Eli5 what is math and how do we find math in space and stuff ?
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Math is a huge field. It includes, among other things, the study of the properties numbers, shapes (geometry), formulas (algebra), and how numbers change (calculus) plus lots of other more esoteric things.
We “find” math by studying it and studying that it will/won’t do. It’s not at a physical location, we don’t find it in space, but we can find physical things in space that we can try to use math to describe, or even predict, and that helps increase both our understanding of the physical universe and, sometimes, math.
Math is patterns. Patterns that are self-consistent and that describe things well.
We notice that if you have one thing, and you add one more thing, you have two things. So we write that down as “1+1=2.” That’s a pattern, it’s what happens every single time. So we collect more and more patterns, and we make sure that none of them contradict each other (e.g. “1+1=2” and “1+1=3” can’t both be true, so we throw one of them out).
And these patterns are useful because they accurately describe real events. It’s less that we find math in nature, and more that we define our math to match what happens in nature. As our patterns get more and more complicated, we go check space and stuff to make sure that it all still matches.
Math is simply the way humans have devised for measuring and predicting relationships between numbers. By itself, math isn’t terribly useful, but people have found countless ways to integrate mathematics into numerous facets of everyday life. Science and engineering for example rely heavily on being able to measure and predict things, so math is heavily used in these fields.
For example, in general, we know math equations for what happens when you apply a force to an object. Depending on where you push and how hard you push, you’ll get different movement. You can use math to predict what will happen to an object before you actually act upon it. This is especially useful for anything dealing with space, as stuff like rockets, probes, and space telescopes are incredibly expensive. So a team of engineers trying to get something in space to go where they want and do what they want will do a whole bunch of math to determine when to launch, what direction things need to be headed and at what speed so the thing can get in position without a whole lot of expensive trial and error.
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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