The oldest unanswered math problem known, based on (https://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics https://mathoverflow

The oldest unanswered math problem known, based on (https://mathoverflow.net/questions/27075/what-is-the-oldest-open-problem-in-mathematics https://mathoverflow.net/questions/27075/what-is-the-oldest-...), is whether there are any odd perfect numbers (= numbers that are equal to the sum of their divisors). It's been open for 1900 years. Math is very hit-or-miss; the complexity of a question does not give much of an indication about how complex the answer will be. Look up the formula for solving a degree-4 polynomial equation to get a purely visual idea how this can look (and then degree-5 suddenly forces you to use complicated new functions). And there are problems (like the Collatz conjecture or P vs. NP) that there doesn't seem to be any promising angle of attack for over at least decades. I would wager that this is a fundamental part of the structure of math that has been a constant from ancient Greece till LLMs. There are even some formal results, similar to Gödel's theorems, that say that the maximum necessary length of a proof grows arbitrarily fast (e.g. more than exponentially, double-exponentially, or any function with a formula) with the length of the statement being proven. Point is, math will most likely never suffer from this particular problem.