About this channel
A puzzle can open into a much larger mathematical question on 3Blue1Brown. The channel's selection moves between geometric arrangements, probability problems and the ideas behind information and…
A puzzle can open into a much larger mathematical question on 3Blue1Brown. The channel's selection moves between geometric arrangements, probability problems and the ideas behind information and compression. Some videos begin with familiar objects such as cubes or tied ends; others ask how language can be measured or how an encoding can be judged.
One thread develops entropy and cross-entropy through a series connecting compression with intelligence. Questions about the entropy of English and the properties of an ideal encoding make information itself the object of study. This gives viewers a way to approach abstract quantities through the concrete problem of representing something efficiently.
The puzzle material offers a different route into mathematical reasoning. Random chords raise questions about intersections, while joining loose ends leads to a question about how many loops will form. Arrangements of points, jumping pegs and sugar cubes add geometric and combinatorial challenges. An episode concerning an olympiad problem that AI could not solve links mathematical difficulty with the limits of automated problem-solving.
Curious viewers, students and anyone who likes to work through an unfamiliar problem can find a starting point in this selection. A self-contained puzzle invites an attempt before the explanation, while the information-theory sequence offers connected ideas to follow across videos. The appeal is the movement from a simple statement to the reasoning needed to understand it. People interested in the mathematics surrounding AI can also approach that interest through compression and uncertainty, alongside viewers who simply enjoy the structure of a good mathematical problem.
Latest episode
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…
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
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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/album/the-music-of-3blue1brown
https://open.spotify.com/album/1dVyjwS8FBqXhRunaG5W5u
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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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Patreon: https://patreon.com/3blue1brown
Website: https://www.3blue1brown.com
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