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> Mathematics is by far the biggest and longest running open source project on this planet and we are absolutely able to traverse it by centuries or millenia. T

> Mathematics is by far the biggest and longest running open source project on this planet and we are absolutely able to traverse it by centuries or millenia. This works across languages and cultures. This goes against what I understand about mathematics. I've tried to break it into a few sections. Open source: Things in mathematics once defined, tend not to change, even when changing would be beneficial. Open source software tends to be a bit more malleable, but even long running things that can't change for fear of breaking things like POSIX or the X Window System end up getting alternatives that the industry slowly turns towards. But mathematics just stays stuck. Multiple subfields will end up using the same glyph to mean two different things and when those subfields intersect it gets very bad very fast. Even small quality-of-life fixes never end up getting accepted into use. Here's a great example by 3Blue1Brown: https://www.youtube.com/watch?v=sULa9Lc4pck https://www.youtube.com/watch?v=sULa9Lc4pck Another example (if you're interested in going down a bit of a rabbit hole) is the history of vector algebra vs quarternions. We ended up going with vector algebra, then learned that quarternions were actually better, but we continued to teach / and be taught vector algebra. > we are absolutely able to traverse it by centuries or millenia Well, this seems easy to disprove since knowledge does get lost and things keep getting rediscovered. For example, Calculus was rediscovered multiple times: - Archimedes (at least part of it with his method of exhaustion) - Leibnitz / Newton (separately) - and recently: medical doctors rediscovering integration and publishing papers on it in the 90s. Other famouse examples would be Fast Fourier Transform, and perhaps Fermat's Last Theorem

wwweston 5y ago
> We ended up going with vector algebra, then learned that quarternions were actually better Wait, what? I'm still mostly familiar with assessments like "Quaternions... have been an unmixed evil to those who have touched them in any way" and "quaternions appear to exude an air of nineteenth century decay" (but not actually familiar with quaternions beyond a vague understanding of them as kind of 4d version of complex numbers).
epolanski 5y ago
> Things in mathematics once defined, tend not to change, even when changing would be beneficial. Can you provide an example? Mathematics definitely change as soon as someone provides a proof that something isn't correct.
- rocqua 5y ago
  This is not about correctness but about ergonomics and clarity. Consider the 'standard' definition of the complex numbers, whilst we know there are more intuitive options. Consider tau vs pi. And how hard it is for anyone to write mathematics based on tau. Consider the rather lacking notation for probability with conditionals.

wwweston 5y ago

> We ended up going with vector algebra, then learned that quarternions were actually better Wait, what? I'm still mostly familiar with assessments like "Quaternions... have been an unmixed evil to those who have touched them in any way" and "quaternions appear to exude an air of nineteenth century decay" (but not actually familiar with quaternions beyond a vague understanding of them as kind of 4d version of complex numbers).

epolanski 5y ago

> Things in mathematics once defined, tend not to change, even when changing would be beneficial. Can you provide an example? Mathematics definitely change as soon as someone provides a proof that something isn't correct.

rocqua 5y ago
This is not about correctness but about ergonomics and clarity. Consider the 'standard' definition of the complex numbers, whilst we know there are more intuitive options. Consider tau vs pi. And how hard it is for anyone to write mathematics based on tau. Consider the rather lacking notation for probability with conditionals.