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I agree with virtually everything he says about teaching (this is ironic because I really hated his ODE lectures as a student). But the idea of "mathematics is
by pixcavator 17y ago
I agree with virtually everything he says about teaching (this is ironic because I really hated his ODE lectures as a student). But the idea of "mathematics is a part of physics" isn’t well justified in the article and is, with all due respect to such a luminary, ridiculous. Instead of dozens of examples we all can think of here’s my own: I am working on applications of topology in computer vision and data analysis. No physics in sight! His attitude toward proofs (outside teaching) is also very odd.
- sandGorgon 17y agoi think what Arnold is trying to convey is mathematics needs to be "learned" intuitively, rather than in an abstract manner. Pure mathematics may, however, be practiced (though one can argue that intuition will continue to play a significant role ) The essential bit is about being able to visualize a mathematical concept, before being able to express it in mathematical language. For example, I think the visualizations of sorting algorithms give a intuitive understanding of how something should work, that you will be able to see quicksort in your mind, before you code it up. Physics can easily be interchanged for computer vision as a tool for aiding in mathematical intuition. Learning is hard, practice is easy.
- pixcavator 17y ago>Physics can easily be interchanged for computer vision as a tool for aiding in mathematical intuition. I came from topology to computer vision, not vice versa. This experience showed to me (as if I needed another proof) the "unreasonable effectiveness" of abstract(!) mathematics.