3Blue1Brown
Why do prime numbers make these spirals?
A curious pattern in polar plots with prime numbers, together with discussion of Dirichlet's theorem
3Blue1Brown
How secure is 256 bit security? Cryptocurrency - Part 2 of 2
When a piece of cryptography is described as having "256-bit security", what exactly does that mean? Just how big is the number 2^256?
3Blue1Brown
What is backpropagation really doing? | Chapter 3, deep learning
An overview of backpropagation, the algorithm behind how neural networks learn.
3Blue1Brown
What they won't teach you in calculus
A visual for derivatives which generalizes more nicely to topics beyond calculus.
3Blue1Brown
What does area have to do with slope? Essence of Calculus - Part 9 of 11
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
The determinant | Essence of linear algebra, chapter 5
The determinant has a very natural visual intuition, even though it's formula can make it seem more complicated than it really is.
3Blue1Brown
Inverse matrices, column space and null space | Essence of linear algebra, chapter 7
How do you think about the column space and null space of a matrix visually? How do you think about the inverse of a matrix?
3Blue1Brown
Three-dimensional linear transformations | Essence of linear algebra, footnote
How to think of 3x3 matrices as transforming 3d space
3Blue1Brown
Linear combinations, span, and basis vectors | Essence of linear algebra, chapter 2
Some foundational ideas in linear algebra: Span, linear combinations, and linear dependence.
3Blue1Brown
Visualizing the Riemann zeta function and analytic continuation
What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
3Blue1Brown
Triangle of Power
Logarithms are confusing, but perhaps some alternate notation could make them more intuitive.
3Blue1Brown
Three-dimensional linear transformations | Essence of linear algebra, chapter 5
How to think of 3x3 matrices as transforming 3d space
3Blue1Brown
Binary, Hanoi, and Sierpinski - Part 2 of 2
How counting in Ternary can solve a variant of the Tower's of Hanoi puzzle, and how this gives rise to a beautiful connection to Sierpinski's triangle.
3Blue1Brown
Bayes theorem
A visual way to think about Bayes' theorem, together with discussion on what makes the laws of probability more intuitive.
3Blue1Brown
Limits, L'Hopital's rule, and epsilon delta definitions: Essence of Calculus - Part 7 of 11
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
3Blue1Brown
Visualizing the Riemann hypothesis and analytic continuation
What is the Riemann zeta function? What is analytic continuation? This video lays out the complex analysis needed to answer these questions.
3Blue1Brown
Pure Fourier series animation montage
A montage of "fourier series" drawings, in which the sum of many rotated vectors traces an image
3Blue1Brown
Feynman's Lost Lecture (ft. 3Blue1Brown)
This video recounts a lecture by Richard Feynman giving an elementary demonstration of why planets orbit in ellipses. See the excellent book by Judith and David Goodstein, "Feynman's lost lecture”, for the full story behind this lecture,...
3Blue1Brown
Euler's Formula and Graph Duality
A very clever proof of Euler's characteristic formula using spanning trees.
3Blue1Brown
Matrix multiplication as composition: Essence of Linear Algebra - Part 4 of 15
How to think about matrix multiplication visually as successively applying two different linear transformations.
3Blue1Brown
Linear transformations and matrices | Essence of linear algebra, chapter 3
When you think of matrices as transforming space, rather than as grids of numbers, so much of linear algebra starts to make sense.
3Blue1Brown
But why is a sphere's surface area four times its shadow?
Two proofs for the surface area of a sphere
3Blue1Brown
Implicit differentiation, what's going on here? | Essence of calculus, chapter 6
How to think about implicit differentiation in terms of functions with multiple inputs, and tiny nudges to those inputs.