How in the world was math discovered? Who/what dictates what sort equations work and stuff?
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I’d highly recommend the book “mathematics for non mathematicians” it walks through basically the whole history of how and why… What problems people had that they kept inventing new math to solve, or new observations that required new math to describe…
I think it basically starts with commerce… Tracking who bought/sold how much of what to whom and who paid or still owes how much
If you start generalizing and want some math to define the relationship between thing you get algebra pretty quickly which is good for figuring out weights, volumes, or dimensions of things given partial information… Which is super practical for everyday life… Cooking, shipping, storage…
Later on when Newton started figuring out gravity, he started running into situations where values affect each other over time… Two things get closer, which increases the pull, which brings them closer faster, which increases the pull faster… And I think previously people addressed these sort of problems by dividing up the time into steps… Crunch the numbers for each step and you get pretty close like tracing someone’s path on gps… if it reported every hour you’d get a pretty rough, angular trail. Vs if it reported every minute, that’d be better, vs every second you’d get pretty close… But Newton figured out how to use an infinite number of steps to get the true answer, and this is the jist of calculus… It let’s you get true answers for systems where the values that are changing affect each other over time (among many other uses)
There’s a bunch more, like, it seems obvious to me that fractions and decimals make sense, being able to describe partial things… And that negative numbers make sense… Being able to talk about a lack of something, or debt? But it took people a long time to figure out they needed a 0 in their number system, let alone negative numbers… Then there a whole story about why imaginary number exist and the journey to proove they’re useful for real-world applications and not just a quirk that looks like you broke math…
But there’s also always some math that mathematicians have discovered but seems like nonsense until we find a way to apply it to describe real world phenomena… But historically, we tend to find one eventually
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