The last IMO problem AI could not solve

A beautiful puzzle that eluded AI, and the intuition it requires.
Check out our virtual career fair: https://3b1b.co/talent
See new videos early: https://3b1b.co/support
An equally valuable form of support is to simply share the videos.
Home page: https://www.3blue1brown.com

Guest post I referenced on Terry Tao's blog:
https://terrytao.wordpress.com/2026/09/18/if-math-is-more-than-proof-we-need-to-better-celebrate-the-rest-of-it/

Evan Chen also wrote up nice solution notes for this problem, along with all the others on that year's test.
https://web.evanchen.cc/exams/IMO-2025-notes.pdf

The channel Dedekind Cuts has a video about this solution:
https://youtu.be/fgXg9CdCDcs

Timestamps:
0:00 - The one that AI missed
4:09 - Problem statement
6:45 - Finding the Optimal Construction
18:51 - A weak lower bound
23:45 - 3b1b Talent
24:41 - Proving the Construction is Optimal
34:08 - One final conjecture
39:42 - The Erdos-Szkeres Theorem
45:56 - Reflections on AI in Math

Secret Endscreen Vlog: https://youtu.be/UbHoWA0X1e8

------------------

These animations are largely made using a custom Python library, manim. See the FAQ comments here:
https://3b1b.co/faq#manim

Music by Vincent Rubinetti.
https://vincerubinetti.bandcamp.com/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u

------------------

3blue1brown is a channel about animating math, in all senses of the word animate. If you're reading the bottom of a video description, I'm guessing you're more interested than the average viewer in lessons here. It would mean a lot to me if you chose to stay up to date on new ones, either by subscribing here on YouTube or otherwise following on whichever platform below you check most regularly.

Mailing list: https://3blue1brown.substack.com
Twitter: https://twitter.com/3blue1brown
Bluesky: https://bsky.app/profile/3blue1brown.com
Instagram: https://www.instagram.com/3blue1brown
Reddit: https://www.reddit.com/r/3blue1brown
Facebook: https://www.facebook.com/3blue1brown
Patreon: https://patreon.com/3blue1brown
Website: https://www.3blue1brown.com