set theory

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.

Techmoan's beginner introduction to the compact cassette, testing metal tapes and Dolby S noise reduction on a Sony TC-S1 deck. He checks whether a cassette can sound close to a CD when good tape and equipment are used.

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.

Professor Brailsford of the University of Nottingham describes how the university set out to print its own mathematics exam papers in the 1980s. The story centers on getting a Mergenthaler Linotron 202 typesetter to work with their own software.

Jared Owen's 3D animated breakdown of how a Brunswick GS-X bowling pinsetter works, showing its mechanisms for sweeping, lifting and resetting pins and balls.

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.

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.

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.

Wendover Productions examines why carbon offsets so often fail to reduce emissions, covering specific examples and the perverse incentives in offset schemes.

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.

Numberphile with Dr Holly Krieger shows how the digits of pi surprisingly emerge from the Mandelbrot set. A short, accessible math explainer.

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.

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

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.

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.

Insider explains how The Mandalorian replaced green screens with LED walls that project real-time 3D environments behind actors, with over half the show filmed on such virtual sets.

Kurzgesagt animated explainer on the Dark Forest answer to the Fermi Paradox. It argues that if advanced civilizations exist, staying silent may be the safest strategy because revealing yourself invites a first strike.

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.

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.

Physicist Angela Collier argues that dark matter is not a theory but a set of observations, covering rotation curves, the CMB and why modified gravity struggles to explain them.

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.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

Not Just Bikes explains how North American speed limits are set and why posted limits matter far less than street design. It argues that drivers follow the road's cues, so safe speeds have to be built into the street.

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.

Vsauce explores how human reasoning works, drawing on the social theory of reason and the extended mind thesis, made in partnership with Bill Gates around climate change.

CGP Grey's sarcastic animated video adapted from the book How to Be Miserable, listing habits that reliably make people unhappy. By inverting the advice, it shows what to avoid and prompts reflection on goals and routines.

Vox Earworm explains why John Coltrane's Giant Steps is so hard to improvise over: it is fast and moves through three keys. Musicians Braxton Cook and Adam Neely walk the host through the underlying music theory.

Isaac Arthur's in-depth look at what it would take to settle and eventually terraform Mars. He covers the challenges and the scale of the work needed to make it a home for humanity.

Veritasium shows silicone oil droplets bouncing on a vibrating bath, a physical analogue of pilot wave theory that reproduces quantum-like behavior such as double-slit patterns.

Adam Neely tests the claims for tuning to A=432 Hz by trying the unusual tuning systems that its proponents' numerology requires. He compares how they sound against standard tuning and temperaments.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

Captain Disillusion's comedic, fast-paced explainer on how color works in cameras, displays and video. It covers the biology of color perception and what it means for screens.

A short animated TED-Ed lesson in which two competing ice cream vendors on a beach illustrate why rival shops cluster together. It introduces game theory and the Nash equilibrium through the Hotelling model.

A Blender-animated explanation of the Toyota Hybrid Synergy Drive, showing how the engine, two motor-generators, planetary gearset and battery work together as an eCVT.

Veritasium investigates whether a wind-powered vehicle can travel directly downwind faster than the wind, driving the Blackbird craft himself. The video explains the physics behind a claim some physics professors dispute.

PBS Space Time explains the Higgs field and how the Higgs mechanism gives particles mass within quantum field theory. It is a ten-minute overview for a lay audience.

CaspianReport explainer arguing that Russia's geography, especially its vast size and indefensible Moscow core, shapes its political behavior. It frames Russian security thinking through the lens of geographic determinism.