system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: How Mathematicians know that they've correctly solved a complex math equation when other equally skilled mathematicians cannot?

So I was reading the Wiki on Ted Kaczynski, the unabomber, but also a math genius in his own right. I read that he was so good at math that he was able to solve a problem even of the top professors could not. But how do they know what the correct answer is? Because it makes Math sense? 

Also note, and probably obvious, I am terrible at math and its never clicked with me but how can someone have crazy crazy math equation that no one can solve but someone comes along and is like "HA, 2+2=4, not 2+2=5!". If you understand where I'm coming from...
gpt
Here's an analogy. Let's say you're trying to find the solution to a very difficult maze. Everyone might be stuck trying to find their way out, but you're the first to find the solution. How do we know your solution is correct? You showed us the path - it's easy to verify that the path is correct, even though *finding it* is hard.

It's the same in math - finding a solution is hard, verifying it's correct is easy.

Another example is Sudoku - it's hard to solve, but checking whether a solution is correct is easy.

It's true that more difficult math problems might be more difficult to validate, but it's still easier to validate the correctness of a solution (typically a proof) than to find it in the first place.