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Author Topic: THE RENAISSANCE  (Read 5099 times)
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« Reply #105 on: October 17, 2008, 09:08:30 pm »

Like his conception of the history of mathematics, Regiomontanus's vision of its utility is linked to mathematical practice. The outward sign of philosophy's lack of certainty is manifest in the state of contemporary scholarship, namely the endless warfare between the followers of various authorities. Mathematics, on the other hand, suffers from no such divisions. The truths offered by mathematics make the idea of rival camps of "Euclideans" and "Archimedians," as philosophy has its Thomists and Scotists, absurd. Both men's theorems have stood the test of time and, Regiomontanus assures his audience, will continue to do so for "a thousand centuries." Likewise, the implication of juxtaposing a revived Aristotle's presumed inability to understand the work of his followers with the continuing certainty of Euclid's theorems is clearly that Euclid, were he to rise from the grave, would have no trouble understanding his disciples: Regiomontanus and his fellow mathematicians, who continue to build on the certain foundations that he established. The practice of mathematicians, like that of philosophers, relies on the use of authorities, but for mathematicians, this reliance is progressive and cumulative. Geber of Spain can be the "corrector of Ptolemy" and Jordanus can use the number theory in Euclid to produce his own De numeris datis without causing rifts among mathematicians. Certainty is the tie that binds ancient, medieval, and contemporary mathematics together.

In the end, Regiomontanus's vision of mathematics is that of a mathematician, rather than that of a historian, an educator, or a philosopher. It is simultaneously humanist and deeply rooted in the traditional university curriculum because a mathematician can (and for Regiomontanus, probably should) be both of those things. Above all, it is rooted in mathematical texts, both curricular and extra-curricular.   
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