Peter Ramus (1515-72) was, at first sight, the least likely person to write an influential history of mathematics. For one thing, he was clearly no great mathematician himself. His sympathetic biographer Nicholas Nancel related that Ramus would spend the mornings being coached in mathematics by a team of experts he had assembled, and in the afternoon would lecture on the very same subjects.1 But there can be no doubt that Ramus held mathematics in particular esteem and even played a crucial role in linking philosophical discourse to mathematics and in promoting the use of quadrivial reasoning in the study of the world.2The origins for his enthusiasm for mathematics are to be found in his account of the nature of the arts and critique of the curriculum of the universities. From his earliest career, Ramus was a logician and remained one in all his works, whether writing on mathematics or Virgil, and he conceived of all the arts, especially mathematics, as unchanging structures of necessarily true propositions-not prima facie a position which lends itself to notions of historical change and development.3 His career as a historian of mathematics, I will argue, was directed by problems that arose in his theoretical understanding of mathematics as he began to immerse himself in the sciences of the ancient world.RAMUS AND THE REFORM OF DIALECTICRamus set out his fundamental logical positions in his very first printed work, the Dialecticae institutiones (Education in Dialectic) of 1543, a contribution to the ongoing humanist attack on scholastic logic, in which Ramus rehearsed many of the commonplace criticisms of the university dialectic. Humanists complained that logic no longer concerned itself with real human reasoning; instead, it had become a discipline studied for its own sake, using its own incomprehensible jargon, and was of no practical interest. The new humanist dialectics of Lorenzo Valla and Rudolph Agricola attempted to teach the kind of practical reasoning useful for composing a speech or letter, and they borrowed extensively rhetorical works of Cicero and Quintilian to develop a highly rhetoricized logic. Questions about the formal validity of arguments were of little interest; what mattered was whether the arguments were persuasive.4In his Dialecticae institutiones, Ramus took this humanist reformulation of dialectic a step further. Dialectic-or, in fact, any art or scienceconsisted of nature, doctrine, and exercise. The workings of the mind formed the most significant element. Doctrine was nothing more than a record of reasoning; in importance it paled next to nature and practice.5 The logic of the universities bore no resemblance to the true, dialectic, as he argued at length in the companion volume to the Institutiones, the innocuously titled but exuberantly offensive Aristotelicae animadversiones (Observations on Aristotle).6 The question, remained: how can we gain access to this natural reasoning?Ramus's answer was surprising. He asks us to find a group of mennot scholars, but completely uneducated vineyard workers. Question them about the coming year: the fertility of the soil, the quality and quantity of the crop. And then, he writes from their minds as a mirror an image of nature will be reflected.7 In the reasoned replies of these uneducated men, says Ramus, we discover every part of logic needed for any purpose, whether everyday discourse or composition of poetry: the invention of arguments, the assessment of their truth and their proper and orderly presentation. Other humanists had praised man's logical faculties, elevating them over artificial technique, but Ramus was the first to look beyond the walls of the university and the writings of the ancients to find dialectic at work.If even the uneducated have some possession of the arts, then the arts taught at the university should do no more than clear away the misleading junk in the mind, and allow its clarity to shine through. …