THE RENAISSANCE

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He continued, "I omit how Egypt, India, and Ethiopia teemed with many philosophers, geometrists, and astrologers; how many well-known mathematicians were in Chaldea before Greece had any literature. I come back to our times in which, after a long eclipse of letters throughout almost the entire world, suddenly such a wealth of knowledge shone forth, such fertility of talents existed, as no age ever excelled."42 Bodin shared with Bacon and Ramus a cyclical vision of the history of knowledge; but he and Bacon did not map transmissions as Ramus did. [End Page 103]

Bodin dotted his text with "small memorials," and made no great plea for a history of the sciences. But other artes historicae did contain systematic proposals for, and examples of, the sort of history Bacon desired. As Donald R. Kelley has shown, the innovative fifth chapter of Christophe Milieu's 1551 De scribenda universitatis rerum historia outlined a historia litteraria, which began with a discussion of the Pillars of Seth and charted the position of learning in societies from the Pillars to Milieu's present.43 Equally detailed was Reinier Reineck's 1583 Methodus Legendi Cognoscendique Historiam, in which a section on the historia scholarum described the 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's 1572 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 sixteenth-century proposals for a genre that some felt already existed. The self-proclaimed novelty of his proposal was either ill-informed or disingenuous. 

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Through the seventeenth century the Pillars continued to play a central role in histories that located the origins of mathematics in the deep ancient world. In England, for example, Sir Walter Ralegh relied heavily on them in his 1614 History of the World. Ralegh followed Pico, discussing the history of magic within the setting of its postdiluvian corruption, but like Annius treated many of the mathematical arts—including alchemy and astrology—as predating Chaldean corruption.46 John Wallis's 1649 inaugural oration as Savilian Professor of Geometry relied heavily on the Pillars as evidence for the presence of intricate knowledge of mathematics in the ancient world. For Wallis, the astrological knowledge of the Chaldeans, corrupt as it was, proved beyond a doubt the widespread diffusion of mathematical learning.47 [End Page 104]

The Pillars thus served as crucial evidence for mathematics in the ancient 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 by William Whiston, Newton's successor as Lucasian Professor of Mathematics. But the biblical antiquarian Whiston did not debunk the attribution of these Pillars to Seth to stake a claim regarding the history of mathematical learning. Rather, the Unitarian Whiston argued that second-century Jewish redactors had corrupted the true text of scripture by introducing Trinitarian fables. Whiston claimed that Josephus had been working with the authentic Scriptures—indeed, he thought, the Temple's copy of the Bible, which Josephus may have received directly from Titus. Whiston was thus forced to explain away any incongruities within Josephus's text, and he deemed the Pillars of Seth a "strange supposition," which needed to be dismissed.48 Josephus, Whiston claimed, was simply uninformed about Egyptian history, its pharaohs and obelisks, when he attributed the pillars to Seth instead of their rightful builder, the Pharoah "Seth-os, or Sethosis, or Sesotris the Great."49 While still dating the Pillars to almost 1200 BC—easily predating the high cultures of Greece and Rome—Whiston undermined the bedrock evidence for an Annian history of science.50 

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This history of histories illuminates contemporary understandings of mathematics, astrology, and astronomy from the late fifteenth to seventeenthcenturies. Consistent in all of the authors is the understanding that mathematics had a long history. Some virtue always obtained in learning Euclid or Ptolemy; nobody questioned the utility of these arts in agriculture, husbandry, navigation, and chronology. But though none of these scholars condemned all forms of sky-gazing, all agreed that they could be corrupted. The question was where and when corruptions were introduced. For individual [End Page 105] authors real differences existed between astrology and astronomy, even if there was no consensus regarding their boundaries. The issue was whether astrology properly belonged with the constellation of orthodox studies, 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 church and the history of worship. The orthodoxy of various arts was proven neither by showing that they did not abrogate divine authority, nor by simply showing their venerable antiquity. The reputation of the communities that produced these specialized arts licensed or condemned their adoption, and their genealogies argued for or against their orthodoxy. Chamber was not being hysterical when he depicted London as a second Babylon; to him, the city swarmed with an idolatrous lay priest caste performing rites and offending the divine will, exactly as Babylon had under the sway of the erring Chaldeans. A practicing community of Hebraic astrologers in the ancient world, as described by Josephus, served the antithetical purpose. Theological and historical debate provided the terrain for justifying mathematical and astronomical activities.   

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Despite Bacon's claims, there was a healthy history of science in the sixteenth century.

Scholars, admittedly, drew up a history of mathematics quite at odds with a progressive history of science.

Their history of science was a degeneration narrative, a problem of recovery instead of invention, of cleansing rather than expansion, with a Golden Age behind rather than ahead.

But it was a history, nevertheless, and one that fits neatly with the claims of Vesalius, Scaliger, and others who depicted their innovations as reformations of ancient disciplines.

These scholars conjured an ancient world teeming with mathematical practice, directing them towards various forms of lost or obscured expertise.51


The narrative of their history of science may not have resembled Kepler's, but by directing attention to the ancient authorization for mathematics, they contributed to the process of legitimizing mathematical knowledge. 

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Footnotes



I would like to thank Lauren Kassell, Robert Goulding, James Byrne, Darrel Rutkin, Amy Haley, Anthony Grafton, Simon Schaffer, and Walter Stephens for their invaluable comments, suggestions and improvements. The paper was given in a slightly different form from the 2004 History of Science Society Meeting version at the 2004 Thomas Harriot Seminar, 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 aduancement of learning, diuine and humane (London, 1605), Aa.1.r-Aa.4.v. The history of science literature on Bacon is immense. In this context see Paolo Rossi, Francis Bacon: From Magic to Science, trans. Sasha Rabinovitch (Chicago: University of Chicago Press, 1968); and Wilhelm Schmidt-Biggemann, Topica universalis: eine Modellgeschichte humanistischer und barocker Wissenschaft (Hamburg: Meiner, 1983), 212–25.

2. Bacon, Bb.3.v.

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

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: Harvard University Press, 1997), esp. 20–60. See also Jan N. Bremmer, "The Birth of the Term 'Magic'" in The Metamorphosis of Magic from Late Antiquity to the Early Modern Period, ed. Jan N. Bremmer and Jan R. Veenstra (Leuven: Peeters, 2002) 1–11 and Peter Brown, 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": Stars and the End of the World in Luther's Time (Berlin: W. de Gruyter, 1986); and Ottavia Niccoli, 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 of Traditional, Religious, and Philosophical Systems: with Text, Translation, and Commentary (Phoenix: Medieval & Renaissance Texts & Studies, 1998).

7. Pico della Mirandola, Opera Omnia (Basel, 1601), 80: "Proposuimus & magica theoremata, in quibus duplicem esse Magiam significamus, quarum altera daemonum tota opere & authoritate constat, res medius fidius execranda & portentosa: altera nihil est aliud, cum bene exploratur, quam naturalis philosophiae absoluta consummatio." Recent work on Pico includes H. Darrel Rutkin, Astrology, Natural Philosophy and the History of Science, c. 1250–1700: Studies toward an Interpretation of Giovanni Pico della Mirandola's Disputationes adversus Astrologiam Divinatricem (Ph.D. Dissertation, Indiana University, 2002), esp. 230–467, with considered discussion of the various traditions of Pico scholarship; and Steven Vanden Broecke, The Limits of Influence: Pico, Louvain, and the Crisis of Renaissance Astrology (Leiden: Brill, 2003), 55–81.

8. Pico, 113. "Tota magia, quae in usu est apud modernos, & quam merito exterminat Ecclesia, nullam habet firmitatem, nullam veritatem, nullum firmamentum: quia pendet ex manu hostium primae veritatis, potestatum harum tenebrarum, quae tenebras falsitatis malae dispositis intellectibus offendunt."

9. See Anthony Grafton, Commerce with the Classics: Ancient Books and Renaissance Readers (Ann Arbor: University of Michigan Press, 1997), 93–134; and Rutkin, 338–43.

10. Pico, 483.

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11. See books 11 and 12 of Pico della Mirandola's Disputationes adversus Astrologiam divinatricem, esp. 11.2 at 483. For Abraham's teaching, see 485.

12. For Vergil, see Denys Hay, Polydore Vergil: Renaissance Historian and Man of Letters (Oxford: Clarendon Press, 1952); Brian Copenhaver, "The Historiography of Discovery in the Renaissance: The Sources and Composition of Polydore Vergil's De inventoribus rerum, 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 Josephus, the Bible, and History, ed. Louis H. Feldman and Gohei Hata (Detroit: Wayne State University Press, 1989).

15. See On Discovery 139–47. For the references in Josephus, see I.viii.166–68. For the medieval readings of Seth's Pillars, see Cora E. Lutz, "Remigius' Ideas on the Origin and 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 to befuddle sound minds" (On Discovery, 143). This runs contrary to his enthusiasm for letters, mathematics, and other arts that shared its genealogy.

17. For Annius see Walter Stephens, "Berosus Chaldaeus: Counterfeit and Fictive Editors of the Early Sixteenth Century" (Ph.D. Dissertation, Cornell University, 1979); parts of which were integrated into his Giants in Those Days: Folklore, Ancient History, and Nationalism (Lincoln: University of Nebraska Press, 1989); and his "Livres de haulte gresse: Bibliographic Myth from Rabelais to Du Bartas," MLN 120.1 Supplement (January 2005): S60-S83. See also Anthony Grafton, Forgers and Critics: Creativity and Duplicity in Western Scholarship (Princeton: Princeton University Press, 1990).

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 aquarum cladem famosam qua universus periit orbis, multa praeterierunt saecula, quae a nostris Chaldaeis fideliter servata."

19. Annius, 45. "Erant igitur in usu litterae, & ars fusilis, & lateritia & vaticinia, mille annis & amplius ante inundationem terrarum."

20. Annius, 44. "Verum quod ab Adam primo condito coeperint literae & disciplinae infusae, non est ex [fide] tantum, sed etiam historia gentium & traditione Chaldaeorum qui se astronomiam & literas habuisse ante Alexandri monarchiam tribus millibus & sexcentis annis ac trigintaquator asserunt. . . . Quare coniectura & argumentum firmum est, ab ipso Atavo eius primo Adam eundem Enoch suscepisse literas & disciplinas, cuius tempore fuisse literas & disciplinas Adae infusas Theologi asserunt, & eodem tempore se cepisse literas & Astronomiam Chaldaei affirmant."

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21. Stephens, "Berosus Chaldaeus." The notion of the "pious Chaldaean" is explored in depth 57–135, while the Annian Berosus's portrayal of the piety of his sources is discussed from 136–208.

22. See Stephens, "Berosus Chaldaeus," 136–208 for Annian-focused discussion of the importance to early modern scholars of saving ancient historical texts preserved from obliteration, with special focus on the Pillars. Some of this section has been published in Stephens, "Livres de haulte gresse."

23. For the Neohermetic tradition, see Frances Yates, Giordano Bruno and the Hermetic Tradition (London: Routledge & Kegan Paul, 1964); for the Neoplatonic tradition see James 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 mathematics, see Reijer Hooykas, Humanisme, science et réforme: Pierre de la Ramée (1515–1572) (Leiden: E.J. Brill, 1958); and articles by Bruyère-Robinet, Vasoli, and Cifoletti in Revue des Sciences Philosophiques et Théologiques 70.1 (1986).

25. Peter Ramus, Scholae Mathematicarum, Libri Unus et Triginta (Basle, 1569), 1. "Aristoteles igitur 1.coeli & 1.meteor. artes aeternas, ut mundum, arbitratur, sed earum tanquam stellarum varios ortus & occasus esse, ut modo excitentur & floreant, modo jaceant & contemnantur. Haec magni philosophi magna prorsus sententia, artes sunt aeternarum & immutabilium rerum: at ipsarum apud homines notitia nequaquam est aeterna." 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 the vicissitudes of all phenomena in an eternal world.

26. See Joannes Stadius, Tabulae Bergenses aequabilis et adparentus motus Orbium Coelestium . . . (Cologne, 1560), 1–3; Heinrich Rantzau, Catalogus Imperatorum, Regum, ac Principium qui astrologicam artem amarunt . . . (Antwerp, 1580), esp. 19–24; Matthaeus Dresserus, Isagoges historicae pars prima . . . (Leipzig, 1593), 26–29.

27. For Howard see Linda Levy Peck, Northampton, Patronage and Policy at the Court of James I (London: Allen & Unwin, 1982); and her article on Northumberland in The Mental World of the Jacobean Court, ed. Linda Levy Peck (Cambridge: Cambridge University 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 Journal of English and Germanic Philology 52 (1953): 457–79; Don Cameron Allen, The Star-Crossed Renaissance: The Quarrel about Astrology and Its Influence in England (Durham, N.C., Duke University Press, 1941), 121–25; and Nicholas Popper, "The English Polydaedali: How Gabriel Harvey Read Late Tudor London," JHI 66 (2005): 351–81.

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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31. For Gabriel Harvey, see Virginia Stern, Gabriel Harvey, His Life, Marginalia and Library (Oxford: The Clarendon Press, 1979); Anthony Grafton and Lisa Jardine, "'Studied 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 ecclesiasticam . . . (Basle, 1583), 60. BL shelfmark C.60.f.4. "Duae famosae columnae Mathematicae."

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 omnis Naturalis."

35. Ibid., 141. "Aegiptiorum Arithmetica, et Astronomia, ab Abrahamo: Mathematicarum artium nobili professore."

36. Ibid., 158.

37. Harvey's Freigius, 166. "Radius, Instrumentum, Perantiquum, omnium Geometricorum Instrumentorum praestantissimus; vulgo Baculus Jacobi dicitur, tanquam a sancta patriarcha illo iam olim inventus sit. Ram. Geometriae lib.9. Nimirum hoc Jacobi, mathematicum inventum, superioribus avi Abrahami inventis Mathematicis addendum videbatur."

38. Thomas Hood, A Copie of the Speache: made by the Mathematicall Lecturer, unto the Worshipfull Companye of present (London, 1588), A.iiii.v-B.i.r.

39. John Chamber, A Treatise Against Iudicall Astrologie (London, 1601), 118, 121.

40. Christoper Heydon, A Defence of Iudiciall Astrology (Cambridge, 1603), Zzz.4.v

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41. [George Carleton], AΣTPOΛOΓOMANIA: The Madnesse of ASTROLOGERS. Or an Examination of Sir Christopher Heydons Booke, Intituled A Defence of Iudiciarie Astrologie. Written nearly 20 yeares ago by G.C. (London, 1624), 56. Since there were multiple ancient figures identified with Zoroaster, it should be noted, both critics and proponents of astrology were able to claim one of them in support of their position. See Lauren Kassell's article in this volume.

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 facilem historiarum cognitionem (Paris, 1566), 358–59: "Neque solum virtutes in nostris hominibus, sed etiam disciplinae pares, atque in veteribus extiterunt. est enim literarum sua quoque 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 sepeliantur: vel bellorum diuturna calamitate: vel quod nimia copia (malum his temporibus valde metuendum) satietatem levissimo cuique afferre soleat: vel quod iustas Deus poenas expetit ab iis qui scientias salutares, in hominum perniciem convertunt. Nam cum disciplinae, apud Graecos sensim adolevissent, ut ad summum pervenisse crederentur, tanta mutatio postea secuta est, ut ne ipsa quidem Graecia ubi nunc est unquam extitisse videatur . . . Omitto quammultos philosophos, geometras, astrologos, peperit Aegyptus, India Aethiopia: quammulti apud Caldaeos nobiles mathematici ante fuerunt, quam ullae essent in Graecia literae: ad nostra tempora relabor, quibus multo postquam literae toto pene terrarum orbe conquierant, tantus subito scientiarum omnium splendor affulsit, tanta fertilitas extitit ingeniorum, ut nullis unquam aetatibus maior."

43. Christophe Milieu, De scribenda universitatis rerum historia (Basle, 1551). See Schmidt-Biggemann, 23–30; and Donald R. Kelley, "Writing Cultural History in Early Modern 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 had indeed addressed his precise concerns.

44. Reiner Reineck, Methodus Legendi Cognoscendique Historiam tam sacram tam profanam. . . . (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 a pedagogical 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 Geometrico, Oxonii, habita . . . (Oxford, 1657). See b.3.r and passim. I thank Tony Mann for this reference. See also Stephens, "Livres de haulte gresse," for the continued resourcing of the Pillars through the eighteenth century.

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 his study of ancient Egypt and the Near East, see John Gascoigne, "'The Wisdom of the Egyptians' and the Secularisation of History in the Age of Newton," in The Uses of Antiquity: 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 they had been attributed to Seth to exaggerate the ancient origins of the Chaldeans rather than on antiquarian criticism (see Giambattista Vico, The New Science, trans. David Marsh (London: Penguin, 2000), [49], p. 43).

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



http://muse.jhu.edu/journals/journal_of_the_history_of_ideas/v067/67.1popper.html#REF21

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                                      Histories of Science in Early Modern Europe







Robert Goulding
University of Notre Dame



In 1713, Pierre Rémond de Montmort wrote to the mathematician Nicolas Bernoulli:



"It would be desirable if someone wanted to take the trouble to instruct how and in what order the discoveries in

mathematics have come about. . . . The histories of painting, of music, of medicine have been written. A good

history of mathematics, especially of geometry, would be a much more interesting and useful work. . . . Such a

work, if done well, could be regarded to some extent as a history of the human mind, since it is in this science,

more than in anything else, that man makes known that gift of intelligence that God has given him to rise above

all other creatures."1



Such a history of mathematics was attempted by Jean-Etienne Montucla in his Histoire des mathématiques (first printed in 1758, and reissued in a [End Page 33] greatly expanded form in 1799).2 Montucla's great work is generally acknowledged as the first genuine history of mathematics. According to some modern historians, previous attempts at such a history had amounted to little more than collections of anecdotes, biographies or exhaustive bibliographies: "jumbles of names, dates and titles," as one writer in the Dictionary of Scientific Biography characterized them.3 Montucla, on the other hand, was thoroughly animated by the Enlightenment project expressed in Rémond's letter, and his Histoire was a philosophical history of the "development of the human mind," as he himself described it.4

It was precisely Montucla's vision of what mathematics meant and his conviction that mathematics itself must change in order to reflect the historical elevation of the human intellect, that allowed him to transform the scattered dates and anecdotes of his predecessors into a genuine history. All subsequent histories of mathematics—until the most recent social histories5 —have been in a sense "footnotes to Montucla."



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The papers here argue that there were indeed histories of mathematics before Montucla which are worthy of scholarly attention, and that the dismissal of Renaissance histories of science as nothing more than a "cloud of fine adjectives and metaphors" is unfair (although it contains a germ of truth). Anthony Grafton has argued in an article on the historical writings of Cardano, Rheticus, and Kepler, that the purpose of such texts was not so much to trace what actually happened, as to justify the study of a subject often derided—by both humanist and scholastic writers—as obscure, useless and undignified.6 The following four papers go further in arguing that writings in this genre (or, at least, some writings in this genre) were not limited to this characteristically humanist objective. Authors did not just use their histories to persuade others. They themselves relied on historical narratives in order to think about their discipline, define its parts, distinguish among its acceptable and unacceptable forms and prescribe its content [End Page 34] and method of teaching. By placing their discipline into a historical context shared by other, more mainstream humanistic arts, moreover, they could draw upon the large, narrative structures which Renaissance humanists had adapted to understand human intellectual and cultural development, origins, progress and decline.

James Byrne's article highlights a disparity of vision between those humanists who treated the origin of the arts as just another subject for humanistic display; and those (like Regiomontanus) who were invested in the arts and wrote their histories from an insider's perspective. Alongside Regiomontanus, one could include several other authors treated in this collection, such as Thomas Vaughan, Peter Ramus, and Henry Savile. In each case, history provided a means for working through problems of the legitimacy and nature of their disciplines. While their writings are not "histories of the human mind," their interests went beyond mere rehearsal of anecdotes. Ramus's histories, for instance, written 200 years before Montucla's Histoire, had the kind of unifying vision which de Montmort demanded, and shared Montucla's concern to find a meaning in the development of mathematics. Ramus, and the supporters and detractors he spawned, were convinced that constructing the history of this science was crucial to understanding how and why human beings have knowledge, and how that knowledge should be taught in the academies of Europe. 

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Three of the papers in this collection address histories of mathematics which were written from the late fifteenth century to the early seventeenth century. The fourth examines seventeenth-century histories of another despised subject—magic—and reveals a surprising degree of common ground, in both techniques and sources, with the less controversial historians of mathematics. These papers show how Renaissance scholars used history to underpin larger claims about the usefulness and potential of the sciences for their society. In the case of mathematics, their writings also helped to overcome the indifference of university authorities and students—and even the lay public—towards the teaching of the sciences, and to frame the forms in which the sciences were eventually established in the academy.

The writing of history is the most humanist of activities, and to that extent the following four papers contribute to the debate about the role of humanism in the Scientific Revolution. As Owen Hannaway wrote in this journal, "humanism and science, like science and religion, form one of those subjects that invite periodic reassessment."7 It is a subject which has, perhaps, [End Page 35] become less urgent in recent years. The so-called antagonism between humanism and science was most evident when historians identified Renaissance science with astronomy and mathematics—subjects which, it is true, many humanists from Petrarch to Erasmus dismissed as petty-minded and reeking of the scholastic classroom. Even so, scholars who worked in these fields found much that humanism contributed even to the "hard" sciences—most importantly in the editing and translation of Greek scientific texts.8 

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As historians' interests have extended beyond astronomy and mathematics to natural history in particular, as well as to "pseudo-sciences" such as alchemy and magic,9 the problem of humanism has all but vanished, in part because humanists themselves found such fields natural. Further, a more nuanced view of humanism itself has taken root, whereby humanism cannot be conveniently separated out as just one of the factors influencing a scientist or a scientific text, whether for good or ill.10 It was neither an ideology with a particular stance towards the world and humanity's place in it (as Burckhardt had it), nor did it in practice turn young boys into virtuous orators , "good men speaking well" (as the humanists themselves advertised the goal of their teaching) who would have little use for mathematics and the sciences.11 Rather, humanist education instilled a range of mental habits and (just as importantly) techniques for reading, gathering information and putting it to use, which were the common scholarly foundation of all writers in this period, whether they were reading history itself,12 or investigating natural philosophy13 —or even magic [End Page 36] and alchemy.14 In a survey article in this journal, Ann Blair and Anthony Grafton reminded us of the continuing work in this field, while warning us against taking too literally the claims of practitioners in the new disciplines that they had shaken off the baleful influence of humanism and made themselves over anew.15

The papers in this forum provide a new approach to considering the relationship which humanist culture had with the emerging new sciences. The histories considered here are clearly not stories of opposition; nor, however, are they straightforward examples of humanist research in practice. Peter Ramus's Aristotelian opponent Jacques Charpentier accused him of plagiarizing his influential history from Johannes Stadius's Tabulae Bergenses, a claim which, despite Charpentier's personal animus against Ramus, seems to have some merit.16 Henry Savile, another opponent of Ramus, cribbed much of his history (itself critical of Ramus) from the French philosopher. The histories of magic outlined in Kassell's paper again draw second-hand on well-established narratives of disciplinary history. Such histories do not fit easily into the modern scholarship on Renaissance historiography, with its emphasis on the role of antiquarian research and the development of the notion of the fact (even though some of the same authors, such as Savile and, arguably, Ramus, were important contributors to this kind of historiography as well). The papers presented in this forum suggest, however, that it was in part the very ubiquity of the historical narratives that helped to establish and define the disciplines within a wider intellectual community. The authors' hermeneutic interventions constituted their originality, and were their means for fashioning a distinctive response both to external criticisms and to internal issues of the material and organization of their arts. 

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In general, then, the "facts" themselves were not in question. Most authors from this period agreed on a few fixed points: that, for instance, the earliest Hebrew patriarchs had an excellent knowledge of the arts, and that they preserved their discoveries from the Flood by inscribing them on stone and brick pillars; or that Abraham, "planter of mathematics" (as Gabriel [End Page 37] Harvey marginally honored him) played an important role in transmitting the sciences to other cultures. In hunting down the prisca scientia, their beliefs were underlined by the testimony of Josephus, as well as the mind-boggling detail provided in Annius of Viterbo's forged chronicles of ancient history. They may have molded their narratives to make their larger points, but there can be no doubt that most trusted the broadly-agreed accounts of origins.

Substantial divergences from this standard narrative were made with explicit and usually polemical intent. Rheticus, for instance, insisted quite idiosyncratically that the origins of astronomy were to be found in the construction of obelisks;17 while Popper's article below demonstrates Pico della Mirandola's historical creativity in rejecting claims to the great antiquity of astrology. It is arguable also that Paracelsians such as Richard Bostocke (in his 1585 work The difference betwene the auncient Phisicke . . . and the latter Phisicke) were engaged in the construction of a new historical narrative,18 sharing a common physicians' concern with history and the search for causes for contemporary phenomena.19 Their accounts could diverge widely from the broadly-accepted narrative found in most of the authors considered here.

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Claims to antiquity—whether for mathematics, astronomy or magic—were an essential element in demonstrating the legitimacy and dignity of a science. But it also placed the historian-practitioner in an awkward situation. While it may be impressive to discover the sciences being practiced in the Garden of Eden, taught to the first human beings by God Himself, what room is then left either for individual accomplishment or (and this is most important) the extraordinary achievements of the Greeks?

Here, arguably, the historian of magic was in a happier position. Magical texts have always delighted in impossibly antique claims, and the practice of magic itself—although continuously improvised and transformed—put enormous emphasis on stasis: the preservation of every step of every ritual, down to the letters themselves of the barbarous magical words. Woven into the very documents used by historians were promises of the original and divine nature of their contents. It is not surprising that Thomas Vaughan could take over the traditional account of the origin of the arts in [End Page 38] Paradise—and even borrow the brick and stone pillars, now as repositories of occult learning—since his art owed not only its legitimacy and dignity, but also its efficacy to the very fact of its continuous preservation. Even Vaughan, however, had to explain the periodic disappearances of magic, invoking human forgetfulness (just as Ramus had done for the history of mathematics), while John Aubrey explained that fairy-folk (or, perhaps, belief in them) had taken flight at the noise of technology.