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
Inverse matrices, column space and null space | Essence of linear algebra, chapter 6
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
Rediscovering Euler's formula with a mug (not that Euler's formula) - Part 4 of 4
A classic puzzle in graph theory, the "Utilities problem", a description of why it is unsolvable on a plane, and how it becomes solvable on surfaces with a different topology.
3Blue1Brown
Backpropagation calculus | Deep learning, chapter 4
The math of backpropagation, the algorithm by which neural networks learn.
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
Taylor series | Chapter 10, Essence of calculus
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 paradox of the derivative: Essence of Calculus - Part 2 of 11
An introduction to what a derivative is, and how it formalizes an otherwise paradoxical idea.
3Blue1Brown
Essence of calculus, chapter 1
An overview of what calculus is all about, with an emphasis on making it seem like something students could discover for themselves. The central example is that of rediscovering the formula for a circle's area, and how this is an...
3Blue1Brown
Essence of linear algebra preview
The introduction to a series on visualizing core ideas of linear algebra.
3Blue1Brown
Science YouTubers attempting a graph theory puzzle
A classic puzzle in graph theory, the "Utilities problem", a description of why it is unsolvable on a plane, and how it becomes solvable on surfaces with a different topology.
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
Music And Measure Theory
How one of the introductory ideas in a field called "measure theory" can be thought of in terms of musical harnomy and dissonance.
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
What does it feel like to invent math?
A journey through infinite sums, p-adic numbers, and what it feels like to invent new math.
3Blue1Brown
Gradient descent, how neural networks learn: Deep learning - Part 2 of 4
An overview of gradient descent in the context of neural networks. This is a method used widely throughout machine learning for optimizing how a computer performs on certain tasks.
3Blue1Brown
Gradient descent, how neural networks learn | Chapter 2, deep learning
An overview of gradient descent in the context of neural networks. This is a method used widely throughout machine learning for optimizing how a computer performs on certain tasks.
3Blue1Brown
Integration and the fundamental theorem of calculus: Essence of Calculus - Part 8 of 11
What is integration? Why is it computed as the opposite of differentiation? What is the fundamental theorem of calculus?
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
Simulating an epidemic
SIR models for epidemics, showing how tweakign behavior can change an outbreak.
3Blue1Brown
Sneaky Topology (The Borsuk-Ulam theorem)
Solving a discrete math puzzle, namely the stolen necklace problem, using topology, namely the Borsuk Ulam theorem
3Blue1Brown
Backpropagation calculus | Appendix to deep learning chapter 3
The math of backpropagation, the algorithm by which neural networks learn.
3Blue1Brown
Higher order derivatives | Footnote, Essence of calculus
What is the second derivative? Third derivative? How do you think about these?
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?