyter, 1986); and OttaviaNiccoli, Prophecy and People in Renaissance Italy, trans. Lydia G. Cochrane (Princeton:Princeton University Press, 1990).6 See S.A. Farmer, Syncretism in the West: Pico’s 900 theses (1486): The Evolution ofTraditional, Religious, and Philosophical Systems: with Text, Translation, and Commen-tary (Phoenix: Medieval & Renaissance Texts & Studies, 1998).7 Pico della Mirandola, Opera Omnia (Basel, 1601), 80: ‘‘Proposuimus & magica theo-remata, in quibus duplicem esse Magiam significamus, quarum altera daemonum totaopere & authoritate constat, res medius fidius execranda & portentosa: altera nihil estaliud, cum bene exploratur, quam naturalis philosophiae absoluta consummatio.’’ Recentwork on Pico includes H. Darrel Rutkin, Astrology, Natural Philosophy and the Historyof Science, c. 1250–1700: Studies toward an Interpretation of Giovanni Pico della Miran-dola’s Disputationes adversus Astrologiam Divinatricem (Ph.D. Dissertation, IndianaUniversity, 2002), esp. 230–467, with considered discussion of the various traditions ofPico scholarship; and Steven Vanden Broecke, The Limits of Influence: Pico, Louvain,and the Crisis of Renaissance Astrology (Leiden: Brill, 2003), 55–81.

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which is in use amongst the moderns, and which the Church has rightlybanished, has no firmness, nor truth, nor support, because it is manipulatedby the first enemy of truth.’’8 In defining contemporary magic as diabolic,Pico suggested that a legitimate natural magic had been corrupted, lost, or,he suggested, enclosed within the ancient Jewish tradition of cabala—orallytransmitted and secret wisdom—that Pico firmly supported and to whichhe claimed unique access. Pico’s dismissals of modern astrology enabledhim to advertise himself as the lone point of entry to this alternative tradi-tion that would lead to the recovery of an unimaginably potent ancientknowledge.

Pico did not construct a thorough account of the fall of magic in hisApologia, but he did towards the end of his life in his Twelve Books AgainstDivinatory Astrology. Unpublished in Pico’s lifetime, this tract was com-piled from his remaining manuscripts and published in 1496 under the closesupervision of his nephew, Gianfrancesco. This younger scholar was notori-ously unsympathetic to the astrological arts and the publication cementedthe family anti-astrological reputation by comprehensively critiquing thephilosophical, theological, and rational grounds for astrological divina-tion.9 In the Twelfth Book, the elder Pico dismantled the historical datawith which proponents of astrology supported their claims. Two of hispoints were particularly effective. According to Cicero, the Chaldean as-trologers claimed to found their art on 470,000 years of observation. Sincethis claim set the beginnings of observation roughly 466,000 years beforeGod created the universe, Pico noted, it was extremely unlikely.10 FollowingPtolemy, the greatest ancient authority on both astronomy and astrology,he instead allotted relatively modern origins to astrology, an effective meansof diminishing its legitimacy. Second, Pico argued that astrology’s Chaldeanorigins did not indicate venerable antiquity. Rather the birth of astrologyformed a significant part of Babylon’s notorious corruption of true reli-gion.11 Pico’s devastating expose grounded astrological criticism for thenext century.

8 Pico, 113. ‘‘Tota magia, quae in usu est apud modernos, & quam merito exterminatEcclesia, nullam habet firmitatem, nullam veritatem, nullum firmamentum: quia pendetex manu hostium primae veritatis, potestatum harum tenebrarum, quae tenebras falsitatismalae dispositis intellectibus offendunt.’’9 See Anthony Grafton, Commerce with the Classics: Ancient Books and RenaissanceReaders (Ann Arbor: University of Michigan Press, 1997), 93–134; and Rutkin, 338–43.10 Pico, 483.11 See books 11 and 12 of Pico della Mirandola’s Disputationes adversus Astrologiamdivinatricem, esp. 11.2 at 483. For Abraham’s teaching, see 485.

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Pico’s critical genealogy of Chaldean magic was not universally accept-ed. In the last years of the fifteenth century, two substantial works chal-lenged Pico’s claims. The first came from Polydore Vergil. An arch-human-ist, Vergil argued with Erasmus over which of them had invented themodern genre of collections of sayings, and wrote a hefty history of En-gland that discredited Geoffrey of Monmouth.12 In his 1499 De inventori-bus rerum, Vergil devoted the eighteenth chapter of the first book to theorigin of mathematics. He began with the proposition, expressed most fa-mously by Proclus, that the Egyptians were the first to practice mathemat-ics. Vergil, however, did not subscribe to this theory. Instead, he turned tothe first-century Jewish general and historian, Flavius Josephus.13

According to Josephus, Adam received all knowledge available to man,wisdom he taught his son Seth. Seth’s progeny, Josephus wrote,

discovered the science of heavenly bodies and their orderly array.Moreover, to prevent their discoveries from being lost to mankindand perishing before they became known—Adam having predicteda destruction of the universe, at one time by a violent fire and atanother by a mighty deluge of water—they erected two pillars, oneof brick and the other of stone, and inscribed these discoveries onboth; so that, if the pillar of brick disappeared at the deluge, thatof stone would remain to teach men what was graven thereon andto inform them that they had also erected one of brick.

‘‘It exists to this day,’’ Josephus claimed, ‘‘in the land of Seiris.’’14 Vergilheld Josephus in the utmost respect, and he first referred to this passage toprove that the Hebrews had invented letters, despite Greek and Latin claimsto the contrary. He then used it to prove the Hebraic origins of mathemat-ics, and finally to trace the origins of astrology. Vergil also followed Jose-phus in his postdiluvian histories, claiming that the mathematical arts were

12 For Vergil, see Denys Hay, Polydore Vergil: Renaissance Historian and Man of Letters(Oxford: Clarendon Press, 1952); Brian Copenhaver, ‘‘The Historiography of Discoveryin the Renaissance: The Sources and Composition of Polydore Vergil’s De inventoribusrerum, 1–111,’’ Journal of the Warburg and Courtauld Institutes 41 (1978): 192–214;and Copenhaver’s introduction to Polydore Vergil: On Discovery, ed. and trans. Brian P.Copenhaver (Cambridge: Harvard University Press, 2002) vi-xxx.13 On Discovery, 147–49.14 Flavius Josephus, Jewish Antiquities, trans. H. St. J. Thackeray (Cambridge, Mass.:Loeb Classical Library, 1930), I.ii.68–71. For Josephus, and his later reputation, see Jose-phus, the Bible, and History, ed. Louis H. Feldman and Gohei Hata (Detroit: WayneState University Press, 1989).

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recovered in Assyria, and that the Jewish Patriarch Abraham, an Assyrian,transported them to Egypt 430 years later. Assuming that the ‘‘science ofheavenly bodies’’ required mathematics, Vergil yoked the history of star-gazing to the history of mathematics, and installed astrology within a sa-cred lineage opposed to Pico’s diabolic genealogy.15

Pico too had cited Josephus’s assertion that Abraham disseminatedknowledge in Egypt. But for Pico, this learning amounted only to the math-ematical observation of the heavens necessary to formulate a divine calen-dar; a form of licit, human knowledge similar to the interpretations of na-ture necessary for sailors, farmers, and physicians. Indeed, Pico claimed,idolatry and astrology had received a nefarious twin birth when the Chal-deans overextended this science, confusing celestial objects with divineentities. Both Pico and Vergil accepted astronomy—and therefore mathe-matics—as a practice of the ancient Hebrews, but Pico strenuously insistedthat all arts that attributed divine agency to natural objects were corrup-tions of this accepted, Hebraic knowledge. His critique pursued a reforma-tion of natural, non-revealed knowledge.

Vergil launched an extremely cautious challenge: he stated that astrolo-gy was extremely venerable, not revealed, and expressed doubts regardingits utility.16 The other response to Pico lacked any moderation. It came fromanother individual of immaculate humanist pedigree and possessed of afirm respect for and constant attention to Josephus. However, the Domini-can Giovanni Nanni, otherwise known as Annius of Viterbo, was not pos-sessed of a scrupulous moral fiber. Rather, he was blessed with a fanaticalconviction that the ancient Romans had derived from Etruscan stock, abelief he bulwarked through a series of forgeries and planted archaeologicalfinds.17

15 See On Discovery 139–47. For the references in Josephus, see I.viii.166–68. For themedieval readings of Seth’s Pillars, see Cora E. Lutz, ‘‘Remigius’ Ideas on the Originand the Classification of the Seven Liberal Arts,’’ Medievalia et humanistica 10 (1956):32–49.16 It should be noted that Vergil expressed caveats about astrology despite his genealogy:‘‘Such was the beginning of the art of astrology, which doubtless was devised simply tobefuddle sound minds’’ (On Discovery, 143). This runs contrary to his enthusiasm forletters, mathematics, and other arts that shared its genealogy.17 For Annius see Walter Stephens, ‘‘Berosus Chaldaeus: Counterfeit and Fictive Editorsof the Early Sixteenth Century’’ (Ph.D. Dissertation, Cornell University, 1979); parts ofwhich were integrated into his Giants in Those Days: Folklore, Ancient History, andNationalism (Lincoln: University of Nebraska Press, 1989); and his ‘‘Livres de haultegresse: Bibliographic Myth from Rabelais to Du Bartas,’’ MLN 120.1 Supplement (Janu-ary 2005): S60-S83. See also Anthony Grafton, Forgers and Critics: Creativity and Du-plicity in Western Scholarship (Princeton: Princeton University Press, 1990).

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Annius believed that the ancient Greeks had been inveterate liars, givento taking credit for arts and practices they did not invent, and guilty ofcorrupting arts as they inherited them. To uncover their lies, he sketchedgenealogies of all peoples from the Creation onward, focusing on the after-math of the Flood. Within these he traced the histories of various arts,showing that the sciences that the Greeks claimed to have pioneered hadactually been stolen from Chaldeans, Phoenicians, Egyptians, Italians,Franks, and Jews. Annius concocted these claims in the form of commentar-ies on a set of ancient documents that he allegedly discovered, publishingthe entire package in 1498 as Vetustissimi Auctores. . . . Though the textswere denounced as shams within a decade of their publication, for the nextcentury and more scholars treated them as providing legitimate insight intothe ancient world.

The prize piece amongst Annius’s forgeries was the lost annalistic workof Berosus. The authentic Berosus, a Chaldean priest of the late fourth cen-tury BCE, was known largely via fragments quoted in Josephus. The Anni-an Berosus gave a complete history of the pre-Greek world, rife with proofthat the Chaldeans had been notable practitioners of astrology and mathe-matics well before the flood. Annius made Berosus begin his first book:‘‘Before the famous destruction of the waters in which the entire worldperished, many generations went past, which we Chaldeans faithfully pre-served.’’18 The source, as most readers would have immediately grasped,was the Pillars of Seth. Annius granted them expansive significance:‘‘Therefore there were letters in use, and the arts of smelting, and brick-work, and prophesying, one thousand years and more before the inunda-tion of the earth.’’19 But Annius was not content merely to note that suchknowledge had been available at that time. Instead, he showed that theChaldeans had absorbed this knowledge in its very first stages:

But that letters and disciplines began and were disseminated bytheir first founder Adam, is proven not only by faith alone, butalso from the history of peoples and the tradition of the Chal-deans, which asserts that they themselves knew astronomy andletters 3634 years before the monarchy of Alexander . . . therefore

18 I have used the 1552 Antwerp edition [Annius of Viterbo], Berosi sacerdotis Chaldaici,antiquitatum Italiae ac totius orbis libri quinque . . . (Antwerp, 1552), 41. ‘‘Ante aquar-um cladem famosam qua universus periit orbis, multa praeterierunt saecula, quae a nos-tris Chaldaeis fideliter servata.’’19 Annius, 45. ‘‘Erant igitur in usu litterae, & ars fusilis, & lateritia & vaticinia, milleannis & amplius ante inundationem terrarum.’’

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the conjecture and argument are firm, that Enoch received lettersfrom Seth the first son of Adam, in whose time, Theologians assert,letters and disciplines were infused into Adam, and in which sametime the Chaldeans affirm themselves to have grasped letters andastronomy.20

Annius thus dated the origins of Chaldean learning to around 4000 BC;within the first generation of humankind. The Chaldeans and the Patriarchsdeveloped wisdom at the same moment, from the same fount. Indeed, thetransparent implication was that Seth and Enoch developed these arts be-cause they were themselves Chaldeans.

Annius’s Berosus provided another source, alongside Moses, for thehistory of early time, but one that overturned the traditional theologicalstatus of Chaldeans. But this conflict with scripture did not discredit thetext. While for Pico, Chaldean origins had been an incontrovertible demon-stration of astrology’s illicitness, Annius’s forged genealogies made theChaldeans entirely orthodox, an integral and esteemed part of the scripturalgenealogy of knowledge, and Annius’s Berosus presented himself as themouthpiece of what Walter Stephens has called the ‘‘pious Chaldean.’’ TheAnnian Berosus described the Chaldeans as God’s first chosen people.21

And the Hebrews inherited and preserved astrology, a pure, original anddivine Chaldean practice.

Pico’s initial argument had relied on a particular vision of the earlyAssyrian empire and of Assyrian culture, and debate regarding the propri-ety of astrological knowledge was framed by discussion of this historicalcontext. Scholars either approved of or denounced astrological arts by lo-cating their origins before or after the Chaldeans abandoned true religion.The very tool that Pico used to criticize and condemn astrology, then, couldbe recalibrated, given a slightly different history in order to support it.Moreover, the history could also be adjusted to condemn any range of arts:one could further constrict Pico’s range of acceptable mathematics by dat-

20 Annius, 44. ‘‘Verum quod ab Adam primo condito coeperint literae & disciplinae infu-sae, non est ex [fide] tantum, sed etiam historia gentium & traditione Chaldaeorum quise astronomiam & literas habuisse ante Alexandri monarchiam tribus millibus & sexcen-tis annis ac trigintaquator asserunt. . . . Quare coniectura & argumentum firmum est, abipso Atavo eius primo Adam eundem Enoch suscepisse literas & disciplinas, cuius tempo-re fuisse literas & disciplinas Adae infusas Theologi asserunt, & eodem tempore se cepisseliteras & Astronomiam Chaldaei affirmant.’’21 Stephens, ‘‘Berosus Chaldaeus.’’ The notion of the ‘‘pious Chaldaean’’ is explored indepth 57–135, while the Annian Berosus’s portrayal of the piety of his sources is discuss-ed from 136–208.

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ing the origins of any mathematical art to after the Chaldean lapse. WhilePico had fixed the site of the debate, its terms remained plastic.

Annius provided a powerful genealogical sanction for astrology byevoking a world history that rubbed uncomfortably against the convention-al historical narrative derived from scripture. Like those Neoplatonic andNeohermetic scholars who argued for their sources’ legitimacy by claimingthat all peoples, not just Israel, had received some divine revelation, Anni-us’s vision of history potently suggested that Moses’s books were not theonly creditable sources for deep ancient history. And Annius’s bookish so-lution, in some ways, hewed more closely to theological orthodoxy thenthe cabalist tradition glorified by Pico. Pico’s vision described a shadowygroup of initiates possessing secret, oral knowledge—a vision that displacedthe Papacy from the center of the history of learning and described revealedknowledge as fundamentally unwritten. Annius’s version, by contrast, root-ed the lineage of divine learning in the production and custody of texts andmonuments, and granted a continuous, documented history to the Churchfrom the 4000 BC to his present. Perhaps for countering Pico’s challenge,Pope Alexander VI appointed Annius Maestro del Sacro Palazzo, or officialpapal theologian.22

Still, scholars found Annius’s claims unsettling, and over the course ofthe sixteenth century, more cautious commentators—often Protestant andNorthern European—reclaimed the infallibility of scripture as a historicalsource. Rather than turning directly to the Bible, however, they used Jose-phus to secure the mathematical arts’ linkage to the scriptural genealogy.23

Vergil’s fragmentary Josephan history met Annius’s strident and ex-pansive version in Peter Ramus’s 1569 Scholae Mathematicae. From the1540s until his murder in the St. Bartholomew’s Day Massacre, Ramusspearheaded a movement to reform the curriculum of Parisian universi-ties.24 His myriad publications included textbooks on geometry and mathe-

22 See Stephens, ‘‘Berosus Chaldaeus,’’ 136–208 for Annian-focused discussion of the im-portance to early modern scholars of saving ancient historical texts preserved from oblit-eration, with special focus on the Pillars. Some of this section has been published inStephens, ‘‘Livres de haulte gresse.’’23 For the Neohermetic tradition, see Frances Yates, Giordano Bruno and the HermeticTradition (London: Routledge & Kegan Paul, 1964); for the Neoplatonic tradition seeJames Hankins, Plato in the Italian Renaissance, 2 vols. (Leiden: E.J. Brill, 1990).24 For Ramus in general, see French Renaissance Studies, 1540–70, ed. Peter Sharratt(Edinburgh: Edinburgh University Press, 1976). For Ramus and the history of mathemat-ics, see Reijer Hooykas, Humanisme, science et reforme: Pierre de la Ramee (1515–1572)(Leiden: E.J. Brill, 1958); and articles by Bruyere-Robinet, Vasoli, and Cifoletti in Revuedes Sciences Philosophiques et Theologiques 70.1 (1986).

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matics, and in his influential 1569 Scholae Mathematicae, Ramus presentedan exhaustive vision of the history of mathematics. As he explained, ‘‘Aris-totle judged the arts to be eternal, as the world is, but that just as stars riseand set, the arts sometimes are excited and flourish, and at other times aredebased and condemned. This was the great verdict of that great philoso-pher: that the arts deal with eternal and immutable things; but that theknowledge of them among men is not eternal.’’25 Ramus’s history coveredmore ground than his predecessors, including the entire sweep of historyfrom creation to his present, and he incorporated all mathematical arts,from philosophy to hydraulics.

The revolutions in the fortunes of mathematics, Ramus claimed, couldbe analyzed by modifying the exegetical theory of the Four Monarchies forperiods of mathematics. The first was the Chaldean period, lasting fromAdam to Abraham. Ramus needed only the Pillars as evidence. The Abra-hamic diffusion inaugurated the second era, but Ramus made clear thatAbraham was hardly alone in his divine knowledge of mathematics: Dio-dorus Siculus, (pseudo-)Berosus, Pliny, and Cicero showed that the ancientworld had recognized a general Chaldean mastery in the discipline. ForRamus this did not substantiate a uniform condemnation. Overzealous de-ployment of these arts was troublesome, but the arts themselves were not.

The Egyptian period that followed, Ramus noted, had witnessed in-creased sophistication of mathematical knowledge. Ancient Egyptians usedmathematics for commercial and mercantile purposes, and for surveyingflooded lands. Thales of Miletus transported mathematics from the Egyp-tians to the Greeks, inaugurating the third age. The final age was emergingin Ramus’s time, a rehabilitation of mathematical knowledge similar to theReformation.

Ramus, Vergil, and other humanists such as Joannes Stadius, HeinrichRantzau, and Matthew Dresserus agreed on a history of mathematics thattraced its origins to the Hebrew Fathers in ancient Assyria.26 This polemic

25 Peter Ramus, Scholae Mathematicarum, Libri Unus et Triginta (Basle, 1569), 1. ‘‘Aris-toteles igitur 1.coeli & 1.meteor. artes aeternas, ut mundum, arbitratur, sed earum tan-quam stellarum varios ortus & occasus esse, ut modo excitentur & floreant, modo ja-ceant & contemnantur. Haec magni philosophi magna prorsus sententia, artes suntaeternarum & immutabilium rerum: at ipsarum apud homines notitia nequaquam estaeterna.’’ Ramus is here extrapolating from Aristotle, The Complete Works of Aristotle:The Revised Oxford Translation (Princeton: Princeton University Press, 1984) [270b1],and [352b1–353a1], though Aristotle here is not referring to arts specifically, but to thevicissitudes of all phenomena in an eternal world.26 See Joannes Stadius, Tabulae Bergenses aequabilis et adparentus motus Orbium Coeles-tium . . . (Cologne, 1560), 1–3; Heinrich Rantzau, Catalogus Imperatorum, Regum, ac

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emerged in England in the last two decades of Elizabeth I’s reign, whenBacon was just beginning his career in London. The orthodoxy and utilityof mathematics were heavily debated in London at this time, and the issueof the origins of mathematics too faced close scrutiny.

London was a thriving metropolis, flooded with continental texts, andif Bacon did not encounter the history of mathematics from Europeanscholars, local texts too would have offered him cogent histories of mathe-matics and astrology. The discussion in England surfaced early in 1583,when Richard Harvey’s famous apocalyptic prognostication An Astrologi-cal Discourse appeared in London. This mathematical and astrologicalprophecy forecast massive upheaval and turbulence beginning that veryspring. The disorder, Harvey claimed, would swell, culminating with athunderous crescendo in 1588, after which the world would be profoundlyand irrevocably altered.27

Henry Howard, Earl of Northampton, and no friend to the Harveyfamily, adapted Pico’s criticism later in 1583 in his weighty and learnedrebuttal, A defensative against the poyson of supposed prophecies. UnlikePico, who wanted to support true magic while condemning its corruptions,Howard brooked no art tinged by a hint of the magical. Still, Howard’scriticism drew liberally from the criticism Pico had developed almost a cen-tury before. Relying heavily on scriptural condemnations of magical arts,Howard followed Pico in defending the possibility of natural philosophicalknowledge that did not encroach on the domain of God. Using examplesthat astrology’s defenders used to support the viability of their discipline,he distinguished forms of licit natural knowledge: ‘‘We reade not, that ourSaviour Christ condemned those, that deemed of the weather that shouldfollow by the rednes of the skie; nor those that gathered upon the fig treesputting forth her leaves, that Summer was at hand: for that the causes and

Principium qui astrologicam artem amarunt . . . (Antwerp, 1580), esp. 19–24; MatthaeusDresserus, Isagoges historicae pars prima . . . (Leipzig, 1593), 26–29.27 For Howard see Linda Levy Peck, Northampton, Patronage and Policy at the Court ofJames I (London: Allen & Unwin, 1982); and her article on Northumberland in TheMental World of the Jacobean Court, ed. Linda Levy Peck (Cambridge: Cambridge Uni-versity Press, 1991). For the astrological debates of the 1580s, see esp. Margaret Aston,‘‘The Fiery Trigon Conjunction: an Elizabethan Astrological Prediction,’’ Isis 61/2(1970): 159–87; see also Walter B. Stone, ‘‘Shakespeare and the Sad Augurs,’’ The Jour-nal of English and Germanic Philology 52 (1953): 457–79; Don Cameron Allen, TheStar-Crossed Renaissance: The Quarrel about Astrology and Its Influence in England(Durham, N.C., Duke University Press, 1941), 121–25; and Nicholas Popper, ‘‘The En-glish Polydaedali: How Gabriel Harvey Read Late Tudor London,’’ JHI 66 (2005):351–81.

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effects were tyed together, and combine in so streight a lincke of conse-quence, as either swerved not at all, or very seldome, from the course whichkind had limitted. He rather used them as presidents of lawfull gessing &divining, by the proper causes of al things.’’ Mariners too observed theworld in an acceptable fashion. But this neither constituted prophecy, norrelied on mathematics.28

Howard maligned astrology’s Chaldean origins with the standard toolsof genealogical argument:

The Latines give themselves to follow Greece. The Greeks derivetheyr knowledge from Arabia, Arabia from Egypt and Chaldea:whereas Egypt and Chaldea, by the doctrine of our greatest RabbyPtolome, as I sayde before, are cast off and forsaken for theyr er-rours. Beside, the Chaldeis were a wicked and ungodlie kinde ofmen, addicted wholie to the worshipping of false gods, and studdieof unlawfull artes: in which respect, we should detest them ratheras the teachers of abuse then vouch theyr credite as a maske offalse divinitie. Indeed, they gave themselves to practise much aboutthe Mathematicalles, which make not any man more wise, saythAristotle: but more rype and pregnaunt in the skyll of numbering.

And yet Howard finished this section at pains to distinguish between theacceptable star-gazing of the ancients and the horrific pollutions of theChaldeans: ‘‘We doubt not, but the Patriarches and holy Fathers of thecovenant looked uppe to heaven, and praysed GOD in all his mightie work-es: but that any one of them presumed to divine of thinges invisible, byPlanets which they sawe, cannot be prooved by the Scripture.’’29

Howard admitted that Abraham possessed some astronomical knowl-edge, but this was not astrological, nor a product of his Assyrian context.Rather, he developed this knowledge in spite of his surroundings. Thosewho felt otherwise, ‘‘forgette the rule of Plato: that in all countries andClymates under heaven, which bring foorth greater store of badde men thengood, so ofte as any one applies himselfe to better menes, and degsnerateth-[sic] from the comon trade, he prooveth excellent.’’30 The Patriarch’s re-lationship to the Chaldeans again provided the key to understandingastrology.

28 Henry Howard, A defensative against the poyson of supposed prophecies (London,1583), G.iv.r-v.29 Howard, O.i.v.30 Howard, O.i.v-O.ii.r.

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Richard Harvey’s brother, Gabriel, responded by deploying the Joseph-an history.31 Gabriel Harvey never published a work regarding the geneal-ogy of mathematics. Nevertheless his surviving notes in his copy of JoannesThomas Freigius’s 1583 world history Mosaicus accrued evidence for thislineage. Freigius was a prominent disciple of Ramus, and Harvey read himthrough a Ramist filter. While Freigius casually and infrequently mentionedexpertise in many arts held by the ancients, Harvey meticulously annotatedthe passages in Freigius’s narrative that fit a Josephan history. When Freigi-us, in a brief passage on notable individuals between Adam and Noah,included the story of Seth’s ancestors, Harvey wrote, ‘‘The two famousMathematical columns,’’32 and at the bottom of the page, ‘‘The Two Astro-nomical columns, erected by the progeny of Seth.’’33 These notes show Har-vey both conflating astronomy and mathematics, and introducing a generalconcern with the transmission of such knowledge. The margins of the textin Freigius’s chapter on Abraham were especially fertile ground. Here Har-vey wrote: ‘‘Abraham was the planter of Mathematics in Egypt, and fromhim came, not much later, all those mathematical and physical miracles.This was also the origin of almost all natural magic.’’34 On the next pageHarvey noted that, ‘‘The arithmetic and astronomy of the Egyptians camefrom Abraham, a noble professor of the mathematical arts.’’35 Later, hemade clear that Hermes Trismegistus’s knowledge of mathematics was easi-ly explained, since Hermes was a descendant of Abraham.36 Harvey filledout his history of mathematics by noting the invention of mathematicalinstruments: ‘‘The Radius, a very old instrument, most excellent and com-modious of all geometric instruments. It is commonly called the JacobsStaff, ‘as if it was invented then by that sacred Patriarch.’ See Ramus’sGeometry, book 9. Doubtless it seemed necessary to add this mathematical

31 For Gabriel Harvey, see Virginia Stern, Gabriel Harvey, His Life, Marginalia and Li-brary (Oxford: The Clarendon Press, 1979); Anthony Grafton and Lisa Jardine, ‘‘ ‘Stud-ied for Action’: How Gabriel Harvey Read His Livy,’’ Past and Present 129 (Nov. 1990):30–78.32 Gabriel Harvey’s copy of Joannes Thomas Freigius, Mosaicus: continens historiam ec-clesiasticam . . . (Basle, 1583), 60. BL shelfmark C.60.f.4. ‘‘Duae famosae columnaeMathematicae.’’33 Ibid., ‘‘Duae Columnae Astronomicae, a Sethi nepotibus excitatae.’’34 Harvey’s Freigius, 140. ‘‘Abrahamus, primus Mathematicarum plantator in Aegypto:Unde, nec ita multo post, tot Mathematica, et Physica Miracula. Hinc fere Magia omnisNaturalis.’’35 Ibid., 141. ‘‘Aegiptiorum Arithmetica, et Astronomia, ab Abrahamo: Mathematicarumartium nobili professore.’’36 Ibid., 158.

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invention of Jacob’s to the earlier mathematical inventions of his grand-father Abraham.’’37 Harvey thus followed Ramus in grafting the history ofmathematics directly to the history of the Patriarchs while studying mathe-matical history alongside technical texts. In so doing, he found an orthodoxand honored genealogy for the mathematical arts, salvaging the proprietyof his brother’s prognostication, and the dignity of his family reputation.

Harvey never published a response to Northampton, and concern withthe origins of mathematics faded from print for the next two decades inEngland. It would surface without kindling much debate, for example, inThomas Hood’s 1588 inaugural speech as Mathematical Lecturer to theCity of London.38 But in the years surrounding Elizabeth’s death andJames’s accession, the debate flared up again. The clergyman John Cham-ber’s 1601 A Treatise against Judiciall Astrologie expressed militant abhor-rence for the astrologers, augurs and figure-flingers who brimmed in theBabylonian streets of late Tudor London. Chamber claimed that Adam andSeth had held mathematical knowledge. But this did not include astrology;that diabolic practice, he claimed, originated in the later Chaldean corrup-tion of divine knowledge. He memorably described the astrologers as, ‘‘bas-tards, the sons of an hedge hore, their mother was an Hittitie,’’ and regis-tered deep alarm: ‘‘But that is Babylon, where Babylonicall superstitionsare maintained or suffered.’’ Chamber followed Pico in attributing ortho-dox astronomical knowledge to the Patriarchs, that was later corruptedinto astrology by the Chaldeans.39

The godly Protestant soldier Sir Christopher Heydon responded in his1603 A Defence of Iudiciall Astrology by strenuously insisting on the Ada-mic origins of astrology. He conceded that Chaldean corruptions had pro-duced heretical and idolatrous arts such as augury, but insisted that trueastrology, which proceeds from natural causes to natural effects, was a di-vine gift from God to Adam, and had been passed along in an unbrokenchain since. In illustration, he included at the end of his treatise a ‘‘Chrono-logical Index of Astronomers from Adam,’’ which began with the genealogy

37 Harvey’s Freigius, 166. ‘‘Radius, Instrumentum, Perantiquum, omnium Geometricor-um Instrumentorum praestantissimus; vulgo Baculus Jacobi dicitur, tanquam a sanctapatriarcha illo iam olim inventus sit. Ram. Geometriae lib.9. Nimirum hoc Jacobi, mathe-maticum inventum, superioribus avi Abrahami inventis Mathematicis addendum vide-batur.’’38 Thomas Hood, A Copie of the Speache: made by the Mathematicall Lecturer, unto theWorshipfull Companye of present (London, 1588), A.iiii.v-B.i.r.39 John Chamber, A Treatise Against Iudicall Astrologie (London, 1601), 118, 121.

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from Adam to Joseph, and extended to Tycho Brahe and other contempo-raries.40

Heydon’s work prompted a defense from George Carleton, futurechaplain to Prince Charles. Carleton classified astrology as part of magic,and attacked Heydon’s chronology. Heydon, Carleton noted, had tried tohide suspect figures like Zoroaster and Hermes Trismegistus within the ge-nealogy by placing them after the Hebrew Patriarchs, out of chronologicalorder. Heydon’s list was also dressed up with Joseph, Homer, and othersfor whom no evidence of astrological interest existed. Charleton traced amuscular anti-Josephan lineage: he wrote, ‘‘The first invention of Astrolo-gy, is by many learned men attributed to the divels,’’ and its first dissemina-tor was Zoroaster.41

Thus, by the 1605 appearance of the Advancement of Learning, therewere two well-established, yet volatile interpretations of a single, modifi-able chronology for the mathematical arts. While both sides agreed thatsome licit mathematical art could be traced from the time of Adam, astrolo-gy provoked bitter dissension. On the one hand, Pico and his followersrooted powerful criticisms in the historical and cultural conditions of as-trology’s perceived origins: that of idolatrous, Baal-worshiping Assyria. Onthe other hand, defenders posited Assyria as the setting in which astrologyand related mathematical arts had flourished, nurtured by the pious learn-ing of the Chaldeans. When this first flourishing gave way to idolatrouscorruptions, the Jewish Patriarchs remained responsible for the mainte-nance of the discipline. The history of the mathematical arts was less barrenand wanting than Bacon led his king to believe.

Bacon’s proposal, despite his protestations, did not call for the creationof a radically new discipline. In claiming that such histories of the arts didnot exist, Bacon may have been reacting more to the historical methodolo-gies with which he was familiar than to the existing state of mathematicalhistories. For example Jean Bodin, whom Bacon certainly had read, devot-ed considerable but unsystematic attention in his 1566 Methodus ad fac-

40 Christoper Heydon, A Defence of Iudiciall Astrology (Cambridge, 1603), Zzz.4.v41 [George Carleton], AΣTΡOΛOΓOMANIA: The Madnesse of ASTROLOGERS. Or anExamination of Sir Christopher Heydons Booke, Intituled A Defence of Iudiciarie Astro-logie. Written nearly 20 yeares ago by G.C. (London, 1624), 56. Since there were multipleancient figures identified with Zoroaster, it should be noted, both critics and proponentsof astrology were able to claim one of them in support of their position. See LaurenKassell’s article in this volume.

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ilem historiarum cognitionem to describing the conditions of learningthroughout world history. He wrote,

Not only the virtues of our men are equal to those of the ancientsbut also the discipline. Literature suffers changes of fortune. Firstthe arts arise in some places through the practice and labor oftalented men, then they develop, later they flourish for a while ata fixed level, then languish in their old age, and finally begin to dieand are buried in a lasting oblivion by the eternal calamity of wars,or because too great abundance (an evil much to be feared in thesetimes, of course) brings satiety to the frivolous, or because Godinflicts just punishments upon those who direct useful knowledgeto the ruin of men. Although disciplines had gradually developedamong the Greeks, so that they believed these arts reached theirpeak, such a change came about afterward that Greece herself, tojudge from her present predicament, seems never to have existed.

He continued, ‘‘I omit how Egypt, India, and Ethiopia teemed with manyphilosophers, geometrists, and astrologers; how many well-known mathe-maticians were in Chaldea before Greece had any literature. I come back toour times in which, after a long eclipse of letters throughout almost theentire world, suddenly such a wealth of knowledge shone forth, such fertili-ty of talents existed, as no age ever excelled.’’42 Bodin shared with Baconand Ramus a cyclical vision of the history of knowledge; but he and Bacondid not map transmissions as Ramus did.

42 Jean Bodin, Method for the Easy Comprehension of History, trans. Beatrice Reynolds(New York: Norton, 1969), 300. For the original, see Jean Bodin, Methodus, ad facilemhistoriarum cognitionem (Paris, 1566), 358–59: ‘‘Neque solum virtutes in nostris homini-bus, sed etiam disciplinae pares, atque in veteribus extiterunt. est enim literarum suaquoque vicissitudo, ut primum quibusdam in locis ingeniosorum hominum experientia &labore artes oriantur, deinde incrementa suscipiant, post aliquantum in statu vigeant,tandem sua vetustate langueant, denique sensim emoriantur, & oblivione diuturna sepeli-antur: vel bellorum diuturna calamitate: vel quod nimia copia (malum his temporibusvalde metuendum) satietatem levissimo cuique afferre soleat: vel quod iustas Deus poenasexpetit ab iis qui scientias salutares, in hominum perniciem convertunt. Nam cum discipli-nae, apud Graecos sensim adolevissent, ut ad summum pervenisse crederentur, tanta mu-tatio postea secuta est, ut ne ipsa quidem Graecia ubi nunc est unquam extitisse videatur. . . Omitto quammultos philosophos, geometras, astrologos, peperit Aegyptus, IndiaAethiopia: quammulti apud Caldaeos nobiles mathematici ante fuerunt, quam ullae es-sent in Graecia literae: ad nostra tempora relabor, quibus multo postquam literae totopene terrarum orbe conquierant, tantus subito scientiarum omnium splendor affulsit,tanta fertilitas extitit ingeniorum, ut nullis unquam aetatibus maior.’’

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Bodin dotted his text with ‘‘small memorials,’’ and made no great pleafor a history of the sciences. But other artes historicae did contain systemat-ic proposals for, and examples of, the sort of history Bacon desired. AsDonald R. Kelley has shown, the innovative fifth chapter of ChristopheMilieu’s 1551 De scribenda universitatis rerum historia outlined a historialitteraria, which began with a discussion of the Pillars of Seth and chartedthe position of learning in societies from the Pillars to Milieu’s present.43

Equally detailed was Reinier Reineck’s 1583 Methodus Legendi Cognosce-ndique Historiam, in which a section on the historia scholarum describedthe Pillars as a schoolboys’ primer from the time of Enoch to the Flood. 44

Reineck also admiringly described both Vergil’s work and Caspar Peucer’s1572 De Divinatione as exemplary instances of this kind of history.45

Bacon’s plea for a history of science was only a later example of late six-teenth-century proposals for a genre that some felt already existed. The self-proclaimed novelty of his proposal was either ill-informed or disingenuous.

Through the seventeenth century the Pillars continued to play a centralrole in histories that located the origins of mathematics in the deep ancientworld. In England, for example, Sir Walter Ralegh relied heavily on themin his 1614 History of the World. Ralegh followed Pico, discussing thehistory of magic within the setting of its postdiluvian corruption, but likeAnnius treated many of the mathematical arts—including alchemy and as-trology—as predating Chaldean corruption.46 John Wallis’s 1649 inauguraloration as Savilian Professor of Geometry relied heavily on the Pillars asevidence for the presence of intricate knowledge of mathematics in the an-cient world. For Wallis, the astrological knowledge of the Chaldeans, cor-rupt as it was, proved beyond a doubt the widespread diffusion of mathe-matical learning.47

43 Christophe Milieu, De scribenda universitatis rerum historia (Basle, 1551). SeeSchmidt-Biggemann, 23–30; and Donald R. Kelley, ‘‘Writing Cultural History in EarlyModern Europe: Christoph Milieu and His Project,’’ Renaissance Quarterly 52.2 (1999):342–65. Kelley also notes that Bacon seemed unaware of Milieu’s work, though it hadindeed addressed his precise concerns.44 Reiner Reineck, Methodus Legendi Cognoscendique Historiam tam sacram tam pro-fanam. . . . (Helmstadt, 1583), also including his oration on the dignity of mathematics.The section on the historia scholarum, is 22v-29v. For his description of the Pillars as apedagogical tool, see within the Oratio, 36r-v.45 Reineck, 28r.46 Walter Ralegh, The History of the World (London, 1614), 1:199–212.47 John Wallis, Geometriae Professoris Saviliani, Oratio Inauguralis in Auditorio Geo-metrico, Oxonii, habita . . . (Oxford, 1657). See b.3.r and passim. I thank Tony Mannfor this reference. See also Stephens, ‘‘Livres de haulte gresse,’’ for the continued resourc-ing of the Pillars through the eighteenth century.

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The Pillars thus served as crucial evidence for mathematics in the an-cient world, and a history of mathematics that began almost from the Fall.To topple the Pillars was to topple this vision, a feat achieved in 1722 byWilliam Whiston, Newton’s successor as Lucasian Professor of Mathemat-ics. But the biblical antiquarian Whiston did not debunk the attribution ofthese Pillars to Seth to stake a claim regarding the history of mathematicallearning. Rather, the Unitarian Whiston argued that second-century Jewishredactors had corrupted the true text of scripture by introducing Trinitarianfables. Whiston claimed that Josephus had been working with the authenticScriptures—indeed, he thought, the Temple’s copy of the Bible, which Jose-phus may have received directly from Titus. Whiston was thus forced toexplain away any incongruities within Josephus’s text, and he deemed thePillars of Seth a ‘‘strange supposition,’’ which needed to be dismissed.48

Josephus, Whiston claimed, was simply uninformed about Egyptian histo-ry, its pharaohs and obelisks, when he attributed the pillars to Seth insteadof their rightful builder, the Pharoah ‘‘Seth-os, or Sethosis, or Sesotris theGreat.’’49 While still dating the Pillars to almost 1200 BC—easily predatingthe high cultures of Greece and Rome—Whiston undermined the bedrockevidence for an Annian history of science.50

This history of histories illuminates contemporary understandings ofmathematics, astrology, and astronomy from the late fifteenth to seven-teenth centuries. Consistent in all of the authors is the understanding thatmathematics had a long history. Some virtue always obtained in learningEuclid or Ptolemy; nobody questioned the utility of these arts in agriculture,husbandry, navigation, and chronology. But though none of these scholarscondemned all forms of sky-gazing, all agreed that they could be corrupted.The question was where and when corruptions were introduced. For indi-

48 William Whiston, An Essay Towards Restoring the True Text of the Old Testament;and for Vindicating the Citations made thence in the New Testament (London, 1722),clx. For Whiston, see James E. Force, William Whiston: Honest Newtonian (Cambridge:Cambridge University Press, 1985). For Whiston’s biblical exegesis, and especially hisstudy of ancient Egypt and the Near East, see John Gascoigne, ‘‘ ‘The Wisdom of theEgyptians’ and the Secularisation of History in the Age of Newton,’’ in The Uses ofAntiquity: The Scientific Revolution and the Classical Tradition, ed. Stephen Gaukroger(Dordrecht: Kluwer, 1991), 171–212.49 Whiston; the quote is on cxxxix; his analysis is on clix-clx.50 Others in the early eighteenth century dismissed the Pillars just as easily. For example,Vico consigned them to the ‘‘Museum of Credulity,’’ though on the assumption that theyhad been attributed to Seth to exaggerate the ancient origins of the Chaldeans rather thanon antiquarian criticism (see Giambattista Vico, The New Science, trans. David Marsh(London: Penguin, 2000), [49], p. 43).

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vidual authors real differences existed between astrology and astronomy,even if there was no consensus regarding their boundaries. The issue waswhether astrology properly belonged with the constellation of orthodoxstudies, or with the idolatrous divinatory arts of the Chaldeans.

Further, the debate was conducted entirely within ecclesiastical history.The history of mathematics was inseparable from the history of the churchand the history of worship. The orthodoxy of various arts was proven nei-ther by showing that they did not abrogate divine authority, nor by simplyshowing their venerable antiquity. The reputation of the communities thatproduced these specialized arts licensed or condemned their adoption, andtheir genealogies argued for or against their orthodoxy. Chamber was notbeing hysterical when he depicted London as a second Babylon; to him,the city swarmed with an idolatrous lay priest caste performing rites andoffending the divine will, exactly as Babylon had under the sway of theerring Chaldeans. A practicing community of Hebraic astrologers in theancient world, as described by Josephus, served the antithetical purpose.Theological and historical debate provided the terrain for justifying mathe-matical and astronomical activities.

Despite Bacon’s claims, there was a healthy history of science in thesixteenth century. Scholars, admittedly, drew up a history of mathematicsquite at odds with a progressive history of science. Their history of sciencewas a degeneration narrative, a problem of recovery instead of invention,of cleansing rather than expansion, with a Golden Age behind rather thanahead. But it was a history, nevertheless, and one that fits neatly with theclaims of Vesalius, Scaliger, and others who depicted their innovations asreformations of ancient disciplines. These scholars conjured an ancientworld teeming with mathematical practice, directing them towards variousforms of lost or obscured expertise.51 The narrative of their history of sci-ence may not have resembled Kepler’s, but by directing attention to theancient authorization for mathematics, they contributed to the process oflegitimizing mathematical knowledge.

Princeton University.

51 For this point, see Anthony Grafton, Joseph Scaliger: A Study in the History of ClassicalScholarship 2 vols. (Oxford: Clarendon Press, 1983–1993), 2: 253–62; and Dear,116–19.

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Abraham, Planter of Mathematics: Histories of Mathematics and Astrology in Early Modern Europe

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