Comments by "" (@tinkeringtim7999) on "Визуализация теоремы Пифагора: лучшие доказательства и неожиданные повороты" video.

  1. That last hyperdimensional proof is an astonishing insight, thanks so much! Does the fact that modern mathematics doesn't seem to worry about whether or not mapping a plane to a line is with or against the logical ordering of which fact supports the other in a proof? In my mind there's something very deep in the Greek insistence that comparing lines built by ruler and compass was entirely different from shapes made by cutting/rotating/joining. The fact the wellspring of modern mathematics can be traced back to essentially sweeping all that under the rug in exchange for apparent utility does not sit easily with me. In particular, if we take seriously that they had a point (look how critical dimensional analysis is to applications), then suddenly some proofs are true and others are not, which amounts to at least two (three by my count) ways of carving mathematics into naturally distinct sets, rather than just the pedagogical/apparent distinct sets of geometry/algebra/analysis we are used to. It appears to me; doing so and then carefully establishing the cases in which they can be viewed as mutually consistent, would be an extraordinarily fruitful programme to develop a rational/algorithmic map of the structure underlying mathematics since Pythagorus. I'm often left wondering why that isn't already a centrepiece of research in philosophy and foundations/structure of mathematics.
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