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I ventured down a series of paths today, no doubt related, but with no quick and easy way to tie them together. So I decided to invite you to look with me and let your mind play. I started with a couple of talks at a recent at a recent Foundational Questions Institute conference on […] Today, I was working on a piece I’m writing about 19th century developments in mathematics and I saw something interesting. In the piece, I draw particular attention to a few things. One of these is the precision Weierstrass brought to the concept of a limit, removing all references to motion or geometry, and giving it […] Some of George Berkeley’s fame comes from his vehement critique of Newton’s calculus. His criticism was harsh and inspired a number of responses from contemporaries who accepted the vanishing quantities Newton used to formulate his notion of fluxions or, in modern terms, his understanding of instantaneous rates of change. The discussion that followed Berkeley’s 1734 […] I don’t think it’s actually possible to answer the question in the title of this post, but I still believe it’s worth asking. We’ve thought of things ‘hidden under a microscope,’ or obscured by great distances, but in mathematics when something is hidden, it’s because we haven’t been able to imagine it yet. And when […] Mathematics today can seem an isolated discipline, removed from the questions of life and questions of meaning. But even a brief look at some of the writing of individuals like Leibniz, Weyl, and Poincare demonstrates substantial interest on the part of the mathematician to reconcile mathematics with common human experience. I remember one of my […] When I looked recently at Riemann’s famous lecture On the Hypotheses which lie at the Bases of Geometry, I gave some attention to this remark: besides some very short hints on the matter given by Privy Councillor Gauss in his second memoir on Biquadratic Residues, in the Göttingen Gelehrte Anzeige, and in his Jubilee-book, and […] |
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