SciShow
How the Internet Was Invented | The History of the Internet, Part 1
The Internet is older than you might think!
3Blue1Brown
Eigenvectors and eigenvalues | Essence of linear algebra, chapter 14
Eigenvalues and eigenvectors are one of the most important ideas in linear algebra, but what on earth are they?
3Blue1Brown
Integration and the fundamental theorem of calculus | Essence of calculus, chapter 8
What is integration? Why is it computed as the opposite of differentiation? What is the fundamental theorem of calculus?
3Blue1Brown
Cross products in the light of linear transformations | Essence of linear algebra chapter 11
The formula for the cross product can feel like a mystery, or some kind of crazy coincidence. But it isn't. There is a fundamental connection between the cross product and determinants.
3Blue1Brown
The more general uncertainty principle, beyond quantum
The general uncertainty principle, about the concentration of a wave vs the concentration of its fourier transform, applied to two non-quantum examples before showing what it means for the Heisenberg uncertainty principle.
3Blue1Brown
Change of basis | Essence of linear algebra, chapter 13
What is a change of basis, and how do you do it?
3Blue1Brown
Thinking outside the 10-dimensional box
A method for thinking about high-dimensional spheres, introduced in the context of a classic example involving a high-dimensional sphere inside a high-dimensional box.
3Blue1Brown
Some light quantum mechanics (with minutephysics)
An introduction to the quantum behavior of light, specifically the polarization of light. The emphasis is on how many ideas that seem "quantumly weird" are actually just wave mechanics, applicable in a lot of classical physics.
3Blue1Brown
Fractals are typically not self-similar
What exactly are fractals? A common misconception is that they are shapes which look exactly like themselves when you zoom in. In fact, the definition has something to do with the idea of "fractal dimension".
3Blue1Brown
What does area have to do with slope? | Essence of calculus, chapter 9
Derivatives are about slope, and integration is about area. These ideas seem completely different, so why are they inverses?
3Blue1Brown
Winding numbers and domain coloring
An algorithm for solving continuous 2d equations using winding numbers.
3Blue1Brown
The Brachistochrone, with Steven Strogatz
A classic problem that Johann Bernoulli posed to famous mathematicians of his time, such as Newton, and how Bernoulli found an incredibly clever solution using properties of light.
3Blue1Brown
Dot products and duality | Essence of linear algebra, chapter 9
What is the dot product? What does it represent? Why does it have the formula that it does? All this is explained visually.
3Blue1Brown
Gradient descent, how neural networks learn | Deep learning, chapter 2
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
But how does bitcoin actually work?
How does bitcoin work? What is a "block chain"? What problem is this system trying to solve, and how does it use the tools of cryptography to do so?
3Blue1Brown
Nonsquare matrices as transformations between dimensions | Essence of linear algebra, chapter 8
How do you think about a non-square matrix as a transformation?
3Blue1Brown
Cross products | Essence of linear algebra, Chapter 10
The cross product is a way to multiple to vectors in 3d. This video shows how to visualize what it means.
3Blue1Brown
But what is a Neural Network? | Deep learning, chapter 1
An overview of what a neural network is, introduced in the context of recognizing hand-written digits.
3Blue1Brown
Vectors, what even are they? | Essence of linear algebra, chapter 1
What is a vector? Is it an arrow in space? A list of numbers?
3Blue1Brown
The three utilities puzzle with math/science YouTubers
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
Binary, Hanoi and Sierpinski, part 1
How couting in binary can solve the famous tower's of hanoi problem.
3Blue1Brown
Divergence and curl: The language of Maxwell's equations, fluid flow, and more
Divergence, curl, and their relation to fluid flow and electromagnetism
3Blue1Brown
The hardest problem on the hardest test
A geometry/probability question on the Putnam, a famously hard test, about a random tetrahedron in a sphere. This offers an opportunity not just for a lesson about the problem, but about problem-solving tactics in general.
3Blue1Brown
Pi hiding in prime regularities
A beutiful derivation of a formula for pi. At first, 1-1/3+1/5-1/7+1/9-.... seems unrelated to circles, but in fact there is a circle hiding here, as well as some interesting facts about prime numbers in the context of complex numbers.