3Blue1Brown
Who cares about topology? (Inscribed rectangle problem)
This is an absolutely beautiful piece of math. It shows how certain ideas from topology, such as the mobius strip, can be used to solve a slightly softer form of an unsolved problem in geometry.
3Blue1Brown
Binary, Hanoi, and Sierpinski, part 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
Abstract vector spaces | Essence of linear algebra, chapter 15
What is a vector space? Even though they are initial taught in the context of arrows in space, or with vectors being lists of numbers, the idea is much more general and far-reaching.
3Blue1Brown
Why is pi here? And why is it squared? A geometric answer to the Basel problem
A beautiful solution to the Basel Problem (1+1/4+1/9+1/16+...) using Euclidian geometry. Unlike many more common proofs, this one makes it very clear why pi is involved in the answer.
3Blue1Brown
Backpropagation calculus | Deep learning, chapter 4
The math of backpropagation, the algorithm by which neural networks learn.
Crash Course
Representing Numbers and Letters with Binary: Crash Course Computer Science
Today, we’re going to take a look at how computers use a stream of 1s and 0s to represent all of our data - from our text messages and photos to music and webpages. We’re going to focus on how these binary values are used to represent...
3Blue1Brown
Essence of linear algebra preview
The introduction to a series on visualizing core ideas of linear algebra.
3Blue1Brown
Taylor series | Essence of calculus, chapter 11
Taylor series are extremely useful in engineering and math, but what are they? This video shows why they're useful, and how to make sense of the formula.
3Blue1Brown
The Wallis product for pi, proved geometrically
A proof of the Wallis product for pi, together with some neat tricks using complex numbers to analyze circle geometry.
3Blue1Brown
All possible pythagorean triples, visualized
There are a few special right triangles many of us learn about in school, like the 3-4-5 triangle or the 5-12-13 triangle. Is there a way to understand all triplets of numbers (a, b, c) that satisfy a^2 + b^2 = c^2? There is! And it uses...
3Blue1Brown
How secure is 256 bit security?
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? | Deep learning, chapter 3
An overview of backpropagation, the algorithm behind how neural networks learn.
3Blue1Brown
But what is the Fourier Transform? A visual introduction.
An animated introduction to the Fourier Transform, winding graphs around circles.
3Blue1Brown
Hilbert's Curve: Is infinite math useful?
Drawing curves that fill all of space, and a philosophical take on why mathematics about infinite objects can still be useful in finite contexts.
3Blue1Brown
Higher order derivatives | Essence of calculus, chapter 10
What is the second derivative? Third derivative? How do you think about these?
3Blue1Brown
Limits, L'Hôpital's rule, and epsilon delta definitions | Essence of calculus, chapter 7
What are limits? How are they defined? How are they used to define the derivative? What is L'Hospital's rule?
3Blue1Brown
Matrix multiplication as composition | Essence of linear algebra, chapter 4
How to think about matrix multiplication visually as successively applying two different linear transformations.
3Blue1Brown
The other way to visualize derivatives
A visual for derivatives which generalizes more nicely to topics beyond calculus. Thinking of a function as a transformation, the derivative measure how much that function locally stretches or squishes a given region.
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
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