Like the other reply said, each exam has entirely new questions which are of course secret until the test is taken.

Sure, the questions were probably in a similar genre as existing questions or required similar techniques that could be found in solutions that are out there. So what? You still need some kind of world model of mathematics in which to understand the new problem and apply the different techniques to solve it.

Are you really claiming that SOTA LLMs don’t have any world model of mathematics at all? If so, can you tell us what sort of example would convince you otherwise? (Note that the ability to do novel mathematics research is setting the bar too high, because many capable mathematics majors never get to that point, and they clearly have a reasonable model of mathematics in their heads.)