But what is the Fourier Transform? A visual introduction.
3Blue1Brown12.6M viewsA visual introduction to the Fourier transform: winding a signal around a circle to find its frequencies.
Science & Mathematics
785,248 videos · Physics, biology, chemistry, astronomy and the mathematics underneath them.
But what is a neural network? | Deep learning chapter 1
3Blue1Brown25.1M viewsBuilds up what a neural network actually is — neurons as numbers, layers, weights and biases — using handwritten-digit recognition as the running example.
Linear transformations and matrices | Chapter 3, Essence of linear algebra
3Blue1Brown7.32M viewsMatrices as linear transformations of space — the single idea that makes linear algebra click.
The essence of calculus
3Blue1Brown11.9M viewsThe first chapter of Essence of Calculus: discovering derivatives and integrals from the area of a circle.
11:15The hardest problem on the hardest test
3Blue1Brown16.4M viewsWorks through the famously hard Putnam problem about the probability that a random tetrahedron in a sphere contains its centre, by first solving the 2D version.
But what is a Fourier series? From heat flow to drawing with circles | DE4
3Blue1Brown19M viewsFourier series from the heat equation to drawing pictures with rotating circles.
Vectors | Chapter 1, Essence of linear algebra
3Blue1Brown13M viewsWhat a vector really is, from the physics, computer science and mathematics perspectives.
Bayes theorem, the geometry of changing beliefs
3Blue1Brown6M viewsBayes' theorem as a geometric picture, with the classic 'Steve the librarian' example.
22:11But what is the Riemann zeta function? Visualizing analytic continuation
3Blue1Brown5.39M viewsVisualises the Riemann zeta function as a transformation of the complex plane and explains what analytic continuation actually means.
Gradient descent, how neural networks learn | Deep Learning Chapter 2
3Blue1Brown9.73M viewsHow a network 'learns': cost functions, the gradient, and stepping downhill in a space with thousands of dimensions.
Math's Fundamental Flaw
Veritasium30.8M viewsGödel's incompleteness, Turing's halting problem and the limits of mathematics.
Lec 1 | MIT 18.06 Linear Algebra, Spring 2005
MIT OpenCourseWare4.93M viewsGilbert Strang's first lecture of MIT 18.06: the geometry of linear equations.
28:34But why would light "slow down"? | Visualizing Feynman's lecture on the refractive index
3Blue1Brown2.89M viewsExplains why light appears to slow down in glass and where the index of refraction comes from, building from driven oscillating charges.
The Most Misunderstood Concept in Physics
Veritasium31.5M viewsEntropy, the arrow of time and why the Sun is a source of low entropy rather than just energy.
Eigenvectors and eigenvalues | Chapter 14, Essence of linear algebra
3Blue1Brown6.45M viewsEigenvectors and eigenvalues, seen as the directions a transformation only stretches.
Backpropagation, intuitively | Deep Learning Chapter 3
3Blue1Brown6.39M viewsAn intuitive walkthrough of backpropagation — how each training example nudges every weight and bias.
10:04Matrix multiplication as composition | Chapter 4, Essence of linear algebra
3Blue1Brown4.5M viewsMatrix multiplication as composition of linear transformations, chapter 4 of Essence of Linear Algebra.
21:14The medical test paradox, and redesigning Bayes' rule
3Blue1Brown1.43M viewsUses the 'medical test paradox' to motivate rewriting Bayes' rule in terms of odds and Bayes factors.
9:59Linear combinations, span, and basis vectors | Chapter 2, Essence of linear algebra
3Blue1Brown7.62M viewsLinear combinations, span and basis vectors, chapter 2 of Essence of Linear Algebra.
The determinant | Chapter 6, Essence of linear algebra
3Blue1Brown5.02M viewsThe determinant as the factor by which a transformation scales area and volume.
How Imaginary Numbers Were Invented
Veritasium22.7M viewsHow imaginary numbers arose from solving cubic equations in Renaissance Italy.
Lecture 1: Introduction to Superposition
MIT OpenCourseWare9.37M viewsMIT 8.04 Quantum Physics I, lecture 1: superposition, introduced through experiments with 'hardness' and 'color'.
Quantum Computing for Computer Scientists
Microsoft Research2.18M viewsAndrew Helwer's Microsoft Research talk teaching quantum computing to programmers with only linear algebra: qubits, gates, and the Deutsch oracle problem.
Lecture 1: Probability and Counting | Statistics 110
Harvard University1.81M viewsLecture 1 of Joe Blitzstein's Harvard Statistics 110: probability and counting.
28:33Terence Tao on the cosmic distance ladder
3Blue1Brown6.52M viewsTerence Tao and Grant Sanderson walk through how humans measured the size of the Earth, Moon, Sun and the distances to stars and galaxies, rung by rung.
23:01But what is a convolution?
3Blue1Brown3.8M viewsConvolution seen three ways: moving averages, polynomial multiplication and probability, ending with FFT-based fast convolution.
31:15But what is the Central Limit Theorem?
3Blue1Brown4.61M viewsWhat the central limit theorem actually says, its assumptions, and why sums of random variables tend to a bell curve.
34:41But what is a Laplace Transform?
3Blue1Brown2.13M viewsBuilds the Laplace transform from exponentials and the s-plane, showing what poles mean and how it turns differential equations into algebra.
22:21Why do prime numbers make these spirals? | Dirichlet’s theorem and pi approximations
3Blue1Brown7.64M viewsStarts from a curious spiral pattern in plots of primes and uses it to explain residue classes, Euler's totient and Dirichlet's theorem on primes in arithmetic progressions.
1:23:01Lecture 19: Identical Particles
MIT OpenCourseWare142K viewsMIT 8.04, lecture 19: Identical particles, bosons, fermions and the Pauli principle.
How the Krebs cycle powers life and death – with Nick Lane
The Royal Institution389K viewsBiochemist Nick Lane explains the Krebs cycle and its central role in metabolism, ageing and cancer.
1:20:12Lecture 2: Experimental Facts of Life
MIT OpenCourseWare2.27M viewsMIT 8.04, lecture 2: The experimental facts that force quantum mechanics: interference, the photoelectric effect and electron diffraction.
1:22:19Lecture 6: Time Evolution and the Schrödinger Equation
MIT OpenCourseWare725K viewsMIT 8.04, lecture 6: Time evolution of states and stationary states.
Black hole Firewalls - with Sean Carroll and Jennifer Ouellette
The Royal Institution1.77M viewsSean Carroll and Jennifer Ouellette discuss the black-hole firewall paradox and the clash between general relativity and quantum mechanics.
1:20:07Lecture 18: "Hydrogen" and its Discontents
MIT OpenCourseWare97.4K viewsMIT 8.04, lecture 18: The hydrogen atom and where the simple model falls short.
50:149. Independence, Basis, and Dimension
MIT OpenCourseWare843K viewsMIT 18.06, lecture 9: Linear independence, basis and dimension.
Recommended books
- The Joy of x, Steven StrogatzSteven Strogatz's friendly tour of the big ideas in maths
- The Feynman Lectures on Physics (boxed set)The classic set of physics lectures, in print
- Campbell BiologyThe standard intro biology text
- The Gene: An Intimate History, Siddhartha MukherjeeSiddhartha Mukherjee's history of the gene
- Cosmos, Carl SaganThe classic tour of the universe and our place in it
- The Disappearing Spoon, Sam KeanSam Kean's stories behind the periodic table
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