How does new math get invented/discovered?
In: Mathematics
To really get a feel for this it’s probably best to go looking for the specific stories of how specific new concepts were invented, because it’s a little different every time. Sometimes math techniques are invented in order to try and solve a specific real-world problem.
Calculus, for instance, was first invented for the purpose of understanding planetary orbits and figuring out how gravity worked. Newton and Leibniz both, were looking for ways to understand the motion of things whose speeds were always changing, and changing by an amount that’s *also* always changing. It turned out to be useful in a ton of other ways too.
Early geometry was, in great part, a science developed for the purpose of mapping and measuring the Earth. Hence the name geo=earth, metry=measurement.
Some math just kinda suggests itself as a by-product of the practical stuff we do all the time. The ideas of prime and composite numbers and divisibility, for instance, would arise naturally from an everyday problem like “can we share x apples fairly among y people?” … “Oh jeez weird, it seems like 23 apples can’t be shared fairly no matter what, *unless* you have exactly 23 people. Sharing 24 apples yesterday worked great, so what the heck is wrong with 23?”
Sometimes math is discovered by mathematicians exchanging guesses about what they think might be true, called conjectures, and trying to prove each other right or wrong. A famous one called Goldbach’s conjecture was the result of a pen-pal correspondence between Goldbach and Euler.
Sometimes new math is discovered through play. Sometimes mathematicians – or just regular folks doodling with pencils – just idly put different mathematical structures together, just to see if they add up to anything interesting, and sometimes they find patterns which they weren’t expecting and don’t know how to explain.
Some math is just kind of inevitable, and impossible to avoid. Numbers like pi and e, for instance, show up in *so many places* that we basically couldn’t have *not* discovered them.
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