Maths and human understanding

Just finished watching 3Blue1Brown’s recent video titled The last IMO problem AI could not solve, which goes in depth explaining the thought process of arriving at the (a) massively elaborate (in a good way) solution/proof to the (infamous) sixth problem of the International Mathematical Olympiad (IMO) in 2025.

What an adventure indeed! I may need to rewatch it for a few more times to fully grasp the intuition behind the solution.

However, the main topic of this post here is not about the solution itself, but what Grant said during the outro of the video: the importance of promoting human understanding in the development of mathematics as a discipline, rather than racing to obtain a proof to an unsolved mathematical problem.

I fully agree to this. Actually this does not only apply to mathematics; it’s education as a whole. That’s the whole point of education, really: empowering people with an intrinsic understanding of knowledge, craft and their senses of selves.

This sounds like an unrelated sidenote, but it’s what that motivates me to write this post: in the video, there are quotes from some prominent mathematicians about their thoughts on AI in maths which are displayed on-screen, one of which is by Timothy Gowers, and it goes as follows:-

If a society does not have a significant number of people who understand mathematics at some level, we risk becoming passive consumers under the control of these systems. On the other hand, people who do make the effort to understand mathematics will have a large advantage.

“Becoming passive consumers under the control of these systems,” interesting. Considering all those things done and/or said by those big AI companies, who’s to say that this isn’t precisely the goal that those corporations are aiming for?

Tinfoil hat.