Grant Sanderson Profile picture
Nov 11, 2021 18 tweets 4 min read Read on X
Niche/abstract topics rarely get highly illustrated explanations, much less in the form of a bedtime story.

A former prof of mine, Ravi Vakil, made this gem capturing how he thinks about exact sequences, cohomology, etc., which he kindly let me repost.

🧵
You can find the full story here: 3blue1brown.com/blog/exact-seq…

He goes on to talk about exact sequences, cohomology, and more. Admittedly, the audience is relatively niche, since it assumes you already know about those topics, but for the right person it certainly scratches an itch!

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More from @3blue1brown

Jun 14, 2022
Early impressions of @OpenAI's DALL-E 2. 🧵

All images below were produced by AI, with me feeding it the quoted prompt. I was most curious about how helpful such a tool might be in creative work.

"A sloth playing a guitar, photograph 35mm lens"
It seems to try hard to keep an image consistent, often making creative choices to do so. I didn't ask for the cloud to be a wad of yarn, but given the prompt, it actually makes a ton of sense.

“Photo of a thunderstorm where lightning is made of yarn and raindrops are needles”
Likewise here, having a campfire warm the coffee also makes sense conceptually, even if it wasn't explicitly mentioned in the prompt.

"brewing a cup of coffee in the middle of the woods at midnight"
Read 15 tweets
May 7, 2022
Fun puzzle! (This animation shows the first 5 iterations, the one lower in the thread shows the rest and spoils the answer.)

A hallway has lockers numbered 1,...,N, all initially closed.

Student 1 opens all of them.
Student 2 closes lockers 2, 4, 6, 8, etc.
...
Student 3 toggles every third locker, meaning if it’s closed, they open it, if it’s open, they close it.

Student 4 toggles every fourth locker.

Etc., with the k'th student toggling every k’th locker.

After N students do this, which lockers are open, and which are closed?
Try thinking it through yourself before watching, but here's how it plays out.
Read 4 tweets
Mar 14, 2022
I'd like to tell you about a game/puzzle to help celebrate today.

We'll call it "Death's Dice".

(1/9) Image
Death finds you. You plead with him that it's too soon, and he agrees to a concession. Every year, he'll roll a set of dice, and if it turns up snake eyes (both 1's) he'll take your life, otherwise, you get one more year.

But it's not necessarily a normal pair of dice.

(2/9)
On the first year, both "dice" will only have two sides, numbered 1 and 2. So in that first year, there's a 25% chance of rolling snake eyes and ending things there.

(3/9)
Read 9 tweets
Oct 23, 2021
The announcement for SoME1 winners is now out!

Links to winners in the thread below (in no particular order)

That weird light at the bottom of a mug — ENVELOPES

The Beauty of Bézier Curves, by @FreyaHolmer

Read 7 tweets
Apr 23, 2021
James Schloss (@LeiosOS) and I decided to organize a casual discord server for what we're calling the first Summer of Math Exposition (SoME1).

It's a space for people interested in producing online math/physics/cs explanations to self-organized.

discord.gg/Q3cC2GXN2f
There are so many people who have some great idea for a video or blog post or interactive experience that might help others learn a tricky topic, but who aren't sure where to start.
Going by the philosophy that the best way to start is to just start, this is a place to trade tips and ask questions of others in the same boat, and potentially find collaborators for what you're working on.
Read 4 tweets
Dec 13, 2020
It's a very good question! What follows are many tweets attempting to answer in a possibly way-too-verbose manner. No pictures (sorry), but I'll trust in the readers' mind's eye.
Commentary from mathematicians is more than welcome at the bottom of the thread, which includes scattered thoughts on whether there's a purely geometric reason to expect any rotation to have complex eigenvalues, i.e. one that doesn't appeal to the fundamental theorem of algebra.
First, just answering the question, let's review the basics: What it means for an operator to have an eigenvector with eigenvalue λ is that the way this operator acts on that vector is to simply scale it by λ.
Read 54 tweets

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