If math is a such a definite subject with solid answers, how are there still unsolved math problems? How do people even come up with them?
In: Mathematics
There’s a big difference between solving a math equation and solving a generalized math problem
If you have 2 + X = 7 you can solve for X this one time and know that right here, right now, it must be 5
But the unsolved problems are wayyy harder than that. Fermat’s Last Theorem was unsolved for a few hundred years it goes “For any integer n>2, the equation a^n + b^n = c^n has no integer solutions”
You’re probably already familiar with the case of n=2, that’s a^2 + b^2 = c^2 or Pythagoras’s Theorem. But how do you prove that for n>2 there are no integer solutions? You could try brute forcing it but what if it works out when n=51,437? You’d have to try literally every combination of numbers which is, by definition, infinite
Its problems like these that you can’t just set a computer to and crush through the numbers, you have to fall back onto the basic properties of math and other postulates and theorems to show that there is no way that any n>2 results in a, b, and c all being integers. These are the hard ones that require people and hundreds of sheets of paper to prove.
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