As a former problem designer for IMO and similar contests, I deeply enjoyed reading this paper. At the same time, I'd like to point out that it was clear Geometry had to be the first topic to give up against AI (i.e., smart knowledge and inference-method indexing)
Among math olympiad topics, Geometry problems are often the most "mechanical." Once you can express the problem in terms of coordinates (think XY or complex plane) you're looking at a finite set of steps a computer can use to find a solution. Of course, time limits and human error get in the way of this being practical during the IMO itself. Back in the day, I'd use WolframAlpha to verify geometry proofs for problems I designed (+conjectures) using this approach.
Algebra (especially inequalities) can be similar – pull off some intense calculations and you often have your answer.
Where I'm really excited to see intelligent systems make progress is with Number Theory and Combinatorics problems. The search spaces are far more complex and they often require proving that something is impossible. These are the problems that would be difficult to solve with brute force computation.
Algebra (especially inequalities) can be similar – pull off some intense calculations and you often have your answer.
Where I'm really excited to see intelligent systems make progress is with Number Theory and Combinatorics problems. The search spaces are far more complex and they often require proving that something is impossible. These are the problems that would be difficult to solve with brute force computation.