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The last IMO problem AI could not solve

3Blue1Brown

2,711,311 views

A beautiful puzzle that eluded AI, and the intuition it requires.
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Home page: https://www.3blue1brown.com

Note for the quote at the end: The person who wrote that wanted me to relay a desired edit to the second paragraph, asking that it instead read, "I believe the value of this question as a mathematical discovery is no less real than that of frontier mathematics, albeit different in nature."

Guest post I referenced on Terry Tao's blog:
https://terrytao.wordpress.com/2026/0...

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-202...

The channel Dedekind Cuts has a video about this solution:
IMO 2025 Problem 6 - *FINAL BOSS* is here!...

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: Secret Endscreen Vlog #9

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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/a...
https://open.spotify.com/album/1dVyjw...

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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.

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20 Comments

@3blue1brown Creator 13 days ago (edited) Pinned

Here's that 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/

Programming note: I will put out that third part to "compression is intelligence"; it's just that I started prioritizing some of the content in the pipeline related to AI in math, for obvious reasons. Likewise, I promise I will get back to that fourth part of the Laplace series :)

If you're looking for career opportunities, that virtual career fair concept I mentioned is here: https://www.3b1b.co/talent
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@ganbat24 13 days ago

The airport floor foreshadowing the solution is absolute cinema!

@dedekindcuts3589 12 days ago (edited)

47:23 Thank you for the shout out! The visuals in this video are amazing! I got inspired to make math videos regularly thanks to this channel and it's an honour to have my channel mentioned here. 😄 Cheers to more fun math!

@fallenflame8678 13 days ago

I happen to work with someone who was involved in organizing the IMO 2025, and he told me about his delight upon realizing that the tiling was on the floor of the Sunshine Coast airport! Glad to see that fun fact made its way to this video.

@delyurka767 12 days ago

The fact that airport tiling foreshadows hardest problem is a certified Squid Game moment where they showcased the games on walls.

@merrilyElkish 13 days ago

I love how this pattern kinda resembles the arrangement for the most space-efficient sugarcane farm in Minecraft

@KingGrio 13 days ago (edited)

One of the best part of the video is seeing the notebook and hearing that it'd take a really look time to explain all the failed attempts.
I feel like less of an idiot knowing 3b1b also has to work his grey matter sometimes, and that genius 3D animations just don't come flying out when he wiggles his fingers at his keyboard.

@Ellliptic 13 days ago

"Any sufficiently well explained mathematics is indistinguishable from being obvious" --Matt Parker
i feel this is a starting point for formalizing what a 'motivated explanation' should be, and i think was a part of what you were trying to get at in the last part of the video.

@Maramowicz 12 days ago

15:18 I got a flashback: in Factorio there are square solar panels, batteries and electric poles, and when I saw that pattern I immidetally recognized that it was the most optimal pattern to set the solar panels and poles in a way that packs them as efficiently as possible!

@KaasGrater 13 days ago (edited)

We have officially gone from "Look! An AI can solve this problem" to "Look! An AI cannot solve this problem" in just a few years. What a time to be alive.

@perseussmith3274 13 days ago

So, are you telling me that efficient sugarcane farm layouts in Minecraft could help solve an IMO problem? Insane.

@herrvich 13 days ago

No matter how we measure academic progress one thing for certain - 3B1B single handely ignited my love for problem solving and doing math problems in my spare time.

Amazing teacher.

@dinobik9284 8 days ago (edited)

This is without question the best video ever released on youtube.
The ability to give someone an underestanding of something as extraordinary as a P6 at the IMO in under an hour is something only 3blue1brown can do.
The message at the end is necessary, what are we without expression of our understandings? There is no greater gift to humanity or ourselves than that.

Thank you Grant and PolyaMath <3

@MrSleepless 13 days ago

It is absolutely wild to think that we are living through the exact historical window where this was the "final boss" for AI

@NyroSlice 12 days ago

To me the absolute future for math, if we extrapolate that ai will be able to solve any math theorem, is the role of decoding the solution into ways that humans can understand. I think your role 3Blue1Brown is in fact at the heart of this decoding, and points to the exact importance of it. You can know a proof but not understand it. And math is one of those rare feels that rewards understanding over vague knowing.

@f5673-t1h 13 days ago

46:05 I think this is my first time clearly seeing the "3 blue" and the "1 brown", in my 10+ years of watching this channel.

@MasterGeekMX 13 days ago

The technical Minecraft community has also found that windmill pattern as the optimal solution for several farms. Some game mechanics need that a given block needs to be right next to other blocks in order to be productive. Examples of it are sugar cane reeds that can only be planted on top of soil or sand blocks next to water blocks, or water freezing into ice blocks on cold biomes only if said water block it's next to a solid block.

As one can see, this leads to finding a pattern that maximizes the number of productive blocks while making sure each block is adjacent to a "support" block. The solution is to use the windmill pattern with k=2.