3Blue1Brown — searchable YouTube transcripts & AI Q&A

There's never been a better time to go into math

The speaker argues that despite AI's rapid progress in proving theorems, there has never been a better time to enter mathematics because the field's core value—theory building, problem-solving training, and aesthetic joy—remains intact. He suggests that proof should be treated as raw data rather than the ultimate goal, and that mathematicians should focus on building theories and communicating them orally. He advises PhD students to reflect on what they love about math and to lean into that passion, as the community is open to new directions.

The last IMO problem AI could not solve

The speaker argues that the 2025 IMO problem 6, which AI models could not solve, requires patience and an appreciation for beauty, not just computational power. The solution involves a tiling pattern with square tiles and a proof using the Erdős–Szekeres theorem to show the minimum number of tiles is k^2 + 2k − 3 for a k^2 × k^2 grid. The speaker suggests that motivated explanations, not just proofs, are crucial for advancing human understanding in mathematics.

But what is cross-entropy? | Compression is Intelligence Part 2

This video explains cross-entropy, its connection to data compression, and how it's used in training language models.

100 random chords, how many intersections?

Calculates the expected number of intersection points for 10 and 100 random chords drawn on a circle.

Measuring the entropy of English

Learn how Claude Shannon measured English text compressibility using human prediction experiments to estimate information entropy.