I made problems for Math Olympiad, mostly for kids 10-12 y.o., but also some for older students.
For kids, it's hard because it must be interesting and not too hard, mix some interesting math concept and some hidden part that makes it an interesting puzzle.
For a Millenium-like problem it's harder, because it must be interesting so mathematicians care about it, it must be hard so no one can solve it for a few decases, it must have some hints that is possible to solve it in a sensible amount of time (let's say a century!). It's more like discovering a meteorite than making a super nice porcelain pot.
There are plenty of open problems, so once the current wave of solutions in done I guess we will find a few that out of reach of the current LLM but we hope they can be solved in a sensible amount of time (let's say a century!).
Even though AI is getting better at math and can solve harder problems, the question remains: is it truly useful? While it might eliminate bottlenecks in research, most new problems solved by AI are just byproducts with no incremental benefit.
The AI industry is monofocused on difficulty over utility. The NS problem is hard, but it is also useful if solved in a way that it illuminates a lot of areas of math, gives us new techniques etc.
Brute forcing a counter solve has not really changed the game as much.
Knowing whether something or true or isn't true is useful for other lines of inquiry, often practical. For example, a lot could be gained by determining whether P = NP.
Also an initial, cumbersome, complex proof is the first step to a more understandable, formalized proof. AI created a formal proof of Fermat's last theorem. I'm sure the initial proof was not comprehensible to all but a small subset of mathematicians anyway.
For kids, it's hard because it must be interesting and not too hard, mix some interesting math concept and some hidden part that makes it an interesting puzzle.
For a Millenium-like problem it's harder, because it must be interesting so mathematicians care about it, it must be hard so no one can solve it for a few decases, it must have some hints that is possible to solve it in a sensible amount of time (let's say a century!). It's more like discovering a meteorite than making a super nice porcelain pot.
There are plenty of open problems, so once the current wave of solutions in done I guess we will find a few that out of reach of the current LLM but we hope they can be solved in a sensible amount of time (let's say a century!).
Brute forcing a counter solve has not really changed the game as much.
Also an initial, cumbersome, complex proof is the first step to a more understandable, formalized proof. AI created a formal proof of Fermat's last theorem. I'm sure the initial proof was not comprehensible to all but a small subset of mathematicians anyway.