Ask again, with another famously unsolved math problem. Repeat until it stops saying that or you run out of problems you know.
If you ran out, ask the entity to choose a famous math problem not yet solved by human mathematicians, explain the problem to you, and then give you the solution including an elegant proof.
Next time you have internet access, check whether the problem in question is indeed famous and doesn’t have a published solution.
If the entity says “there are no famous unsolved math problems with elegant proofs”, I would consider that significant empirical evidence that it isn’t what it claims to be.
Depending on your definition of “elegant”, there are probably no famous unsolved math problems with elegant proofs. For example, I would be surprised if any (current) famous unsolved math problems have proofs that could easily be understood by a lay audience.
Ask again, with another famously unsolved math problem. Repeat until it stops saying that or you run out of problems you know.
If you ran out, ask the entity to choose a famous math problem not yet solved by human mathematicians, explain the problem to you, and then give you the solution including an elegant proof. Next time you have internet access, check whether the problem in question is indeed famous and doesn’t have a published solution.
If the entity says “there are no famous unsolved math problems with elegant proofs”, I would consider that significant empirical evidence that it isn’t what it claims to be.
Depending on your definition of “elegant”, there are probably no famous unsolved math problems with elegant proofs. For example, I would be surprised if any (current) famous unsolved math problems have proofs that could easily be understood by a lay audience.