3blue1brown

How They Fool Ya

Happy tau day! 

I posted this as a secret video to patreon a few years ago. It's a recording from when I was in London and Matt Parker invited me to do an act for his “Evening of Unnecessary Detail”. I had some vague that that one day it might be nice to record a better version before posting it more publicly. Given that I never quite got around to that, and that the raw live version seems more fun anyway, I figured it's probably high time to just share it.

Adding random variable, and continuous convolutions (Early view for patrons)

Hey everyone,

Continuing with the theme of probability videos, which I plan to eventually coalesce into a proper series sometime this year, this next video covers adding random variables. That is to say, convolutions.

Initially, I intended for this to be "part 2" to the convolution video from a few months ago, this time focused more exclusively on the continuous case. It builds up two visualizations, and for each one, it's very helpful to have freshly seen what it looks like for a...

Stanford Math Department Commencement Speech

I had the honor and pleasure of being invited to deliver an address for the mathematics graduation ceremony at Stanford. In it, I chose to talk about one of the lesser-addressed and awkward-to-talk-about motivations for getting into math.

May Update

Hey everyone,

I was really hoping to have the next video out to you by now. It'll be about convolutions in the continuous case, with a focus on what makes Gaussian distributions special and why they pop up in the central limit theorem. You should be seeing a draft of that within the next week, though.

In the meantime, here are a few other updates from the month:

• I contributed to a Stand-up Maths video, offering a 2023-06-01 06:31:09 +0000 UTC View Post

Thoughts on AI art

The most recent video I published made some use of AI art. I wanted to write some reflections on that, more to clarify my own thoughts than anything else. Feel no obligation to read it all, I know you're subscribed here for math videos. If you have opinions on the topic and feel like adding a comment, I'd love to read it.

Long story short, I don't regret experimenting with using AI art, but for a mixture of reasons I d...

SoME3 begins!

Today we're kicking off the third Summer of Math Exposition, SoME3. It's an event to encourage more people to create online math explanations, with prizes and a chance to have your work surfaced to a larger audience. Learn more at https://some.3b1b.co 

You could make a video, a blog post, or whatever else you dream up, about essentially any topic you'd like, as long as it's loosely related to math. Whether you're a studen...

Shorts

Suppose that over the last few years, there's been an exponential rise in the amount of opium usage. It's especially prevalent among the youth. You've started to notice as you walk through airports and look at how people twiddle away their time, sneaking the occasional glance over the shoulder of a stranger, that quite a few people seem to spend those spare moments happily indulging in the drug.

Obviously, this is not a great situation. Addictions rarely are. Also, some people worry abo...

JPBM Communications Award Lecture, JMM 2023

Hey everyone,

Early this year I had the honor of receiving a communications award from the Joint Policy Board for Mathematics, along with Jordan Ellenberg. A few of you asked if the talk I gave associated with this in January would be public, and I just got the file from the AMS with permission to post it, so here you go. Enjoy!

Grant

Early view, why π is in the normal distribution (beyond integral tricks)

Hey everyone,

Here's an early view for the next video, exploring the pi inside the normal distribution. We start with a classic proof, due to Poisson, then make an attempt to go further to show how this proof relates to a derivation for where the gaussian distribution comes from in the first place.

-Grant

Central Limit Theorem (early view)

(Update: Thanks for all the feedback everyone, the final version is now live!)

Hey everyone,

Originally, my aim was to finish the video about how the pi in the formula for a normal distribution is related to the central limit theorem by, well, pi day. The way it shook out instead is that the primer covering what the central limit theorem is ended up being longer than expected, and I'm still finishing the last touches today. Such is life.

Here's an early view of that primer. ...

Prime number races

Hey everyone,

The third in a little sequence I did with Numberphile about patterns which eventually break is now published. This one is about racing prime numbers in different residue classes, with an intuition for why some of these classes seem to have a systematic advantage.

For those curious about this topic, I highly recommend this expository paper by Andrew Granville and Greg Martin: https://arxiv.org/abs/...

Any requests for what to include in a central limit theorem video?

Hey everyone,

What began as the follow-on to the convolutions video has become a video about the central limit theorem. In particular, I'd like to show how a certain perspective on convolutions makes it easier to "see" why the function e^(-x^2) is the one that shows up so prominently in statistics, as opposed to some other function that bulges in the middle and tapers out in the ends.

The explanation is loosely connected to a delightful, and somewhat classic, argument for why the ...

Manim Q&A Tomorrow

Hi everyone,

Following up on the last post, I'll be doing the Manim Q&A as a live stream tomorrow (Saturday) at 1 pm Pacific time. Here's the link, which will be unlisted, and I'll keep it available after the stream for anyone who can't make it at that time.

I'll be joined by Benjamin Hackl, an active member of the ...

Manim Q&A

Wonderful patrons,

Despite my original plans, I spent a fair bit of this month continuing with efforts I began in December to improve manim. Given that I've been putting so much time into this, and I know some people are curious about the process and workflows behind videos, I thought I'd do a casual Q&A live stream for patrons to answer any questions about manim.

I thought...

JMM, year-end reflections, and what I've been up to

JMM

I'll be at the Joint Mathematics Meeting in Boston next week. If any of you are attending and would like to meet up, please feel free to send me a DM or email me.

On Thursday, January 5th, I'm giving a lecture there in association with having been chosen for the 2023 JPBM Communications Award. It was quite the honor to receive, given that many of the past winners are math exposition heroes of mine. If any of you are there and able to make it do come to say hello!

Refl...

2022-12-30 20:33:26 +0000 UTC View Post

New video! But what is a convolution?

Hey Everyone,

As promised, here's a new video going deeper into convolutions, and in what sense the FFT algorithm can be used to speed up their computation. Originally the plan was to do an overview of both the discrete and continuous cases, but there was enough material I wanted to cover that I decided to pull out the continuous discussion into its own video. Given that many of the visuals for that are already made, in theory, it shouldn't be too long before that one is out as well. 2022-11-18 16:13:17 +0000 UTC View Post

A few Numberphile videos + Final version of Borwein integrals

Hey folks,

I recently made a few videos with Numberphile, the first of which is posted above. The second one is here, and the third will be out in the not-too-distant future. Each one is about some pattern related to primes that only holds for small numbers. The first two aren't especially deep, but they are fun. The third one will relate to some more "real" number theory, though I did come out only scratching the surf...

A bizarre integral pattern (early view)

Hey everyone,

Here's a rough cut for a new video, about a strange series of computations that compute pi...until they don't.

As always, comments and feedback are welcome. I still have yet to do a proper comb-through for little errors, and there are a number of animations I'll amend, so feel free to throw in any requested changes while I'm at it. At the very least I'll probably add a bit more about variations on this phenomenon that result in patterns that break much later.

T...

Summer of Math Exposition conclusion

In this video I talk about the results of the summer of math exposition, and highlight four criteria for what I think makes a math video (or article) great. Enjoy!

August update

Hello patrons,

First off, I want to express a bit of guilt for not having any new videos out this month. Knowing that the current pace of output probably does not live up to the spirit of the generous pledges you all have made, if any of you would like a refund on the pledges for the last month or two, feel free to DM me and I'll happily process it, no hard feelings taken.

Galois saga status

Wheels have been turning on the Galois project, though I'll a...

The epic of Galois

Hi Everyone,

Thank you for forwarding along the request for artists I posted last week! It did manage to surface some great contributors who can help.

I've sprinkled several vague mentions of "a project about Galois" here and there in past posts this year, but it might be worth laying out the full plan here. It's grown to be the largest project this channel has worked on, and you are, in effect, the producers.

How it started

It all started over a yea...

Seeking more artists

TL;DR, if you know any freelance digital artists who might want to help with with a 3blue1brown project, can you share this application with them?

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As I've mentioned in previous posts, the big project for this year will be about Galois, including his incredible life story, the story of those leading up to and following him, and of course a set of lessons on the actual math he worked on.

Part of the...

How to lie using visual proofs

Since the channel centers so heavily on visual intuition and visual proofs, it seems only right to give a few examples of where visual proofs can lead you astray.

Summer of Math Exposition #2

Hey Everyone,

Last year, Jame Schloss and I organized what we called the Summer of Math Exposition (SoME1), a contest for online math explainers. I can't tell you how fun and rewarding it was to see the quality of some of the entries, so we're doing it again. (See last year's announcement and results).

Last week we've kicked things off for anoth...

Olympiad level counting

Hey everyone,

Thanks for all your feedback on the draft of this one. I was able to incorporate much of it, and it certainly made it better, so I appreciate the thought that so many of you put into responses.

The most notable changes for the final version come in the form of motivation, both in motivating the problem, and also doing the best I can to tee up some of the strange-seeming steps involved in solving it. There's also some new commentary at the end for why we should care, ...

New puzzle video, and updates on the rest

Hey everyone,

I wanted to share a new video draft (linked above), and some updates on what's been new in 3blue1brown.

Puzzle video and messing with new workflows

I spent some time this month updating manim (the animation software behind the channel) to try out some new workflows. The aim is to incorporate more interactivity into the video creation process in two senses. 1) Use GUI interactions as an aid to an otherwise code-dominant process, and 2) Give the ...

Happy pi day, with "Death's Dice"

Happy pi day folks. With the two projects happening now, there wasn't quite room to do a full video in celebration of the day this year. But I did want to share a fun "surprise pi" occurrence, this one in the form of a simple tweet thread.

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Death finds you. You plead with him that it's too soon, and he agrees to a concession. Every year, he'll rol...

New hire, and upcoming projects

Hey everyone, I thought I'd pass along a few updates for what's new and coming up in 3blue1brown land.

First off, I hired an artist this year, Kurt Bruns, both to help outsource some of the production and to extend the visual style in a new direction. He was the one who did the drawings for the Alice/Bob/Cube shadow video. One of the first main projects we've been working on will be a pretty big one, and the way it's shaping up now it'll more likely than not end up being a multi-part se...

Oh, wait, actually the best Wordle opener is not “crane”…

Hey Everyone,

I put together a brief follow-on to last week's video, talking about a small bug which influenced the choice of what starting guess is optimal. Really, though, it's an excuse to go into a bit more detail on what went into that final analysis.

Some Wordle fun (rough cut)

Hey everyone,

I decided to do a digression from the main project I was working on most of January to do a "quick" little video using Wordle as an excuse to teach some information theory.  Here's a preview of the rough cut, which I'll aim to finalize today and publish tomorrow. If you catch any errors (which are inevitably in there, I have yet to do a proper final pass), do let me know.

(Edit: And now the final video is up, thanks for all the helpful catches!)

-Grant