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Grant Sanderson

@3blue1brown

23 Apr

@LeiosOS

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

Grant Sanderson

@3blue1brown

13 Dec 20

https://twitter.com/saha_sidharth/status/1337519170011820032

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.

https://twitter.com/saha_sidharth/status/1337519170011820032

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

Grant Sanderson

@3blue1brown

19 Jul 20

Okay, follow through with me on this one and I guarantee you're in for a fun surprise.

We'll start forming rows of numbers, kind of like Pascal's triangle, but with a different rule.

The first row is simple "1, 1"

For row 2, copy the first row, but insert a 2 between any elements that add to 2.

In this case that just means sticking a 2 between the two 1's.

For row 3, copy row 2, but insert a 3 between every pair of elements adding to 3.

Read 19 tweets

Grant Sanderson

@3blue1brown

7 Jul 20

In light of the very sad news about Ron Graham's passing, I thought I'd share an interesting tidbit about his famous constant which I only learned recently (thread).

This number has captured the imaginations of many people with its unfathomable size, myself included. I distinctly remember when I was a kid first learning about it spending hours trying to wrap my mind around it and using it as inspiration for writing ever-larger numbers.

The existence of huge numbers is not in and of itself interesting, but what captivated me was how abstraction and recursion even let us _describe_ such numbers. Honestly, it was one of the first times I appreciated how powerful good definitions could be.

Read 11 tweets

Grant Sanderson

@3blue1brown

30 Jun 20

Of all the videos I've made, one of my favorites topics to have covered was a proof of the inscribed rectangle problem by H. Vaughan using a Mobius strip.

But now there's a new result!

@QuantaMagazine

@QuantaMagazine recently did a great article about recent work by Greene and Lobb using a beefed-up version of the same idea, letting a Mobius strip encode geometric properties of the curve to solve a more general result, check it out:

quantamagazine.org/new-geometric-…

From recent comments on the video above, it looks there's a little confusion where some people thought this means the inscribed square problem (i.e. the Toeplitz conjecture) has been solved, but that's not quite the case.

Read 5 tweets

Grant Sanderson

@3blue1brown

7 Nov 19

The birthday paradox is very famous in probability. If you take 23 people, there's about a 50/50 chance that two of them share a birthday. With 50 people, it's a 97% chance.

We could make many other fun examples to illustrate the same counterintuitive phenomenon (thread).

Choose a random card from a deck of 52 cards. Put it back, shuffle well, and choose another. Do this for only 9 draws, and more likely than not, you've pulled the same card twice.

Do it 16 times, and your chances are over 90%. Try it!

Next time you're in an event with more than 118 people, think to yourself that there's a >50% chance that two people there have phone numbers with the same last four digits (assuming those are uniformly distributed).

With more than 250 people, its >95%.

Ditto for ATM pin codes.

Read 12 tweets

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