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the division between the more geometrical or "physical" perception of mathematics and the "pure" or abstract and more algebraic runs very deep. I remember readi
by college_physics 4y ago
the division between the more geometrical or "physical" perception of mathematics and the "pure" or abstract and more algebraic runs very deep. I remember reading somewhere about a 19th(?) century mathematician bragging there was no figure in their book.
most likely the debate reflects two distinct modes our brain is handling mathematical notions, and different people being more adept in one or the other
anybody who went through V.I.Arnold's mathematical methods of classical mechanics has no doubt which way his brain works :-)
- KrugerDunnings 4y agoThere is similar anecdote in the documentary The man who saved geometry[1] about the life of the famous geometer Coxeder. The Bourbake school was in a response to the disaster of the Italian school of algebraic topology which put a lot of focus on rigor and formal proofs vs the hand waving Italians. They where good in reforging existing proofs but when it came to imagining new ideas it where the visual and experimental mathematicians who kept pushing the needle forward. [1] https://www.youtube.com/watch?v=drZEPzb3JY0 https://www.youtube.com/watch?v=drZEPzb3JY0