How are complex mathematical equations “invented”? As in, how do you come up with the formulas and know definitively the answers to them are correct?
In: Mathematics
You take a lot of measurements. You plot the data. You look for trends, and you find the equations that describe those trends. You then look at what the equation says about measurements you haven’t taken. Those are predictions. Then you go do an experiment that lets you take that measurement and see if it agrees with the prediction. If it does, then you have support for your equation. If it doesn’t, then you have more data to refine your equation. Eventually you get to where you’ve got an equation that only has support and nobody finds a contradiction. At that point, it’s presumed to be correct. But it’s never definitively known that it’s correct, at any time a contradictory observation can nullify it (or require further refinement).
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