Grant Sanderson @3blue1brown.com · 18/09/2026The last IMO problem AI could not solve. For when you want to sit down for a longer problem-solving saga, here's the full video: youtu.be/Nbwv5wHQoj0 514518
Grant Sanderson @3blue1brown.com · 12/06/2026Here's an excerpt from the most recent video on how Shannon studied the entropy of English, animated by Mitchell Zemil 111510
Grant Sanderson @3blue1brown.com · 10/06/2026@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...quantabooks.orgThe Proof in the Code - Quanta BooksThe inside story of Lean, a computer program that answers the age-old question: How do you know if something is true? 010419
Grant Sanderson @3blue1brown.com · 10/06/2026Suppose you wanted to reinvent the idea of Shannon Entropy for yourself. This puzzle is a good place to start (Full video on YouTube). 011313
Grant Sanderson @3blue1brown.com · 22/03/2026This 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 626759
Grant Sanderson @3blue1brown.com · 14/03/2026Ah! Correction, as several have pointed out, it should be 4 in the taxicab metric. And the same correction, i.e., measuring the circle in the appropriate metric, the relevant date-shifting-joke-value to be closer to 2.6 0662
Grant Sanderson @3blue1brown.com · 14/03/2026Anyway, the video I was hoping to have out this day will be out closer to the 20th. Some call it “missing your deadline”, but I prefer to think of it as giving the L_{2.2} norm a little love. 21470
Grant Sanderson @3blue1brown.com · 14/03/2026Happy 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. 625728
Grant Sanderson @3blue1brown.com · 27/02/2026Well, 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) 618628
Grant Sanderson @3blue1brown.com · 31/01/2026New video! Memorable for its delightfully absurd name, the Hairy Ball Theorem is extremely beautiful and has some surprising applications: youtu.be/BHdbsHFs2P0 414010
Grant Sanderson @3blue1brown.com · 07/11/2025I 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...open.spotify.comMathematical Objects: 3D wooden puzzle with Grant Sanderson 0576
Grant Sanderson @3blue1brown.com · 05/11/2025The 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. 212510
Grant Sanderson @3blue1brown.com · 12/10/2025Ever 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/j0wJBEZdwLsyoutu.beBut what is a Laplace Transform?YouTube video by 3Blue1Brown 1141163
Grant Sanderson @3blue1brown.com · 18/09/2025In the fifth and final of a series of guest videos I've been posting, @BenSyversen delves into a question anybody who has had to do ruler and compass constructions in a geometry class may have wondered: What's the point? 1301
Grant Sanderson @3blue1brown.com · 18/09/2025Much 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.youtu.beWhy ruler and compass? | Guest video by @bensyversenYouTube video by 3Blue1Brown 49311
Grant Sanderson @3blue1brown.com · 07/09/2025New video about a piece by the modern artist Sol LeWitt, and the group theory behind it. youtu.be/_BrFKp-U8GI 414619
Grant Sanderson @3blue1brown.com · 28/08/2025Guest 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/itRV2jEtV8Qyoutu.beSimulating Phase Change | Guest video by Vilas WinsteinYouTube video by 3Blue1Brown 08010
Grant Sanderson @3blue1brown.com · 23/08/2025Hey, 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...patreon.comExploration & Epiphany (Early view) | 3Blue1BrownGet more from 3Blue1Brown on Patreon 1784
Grant Sanderson @3blue1brown.com · 25/07/2025For context, I knew I'd want to take some time away this year (paternity leave!), so I reached out to a few other creators whose work I respect and asked if they'd be interested in me commissioning a guest video during my absence. It's a pretty good lineup coming! 8972
Grant Sanderson @3blue1brown.com · 25/07/2025New 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.youtu.beBut how do AI videos actually work? | Guest video by @WelchLabsVideoYouTube video by 3Blue1Brown 214413
Grant Sanderson @3blue1brown.com · 04/05/2025In 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/Dlsa9EBKDGIyoutu.beWhere my explanation of Grover’s algorithm failedYouTube video by 3Blue1Brown 118815
Grant Sanderson @3blue1brown.com · 30/04/2025To get around the question P=NP, and whether some clever analysis of the gates could also reveal the answer, the framing here is to assume the only thing you can do with the function is try it out on inputs. 070
Grant Sanderson @3blue1brown.com · 30/04/2025That part of the video could have been better phrased. For any problem you'd want to use this for, you would know the gates, so it's not a black-box in that sense. But to have a catch-all stand-in example, I want to presume there's no insight you gain about the answer by analyzing those gates. 160
Grant Sanderson @3blue1brown.com · 30/04/2025It's known you cannot do better than O(√N), which is certainly not as earth-shattering as an exponential speed-up would be, and questionably useful given the enormous overheads of quantum computing. Nonetheless, it's thought-provoking that such a thing is possible! 1300
Grant Sanderson @3blue1brown.com · 30/04/2025If you translate this setup into a quantum computer (explained in the video), Grover's algorithm offers a "faster" way to do this, in that it's O(√N). 1260
Grant Sanderson @3blue1brown.com · 30/04/2025As a generic stand-in for the kind of problem it solves, suppose you have a function acting on {1, ..., N} which returns True on one and only one value in this set. If all you can do with this function is try it out on numbers, then it takes an average of (1/2)N steps to find the answer. 1160
Grant Sanderson @3blue1brown.com · 30/04/2025What do they do then? This video builds up to Grover’s algorithm, a general method in quantum computing for finding solutions to any NP problem, i.e., anything where you have a quick way to verify solutions, even if finding them in the first place may be hard. 1170
Grant Sanderson @3blue1brown.com · 30/04/2025A common misconception about quantum computers is that they would solve hard problems by trying all possible solutions in parallel. This vaguely gestures at something true, but the reality is more subtle. 1220
Grant Sanderson @3blue1brown.com · 30/04/2025New 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-gUyoutu.beBut what is Quantum Computing? (Grover's Algorithm)YouTube video by 3Blue1Brown 724934
Grant Sanderson @3blue1brown.com · 13/03/2025I hope so too, the thought of a high school teacher using this idea for a lesson was a key motivator in the back of my mind. 090
Grant Sanderson @3blue1brown.com · 13/03/2025The 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/6dTyOl1fmDoyoutu.beThere's more to those colliding blocks computing piYouTube video by 3Blue1Brown 522924
Grant Sanderson @3blue1brown.com · 26/02/2025If you do this, you can reach out to the channel via this page. 3blue1brown.com/contact Be sure to have a link to footage of the experiment. If anyone can get it to work with 100-to-1, I'd be happy, and if anyone can do it for 10,000-to-1, I'd be both delighted and amazed. 0260
Grant Sanderson @3blue1brown.com · 26/02/2025More generally, with a mass ratio of N-to-1, the number of collisions is around π / arctan(1 / sqrt(N)). So any big mass ratio gives you an approximation of pi by multiplying the number of collisions by arctan(1/sqrt(N)) 2230
Grant Sanderson @3blue1brown.com · 26/02/2025Note, there's no reason to restrict yourself to powers of 100. For example, you could use powers of 4 to compute pi in binary. A mass ratio of 64-to-1 should give 25 collisions, which is 11001 in binary, and pi looks like 11.001... 2240
Grant Sanderson @3blue1brown.com · 26/02/2025Also, it's a wildly inefficient way to compute pi. To even get "3.14" you'd need this to work with a 10,000-to-1 mass ratio and have a way to count all 314 collisions. Matt Parker and I actually gave this a go, and the results were...okay, but could definitely have been improved :) 1251
Grant Sanderson @3blue1brown.com · 26/02/2025The original puzzle assumes zero friction and zero energy loss in collisions, so obviously there are limits to how far you can get. I can tell you the real limiting factor is energy lost in collisions, more so than friction. The hardest part is energy lost in collisions, more so than friction. 1200
Grant Sanderson @3blue1brown.com · 26/02/2025Many years ago I made this video about how two colliding blocks on a frictionless plane can compute pi. My challenge to you is simple: Implement this in practice. 1252
Grant Sanderson @3blue1brown.com · 26/02/2025I 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. 41249
Grant Sanderson @3blue1brown.com · 23/02/2025Part 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/hFMaT9oRbs4youtu.beThe cosmic distance ladder with Terence Tao, part 2YouTube video by 3Blue1Brown 532647
Grant Sanderson @3blue1brown.com · 08/02/2025New video! Terence Tao on how we measure the cosmos: youtu.be/YdOXS_9_P4Uyoutu.beTerence Tao on how we measure the cosmos | Part 1YouTube video by 3Blue1Brown 2344180
Grant Sanderson @3blue1brown.com · 06/02/2025I've had fun editing together on a very different kind of video from the norm. Keep an eye out this weekend. 42125
Grant Sanderson @3blue1brown.com · 24/01/2025Holograms! Easily my favorite project from last year. Full video: youtu.be/EmKQsSDlaa4 332635
Grant Sanderson @3blue1brown.com · 24/12/2024Aside from animating this beautiful piece of math better, I had an itch to address new research that’s happened since, and to pull in numerous other mind-bending connections. 2620
Grant Sanderson @3blue1brown.com · 24/12/2024Well, perhaps not “new” new. Books have a notion of a second edition, and while YouTube videos usually don’t, I wanted to make a new edition of one of the earliest videos on the channel, as this is one of my favorite pieces of math. 1620
Grant Sanderson @3blue1brown.com · 24/12/2024New* 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 438251
Grant Sanderson @3blue1brown.com · 03/12/2024I fully hope to pick it back up again one day, but in the mean time, Vince and I wanted to share some nice pieces produced during that time intended to serve as the soundtrack. 2500
Grant Sanderson @3blue1brown.com · 03/12/2024It would make a great video, and ultimately an overwhelming amount of scope-creep led me to set it aside for a while for my own sanity. 2400
Grant Sanderson @3blue1brown.com · 03/12/2024The full story and broader context is not as well known, and has been confused by apocryphal tales and twisted narratives over the years. This piece by Tony Rothman is a pretty good start for anyone curious: sites.tufts.edu/histmath/fil...sites.tufts.edu 2150
