Can you even imagine 2^256? // TRAIN BRAIN

Can you even imagine 2^256?

Originally written as a supplement to an explanation of the cryptography behind Bitcoin: https://youtu.be/bBC-nXj3Ng4

3Blue1Brown

3blue1brown, by Grant Sanderson, is some combination of math and entertainment, depending on your disposition. The goal is for explanations to be driven by animations and for difficult problems to be made simple with changes in perspective. Contact and F...

The meaning within the Mandelbrot set

The scale of training LLMs

This puzzle is tricker than it seems

The Triangle Of Power

The twirling tiles puzzle

Why 4d geometry makes me sad

LLMs are next-word predictors

Hologram preview

Holograms are wild

In the vector space of all advice...

Temperature in LLMs

Simulating the electric field and a moving charge

How the Mandelbrot set is defined

A challenging puzzle about subset sums

Ellipses have multiple definitions, how are these the same?

Three levels of understanding Bayes' theorem

The medical test paradox (well "paradox")

Positioned as the hardest question on a Putnam exam (#6, 1992)

Why does light slowing imply a bend? (Beyond the tank/car analogy)

The cube shadow puzzle

What does it mean that light "slows down" in glass?

Why do we call them "scalars"?

A beautiful international math olympiad problem

Definition of a "bit", in information theory

The Newton art puzzle

What is a group?

How to derive a formula for π

The limit of limiting arguments

For anyone who might not know how links in shorts work

Infinite Lighthouses and π

"Proof" of a sphere's surface area

Can you even imagine 2^256?

Order from chaos

The surface area of a sphere

A short on shorts

A pretty way to add weighted dice

Image blurring

These integrals all equal π, until...

The split necklace puzzle (with a surprise topological solution)

Error correction is incredible

The chessboard and coins puzzle

Prime spirals

The barber pole effect

Fourier series

Seeing with sound

The standard explanation of a prism falls short

I'm still astounded this is true

Don't let it fool you!

Prime spirals

X-rays "faster" than the speed of light, and more refractive index questions | Optics puzzles part 4

You can't explain prisms without understanding springs | Optics puzzles part 3

The origin of light, scattering, and polarization | Barber pole, part 2

This demo tests your understanding of light | Barber pole, part 1

Wanna help judge SoME3?

So why are normal distributions "central limits"?

Explaining the absurd circle division pattern | Moser's circle problem

How They Fool Ya | Mathematical parody of Hallelujah

X+Y, in probability, is a beautiful mess | Visualizing continuous convolutions

Why π is in the normal distribution (beyond integral tricks)

But what is a convolution?

Researchers thought this was a bug (Borwein integrals)

How to lie using visual proofs

Olympiad level counting

The mathematically optimal Wordle strategy

Alice, Bob, and the average shadow of a cube

A few of the best math explainers from this summer

Where Newton meets Mandelbrot (Holomorphic dynamics)

Newton's Fractal (which Newton knew nothing about)

A quick trick for computing eigenvalues | Essence of linear algebra, chapter 15

How (and why) to raise e to the power of a matrix | DE6

Hamming codes part 2, the elegance of it all

Hamming codes, h■w to ov■rco■e n■ise.

Why I love 808,017,424,794,512,875,886,459,904,961,710,757,005,754,368,000,000,000

The impossible chessboard puzzle

Contact Tracing and Privacy Protection (via Nicky Case)

Lockdown math announcement

Exponential growth and epidemics

The quick proof of Bayes' theorem

Bayes theorem, and making probability intuitive

Why do prime numbers make these spirals?