The essence of mathematics lies precisely in its freedom. This statement from Georg Cantor is quoted so very often, and perhaps this is because of the surprise coupling of the words mathematics and freedom, or because of the implications of the word essence, which calls to mind other words like intrinsic, inherent or something that […]
|
|||||
|
I would like to go back today to Riemann, and the significance of his generalized notions of space and magnitude, but with an eye on what neuroscience may be adding to how mathematics gains its effectiveness. In a recent post, I pointed to the influence the philosopher Herbart had on Riemann’s 1854 lecture in which […] 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 […] I’ve been spending a lot of time reading about the significance of Riemann’s Habilitation Dissertation and, today, a little bit of looking into the pervasive human desire to generalize led me yet again to Plato. I keep thinking that a closer look at what Plato actually said is consistent with even the most brain-based thoughts […] Here is an excerpt from a piece by Alain Connes in The Princeton Companion to Mathematics: It might be tempting at first to regard mathematics as a collection of separate branches, such as geometry, algebra, analysis, number theory, etc., where the first is dominated by the attempt to understand the concept of “space,” the second […] For me, one of the more intriguing things that happened in mathematics is what is called the arithmetization of the Calculus. This is not because it contributes to my understanding of fundamental concepts (because it doesn’t). Nor is it because the ideas are exotic (they’re not). I’m captivated, instead, by what it may demonstrate about […] I’ve thought that one of the reasons it’s difficult to resolve questions about the nature of mathematical reality is that we’re not exactly clear on what it means to ‘perceive’ something. Trying to establish whether or not even the data of our senses is somehow independently ‘real,’ has fueled centuries of philosophical debate. I found […] |
|
||||
|
Copyright © 2024 Mathematics Rising - All Rights Reserved Powered by WordPress & Atahualpa |
|||||
Recent Comments