group theory

3Blue1Brown builds intuition for Euler's formula, e^(pi i) = -1, using the core ideas of group theory. It treats exponentiation geometrically as rotation and scaling instead of repeated multiplication.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

The first lecture in Bartosz Milewski's category theory series for programmers. It covers the motivation and philosophy behind category theory and why composition matters for handling complexity.

Eugenia Cheng gives the opening keynote at Lambda World 2017, presenting category theory as very abstract algebra whose abstraction gives it broad applicability. She applies it to everyday questions including privilege and prejudice.

Tom LaGatta's talk on category theory at a 2014 LispNYC meetup, covering objects, morphisms and the basic ideas in an informal, conversational style. It runs about 97 minutes.

Erik Meijer argues that category theory is the mathematicians' version of interface-based design. He shows that Java 8 lambdas and method references form a Cartesian closed category.

A talk by Eric Weinstein on gauge theory and its possible application to economics and inflation. It proposes extending the Wu-Yang dictionary into a geometric tool beyond physics.

Adam Neely examines Phil Ewell's paper arguing Western music theory is framed by a white racial perspective. He covers North Indian theory, alternative frameworks, Schenker and responses to the paper.

Physicist Angela Collier's roughly hour-long video on how string theory was hyped to the public and what that did to science communication. She traces the history of the theory as a narrative and argues it is interesting but was oversold.

Andrew Huang teaches the basics of music theory in about half an hour, covering intervals, chords and patterns. He stresses understanding how music works over memorizing terminology.

The first lecture of David MacKay's Cambridge course on information theory, pattern recognition and neural networks. It introduces the core ideas of his book Information Theory, Inference, and Learning Algorithms.

Sixty Symbols interviews Nottingham cosmologist Tony Padilla, who says string theory deserves to be taken seriously. He explains how strings emerged from the equations rather than being invented.

3Blue1Brown uses Wordle as an excuse to teach information theory and entropy, building a solver that picks guesses by expected information and incorporating word frequencies.

Mathologer shows a simple idea, the commutator, that lets anyone who can solve the first layer design their own full Rubik's cube solution. The same idea carries over to other symmetric twisty puzzles such as the Megaminx.

ScienceClic gives a 15-minute animated introduction to quantum field theory, covering fields, spin, conserved quantities, the standard model and interactions.

Adam Neely analyzes vaporwave through music theory, timbre and nostalgia, and includes a parody track made for the video. He also touches on the phenomenology of music.

Veritasium explores the Prisoner's Dilemma and Axelrod's tournaments, showing why tit-for-tat and forgiving strategies win in repeated games. It extends the ideas to cooperation in evolution and conflict.

A PBS Space Time episode introducing de Broglie-Bohm pilot wave theory, an interpretation of quantum mechanics that avoids much of the strangeness of the mainstream views. It is aimed at curious lay viewers.

Vsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.

Owen Maitzen's animated hour-long introduction to Hackenbush, a simple combinatorial game, and how its strategy leads to surreal numbers and the roots of the number system.

CGP Grey's animated adaptation of The Dictator's Handbook, explaining how rulers stay in power by keeping a small group of key supporters happy rather than ruling fairly. It lays out selectorate theory and how resources shape regimes.

Jérôme Petazzoni explains how Linux containers are built from kernel features like cgroups, namespaces and SELinux. He demonstrates putting the pieces together by hand to make a container and compares runtimes and approaches like jails and zones.

Lex Fridman interviews University of Glasgow chemist Lee Cronin about the origin of life, aliens, complexity and consciousness. The conversation centers on Cronin's assembly theory.

Looking Glass Universe explains de Broglie-Bohm pilot wave theory (Bohmian mechanics) as an alternative to the standard interpretation of quantum mechanics. The video lays out the pros and cons of the theory and links to related videos on contextuality and entanglement.

Isaac Arthur examines the Dark Forest theory, Cixin Liu's proposed solution to the Fermi Paradox in which civilizations stay silent and may destroy any that reveal themselves. He tests the theory's underlying assumptions and arguments.

The first part of a four-part Channel 4 (UK) documentary series presented by Howard Goodall, this episode covers melody and why tunes affect us so deeply. It explains how melody works in Western music with historical background and music theory.

A short Washington Post explainer on Sinclair Broadcast Group, the local TV owner that became widely known after a video showed its anchors reading an identical mandated script.

A video essay from Pop Culture Detective arguing that The Big Bang Theory normalizes sexism and toxic masculinity through its portrayal of nerd men. It analyzes recurring tropes in how the male leads treat women.

A short parody that removes the laugh track from The Big Bang Theory to show how unfunny the scenes are without it.

A feature-length Defunctland documentary on the history of Disney's FastPass and FastPass+ expedited queue systems. It covers how the systems evolved and how they were designed, with simulation of their effects on park lines.

Leonard Bernstein's 1973 Norton Lectures at Harvard, starting with Musical Phonology. He draws analogies between music and linguistics, including references to Chomsky.

Adam Neely's Ableton Loop 2017 talk links rhythm, pitch and synaesthesia. He shows that polyrhythms sped up become chords, so tempo and pitch are related by ratios.

Lex Fridman interviews Jeff Hawkins, founder of Numenta and author of On Intelligence, about the Thousand Brains Theory and reverse-engineering the neocortex. They also cover Hierarchical Temporal Memory and brain-inspired AI architectures.

The Game Theorists analyze how PewDiePie rose to become the most subscribed channel on YouTube. The video looks at why let's plays and gaming channels thrive on the platform.

An animated Sprouts video presenting Dietrich Bonhoeffer's argument that stupidity is more dangerous than evil, because reason cannot reach stupid people. It frames stupidity as a social and moral phenomenon.

3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.

The first video in a 55-part series by Michel van Biezen that introduces the Kalman filter and builds from the rationale through algebraic examples to the full matrix treatment. The videos are short, blackboard-style lectures.

Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.

A Veritasium video on the logistic map, showing how a simple population equation leads to chaos and bifurcation. It connects the idea to convection, neuron firing and the Mandelbrot set, with interactive animations.

Conal Elliott presents his paper on automatic differentiation, deriving a simple, generalized AD algorithm from a natural specification. Varying the representation of derivatives yields forward and reverse mode algorithms that avoid the complexity and statefulness of backpropagation.