Richard Feynman has a really good video lecture on this (https://youtu.be/0KmimDq4cSU). Basically scientists make a guess, then check if it was right. The guess isn’t completely random; it’s based on known data, and they try to find an equation/model that fits that data. This has become easier with tools like excel, Matlab, etc where you can directly plug in data points and have it find a curve that fits the data.
Alternatively, many useful equations can be derived directly from previously known equations, strictly by using math like trig, calc, diff eq, etc.
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