Why is there still a lot of unsolved math problems, despite having really advanced computers?
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In order to solve a problem, you need to show it’s true for **all** cases. Not just many, or most. You could check these one by one, but that would take about infinitely long. Take the Riemann Hypothesis, for instance. Long story short, there is a special function, called the Riemann zeta function, that has been conjectured to only have non-trivial solutions where the real part of the solution is 1/2. So far, we haven’t found a proof. We have found many, many many solutions to this function, but we haven’t found a way to prove all of them have 1/2 as the real part.
Now, that’s not to say that doing it via computer is irrelevant. Sure, you can’t prove it by doing it like that, but it’s possible to disprove it. After all, if there is even one solution where the real part is something else than 1/2, it’s disproven. And that’s as much of a big deal as proving it.
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