There are some math problems with that are simple to ask but very difficult to solve. For example
https://en.wikipedia.org/wiki/Four_color_theorem You need a long explanation to reduce the problem to only a thousand of cases, and then you can test the thousand of cases with a computer or write the solution of each case if you are brave enough.
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem You replace the original integer numbers with integer complex numbers and get a solution for small n. But for big n you realize some properties of factorization don't work anymore, and then have to write a few books of algebra and then understand the conection with eliptic curves (whatever they are [1]) and modular forms (whatever they are [2]) and then write another book just to prove the tricky part of the theorem.
[1] I studies eliptic surves as a small part of a course, only for two or three weeks. I'm not sure how they are conected with this.
https://en.wikipedia.org/wiki/Four_color_theorem You need a long explanation to reduce the problem to only a thousand of cases, and then you can test the thousand of cases with a computer or write the solution of each case if you are brave enough.
https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem You replace the original integer numbers with integer complex numbers and get a solution for small n. But for big n you realize some properties of factorization don't work anymore, and then have to write a few books of algebra and then understand the conection with eliptic curves (whatever they are [1]) and modular forms (whatever they are [2]) and then write another book just to prove the tricky part of the theorem.
[1] I studies eliptic surves as a small part of a course, only for two or three weeks. I'm not sure how they are conected with this.
[2] I have no idea what they are.