Here's an excerpt from the most recent video on how Shannon studied the entropy of English, animated by Mitchell Zemil

@quantabooks.org just released their first book, on the story of Lean by @kevinhartnett.bsky.social. It's a great story, about a pretty significant part of what's happening in math right now. www.quantabooks.org/books/the-pr...

Suppose you wanted to reinvent the idea of Shannon Entropy for yourself. This puzzle is a good place to start (Full video on YouTube).

This video was a complete joy to make. Here's a short preview, but next time you're looking to sit down for 45 minutes of math and art, take a look at the full version on YouTube: youtu.be/ldxFjLJ3rVY

Happy Pi Day! In a certain sense, π is not a constant, but a variable. Using our usual Euclidean distance, it is 3.14159… but applying other L^p norms on ℝ², half the unit circle's perimeter will give other values. For instance, at p=1 (taxicab geometry), “π” = 2√2. At p ≈ 2.2, it's 3.20.

Well, math terminology being what it is, something like this was bound to happen eventually. (If you're curious about why these balls are so puny, the full talk is up on YouTube)

New video! Memorable for its delightfully absurd name, the Hairy Ball Theorem is extremely beautiful and has some surprising applications: youtu.be/BHdbsHFs2P0

The Ladybug Clock puzzle

I had fun joining @peterrowlett.net and @steckl.es recently on their mathematical objects podcast, talking about my wood puzzle collection. Most of the time was spent struggling desperately to describe a highly visual topic in an audio-only context. open.spotify.com/episode/0rRM...

The next video in the Laplace Transform sequence is up! youtu.be/FE-hM1kRK4Y Here, we dig into a concrete example, the forced oscillator. Some of you may remember that this was relevant for studying why light slows down in a medium.

Ever since I made a video about Fourier Transforms, one of the most requested topics on the channel has been its close cousin, the Laplace Transform. I've been having a lot of fun animating a mini-series about this topic, and the main part is now out. youtu.be/j0wJBEZdwLs

Much of Euclid’s Elements is easily misunderstood. Some proofs seem to have logical gaps. Some constructions seem pointless, others seem needlessly convoluted. Each of these provides a window into how the ancient Greeks thought about math and the philosophical role that geometry played.

New video about a piece by the modern artist Sol LeWitt, and the group theory behind it. youtu.be/_BrFKp-U8GI

Guest video 3/5 while I'm on leave is now up! It's by a former SoME winner, covering key ideas in statistical mechanics to create a simple and discrete model mirroring the behavior of a fluid transitioning between a liquid and gaseous state. Enjoy! youtu.be/itRV2jEtV8Q

Hey, psst, you can find early views for two upcoming guest videos on Patreon, one about statistical mechanics and another covering a story of modern art and group theory. Notes on early releases are always helpful before finalizing a video. www.patreon.com/posts/explor...

New video on the details of diffusion models: youtu.be/iv-5mZ_9CPY Produced by Welch Labs, this is the first in a short series of 3b1b this summer. I enjoyed providing editorial feedback throughout the last several months, and couldn't be happier with the result.

In the most recent video about quantum computing, I saw many comments expressing a similar point of confusion regarding Grover's algorithm. I made a follow-up to (hopefully) clarify some of the issues and to address a few other under-emphasized points. youtu.be/Dlsa9EBKDGI

New video! This covers the fundamentals of quantum computing and builds up to a step-by-step walk-through of an important algorithm in the field. youtu.be/RQWpF2Gb-gU

The most viewed thing I've ever made is a short about two colliding blocks computing π. I just made a new edition of the explanation for why π shows up there, setting things up for a (coming soon) follow-on connecting it to quantum computing. youtu.be/6dTyOl1fmDo

I have a pi-day challenge for all the physics students among you (or anyone willing to set up an experiment). If you share your results with me by March 10th, I may feature them in a video, depending on how good the results are and how many I get.

Part 2 of the collaboration with Terence Tao on the cosmic distance ladder is now out. It covers how we first learned the distances to planets, stars, and galaxies far, far away. youtu.be/hFMaT9oRbs4

New video! Terence Tao on how we measure the cosmos: youtu.be/YdOXS_9_P4U

I've had fun editing together on a very different kind of video from the norm. Keep an eye out this weekend.

Holograms! Easily my favorite project from last year. Full video: youtu.be/EmKQsSDlaa4

New* video! If you’ve ever wondered what topology is, this problem is one of the best examples I know of to give an authentic sense of what it’s all about: youtu.be/IQqtsm-bBRU

I'd like to share some music from the channel's regular composer, Vince Rubinetti, for a project never (yet) made: vincerubinetti.bandcamp.com/album/galois