Eli5 what is math and how do we find math in space and stuff ?
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Math is an abstraction of observed and measured reality. We likely first learned to count apples and stuff, two for me two for you. By watching the stars we noticed patterns, which I can’t personally describe as I’m not an astronomer. This influenced how we do math, and by using our observations of the stars and assuming certain patterns would hold, we learned to navigate using them, finding our position on the planet using the sky. This is akin to triangulating your position with cell towers or GPS today.
To describe how we still find math in space, I’ll proceed by an example. A Hilbert space is basically an infinite dimensional vector space, and while that doesn’t mean much to me all by itself, it was developed by David Hilbert to compartmentalize certain pieces of special relativity to explain astronomical phenomena not sufficiently explained by Newton’s mechanics and elementary calculus. The Hilbert space also ended up being useful in quantum mechanics, measuring and predicting very small movements. It is in this spirit that mathematics is developed, designing (hopefully consistent) assumptions and following the consequences to phenomenal real conclusions.
The really neat part is that you can just work with math alone and still find phenomenal real conculsions. Grothendieck formed new foundations for mathematics to solve the Weil conjectures (an analogue to the Riemann hypothesis about the distribution of primes and prime powers), and what he (and many others) developed about modular forms led to the unexpected conclusion that for all n>2: aⁿ+bⁿ=cⁿ has no integer solutions in a, b, and c. That is, the Pythagorean theorem is only true for squares, not cubes, ect. At the same time, he formulated the idea of a topos, which is now the foundational structure of logic. He actually did quite a lot to solve those conjectures, and more applications of his work are found every day, in computer science especially.
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