In lieu of an abstract, here is a brief excerpt of the content:Abraham, Planter of Mathematics":Histories of Mathematics and Astrology in Early Modern EuropeNicholas PopperFrancis Bacon's 1605 Advancement of Learning proposed to dedicatee James I a massive reorganization of the institutions, goals, and methods of generating and transmitting knowledge. The numerous defects crippling the contemporary educational regime, Bacon claimed, should be addressed by strengthening emphasis on philosophy and natural knowledge. To that end, university positions were to be created devoted to (...) "Artes and Sciences at large," rather than to the professions. High salaries would render lecturers "able and sufficient," undistracted from their task. Most famously, he argued that teaching of the "operatiue studie of many Scyences" should involve sophisticated technical education. The study of natural philosophy demanded not only books, but globes, astrolabes, and other "instrumentals." Most significantly, yielding reliable and meaningful knowledge from experiential gleanings required a rigorous system of deductive reasoning.The legacy of this colossal proposal has earned Bacon honored status as devisor of the scientific method.1 But Bacon's educational reform extended [End Page 87] beyond the methods of producing and transmitting knowledge. To facilitate more efficient "vse and administration" of the knowledge produced by his system, he also demanded a searching examination of the history of learning. This history would provide a mirror enabling his contemporaries to deploy the fruits of his method, by considering how learning in the past had been used successfully or ill-advisedly. Producing this history was the ambition of the Advancement, for he explained: "no man hath propounded to himselfe the generall state of learning to bee described and represented from age to age, as many have done the works of Nature, & the State civile and Ecclesiastical." He continued:And yet I am not ignorant that in divers particular sciences, as of the Iurisconsults, the Mathematicians, the Rhetoricians, the Philosophers, there are set down some smal memorials of the Schooles, Authors, and Bookes: and so likewise some barren relations touching the Invention of Arts, or usages. But a iust story of learning, containing the Antiquities and Originalls of Knowledges, & their Sects; their Inventions, their Traditions; their diverse Administrations and Managings; their Flourishings, their Oppositions, 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 be wanting.2Bacon thus positioned himself not only as a Father of Modern Science, but also 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 of astrology—in the sixteenth and seventeenth centuries. My conclusion, however, will not bear out Bacon's claims. Despite his frustration, Bacon was only one of many early modern scholars appraising the role of mathematics within history. And he devoted less energy than others to mapping its origins and tracing its transmissions between communities. In fact, Bacon's 1605 proposal for a history of mathematics was already out-of-date. Discussions [End Page 88] of the history of mathematics had been rife on the continent and in England throughout the previous century.3The evidence that Renaissance scholars inherited was sprawling and inconclusive. Several genealogies for mathematics could be found within classical Greek, Latin, and patristic references. One lineage claimed mathematics began in ancient Assyria, where the priestly caste, the Chaldeans, practiced a form of mathematics that seemed a corrupt admixture of philosophy, medicine, and religion, and relied heavily on observation of the heavens. Other scholars traced the origins to Egypt, claiming that the field developed to survey lands frequently flooded by the Nile. The real problem for ancient, late antique, and medieval scholars had not been the origins of mathematics, but what exactly mathematics were. For some, the term strictly referred to the quadrivium: geometry, arithmetic, astronomy, and music. But for others, mathematics' origins amongst the Egyptians or Chaldeans inextricably linked it to forms of astrological divination, augury, and necromancy that were unsavory to both Latin and Christian traditions. Mathematici were included alongside ghastly lists of Magi, Brahmins, Aruspices, Genethliaci, and other diabolic practitioners of idolatrous magic. These might or might not be distinguished from mathematici such as Pythagoras... (shrink)

In lieu of an abstract, here is a brief excerpt of the content:The English Polydaedali:How Gabriel Harvey Read Late Tudor LondonNicholas PopperHarvey and GauricoIn 1590 Gabriel Harvey read his copy of Luca Gaurico's 1552 Tractatus Astrologicus, a collection of genitures and commentaries for cities and individuals.1 Harvey had spent the previous twenty-five years at Oxford and Cambridge, mastering Greek and Latin, earning renown as a rhetorician, and promoting English letters. He was a well-known partisan of the French Calvinist Peter Ramus, (...) whose works on curriculum reform had sparked vicious [End Page 351] controversies in the English universities. But Harvey read Gaurico far removed from the schools where he had acquired fame and notoriety as an orator and poet. He had recently relocated to London, where he daily faced a dense, active city unlike his native Saffron Walden and the university towns. Nevertheless he read as he always had, carefully recording his reactions in the margins of the printed text, filling blank spaces with his own commentaries on the subjects presented by Gaurico. The notes disclose an experience of reading that intervened in contemporary debates regarding technology, astrology and utility.2 They also place Harvey among a group of scholars in London in the 1590s, such as Francis Bacon and Hugh Plat, who were examining the benefits local artisans might offer the commonwealth and reconsidering the intellectual status of craft knowledge.Harvey read and annotated Gaurico on several occasions, but the particular strain of notes that I will follow, united by a common ink and hand, engages the learning and erudition of Gaurico's subjects.3 Concentrated almost [End Page 352] exclusively in Book Four, which discussed learned men, these annotations evaluate the poets, philosophers, philologists, and others whom Gaurico had canonized as especially learned.There are only spare annotations prior to Book Four. On the title page of Book Two, devoted to churchmen, Harvey observes the quality of the individuals Gaurico presented and details his own method of evaluation:The most excellent Exemplars of this century [are] in Gaurico, and Cardano: Giovio, and Guiccardini. There are as many of the wisest men as of the greatest actors. Still others live, whether inferior, equal, or superior. And it is of interest to every skillful artificer, to know those most outstanding in their class, and the most celebrated professors of all. Certainly it is very profitable to observe exquisitely the most perfect artificers either of the world or of neighboring nations, or at least of your own people, and to consider with most cunning reason what it is, where it comes from, and what is most excellent. But seriously, and solidly, and always to the point, seeing that singular things are efficacious and are useful to polytechnoscopy. It is judicious to avoid all trivial detail, and to consider only the most pregnant theorists and practitioners of operating.4The notion of a sophisticated form of active knowledge labeled "polytechnoscopy" is the most striking element of this passage. This term seems to have been Harvey's own invention, with no direct precedents; nor was it adopted or used by others after him.Harvey repeatedly referred to polytechnoscopy in his notes. A carefully designed triptych annotation on the title page of Book Four clarifies it as a category uniting practice and knowledge. To the left Harvey wrote, "it is my task to observe the most excellent examples of this age which are useful for polytechnoscopy." On the right, "a polytechnic, polymechanic, polydaedalic, and almost panepistemic book; and likewise sufficiently polychristian. For philologists should be skimmed through; while polytechnics should be examined closely; as I did not only in the Lives of Giovio, but also in those of [End Page 353] Laertius, Eunapius, Philostratus, and others."5 The related Greek descriptors "polymechanic" and "polydaedalic" shed further light on polytechnoscopy. This constellation of terms refers to a method of garnering information by deploying technical knowledge. While not a systematic discipline, its practices—active applicability, craft expertise, observation of experience—constitute a significant realm of learning.In the central panel of the triptych, Harvey notes:[I] compared [this] to Giovio's Elegies of Learned Men. Give me the best man outdoors, and his image at home. For even true life is... (shrink)