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.

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.

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.

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.

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.

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.

3Blue1Brown shows how pi emerges from prime numbers via complex numbers and sums of squares, culminating in a formula for approximating pi.

Numberphile's Tony Padilla and Matt Parker discuss Graham's number, once the largest number used in a mathematical proof, and how enormous it is.

Mathologer uses continued fractions to show why the golden ratio is the most irrational number, comparing it with root 2, e and pi and pointing to where this shows up in nature.

A Numberphile video with Dr James Grime on Sloane's Gap, the observation that integers in the OEIS are not evenly represented and some numbers are underrepresented. It explains the clusters of 'interesting' numbers.

Numberphile's James Grime discusses highly composite numbers, nicknamed anti-primes, which have more factors than any smaller number, using 5040 as the central example. It touches on Plato and Ramanujan.

Numberphile with Tim Browning on the sum-of-three-cubes problem and why 33 was the lowest unsolved case. The description notes a later solution for 33.

Veritasium explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

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.

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.

Sabine Hossenfelder asks whether complex numbers are just a convenient tool or necessary in physics. She discusses a recent paper arguing that quantum mechanics cannot be done with real numbers alone.

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.

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.

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.

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.

PBS Space Time explains the Standard Model Lagrangian, the single equation encapsulating the particle physics theory, and visualizes what its terms mean.

Primer uses simulations to compare voting systems such as first-past-the-post, approval, ranked choice and others. It shows how each system behaves and can be manipulated, with links to further voting theory resources.

A PBS Space Time episode on fuzzballs, the string-theory proposal for black holes that replaces the singularity with a tangle of strings. It explains why black holes seem to both have to exist and break known physics.

A short CGP Grey explainer on the overlapping and inconsistent membership arrangements of European countries across the EU, Schengen, the euro and the EEA. It shows why "the EU" is full of exceptions.

Rick Beato analyzes a pop song he argues is among the most harmonically complex ever, breaking down its chords and key changes. It is a music theory deep dive aimed at general music fans.

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.

3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.

An animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.