Why is there still a lot of unsolved math problems, despite having really advanced computers?
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A lot of unproved hypotheses are of the form “There exists no number for which the property X is true” or “Property X, which applies to every known number so far, actually applies to every number.”
For example, the Collatz conjecture is that every integer is part of a hailstone sequence without looping. No matter how strong your computer is, it can’t test whether that is true of every number, individually. It’s an infinite amount of work.
The trick in mathematics is often rephrasing the problem in a different way, so that it becomes a finite amount of work to prove. Maybe computers will one day be advanced enough to help us with that aspect as well, but they aren’t there yet, except for really simple examples.
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