think about convergence but sometimes you really have." Sinai Robins (colloquium suny Binghamton 3/14/02) "I like to think of mathematicians as forming a nation of our own without distinctions of geographical origin, race, creed, sex, age or even. But the choice of a geometric system is not an arbitrary convention. . Die Wurzel aus 1 kann logischerweise nicht 1 sein, weil die Wurzel aus einer Zahl kleiner sein muss als die Zahl selbst. Therefore: There are patterns everywhere in nature." Max Cohen (played by Sean Gullette, in Pi, a film by Darren Aronofsky) "To many, mathematics is a collection of theorems. The contention that any sort of dispute with Mittag-Leffler would be an unlikely reason to leave mathematics out, simply because there were other mathematicians who might win the prize before him, is also inadequate in its reasoning: even if other mathematicians would get it first. Nobel, an inventor and industrialist, did not create a prize in mathematics simply because he was not particularly interested in mathematics or theoretical science. But, Poincar objects, there will be no such consistency proof without induction. . In this way, despite the fact that Poincar was a constructivist, he did not regard all mathematical definitions as constructions. . By David Archard (Cambridge, 1996).
In this way, Poincar's Kantianism about pure mathematics is supported by a Darwinian conception of human evolution a picture that enables his philosophy of mathematics to coexist with his diverse views about natural science. Recommended Reading: Dominic. Auf dieser Sinnlosigkeit, der 1, bauen sich dann alle Werte auf, und in diesen falschen Werten fusst die mathematische Wissenschaft, die 'einzig exakte, unfehlbare'. Do some solutions form closed loops? Intuitive space provides much of the a priori synthetic content for geometry (which is Euclidean for Kant and intuitive time provides the a priori synthetic content for quantitative mathematics. . 35) "1/r2 has a nasty singularity at r0, but it did not bother Newton-the Moon is far enough." Edward Witten (AMS Gibbs Lecture, Baltimore, Jan. (This at least is the natural reading, but not the only possible one.) A final speculation concerning the psychological element. Hence, careful thought about the fundamental nature of the world, the grounds for human knowledge, and the evaluation of human conduct. His point is that when articulating a theoretical framework for a given base of evidence there are almost always alternatives. .