queueing 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.

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.

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.

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.

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.

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.

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.

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.

CGP Grey compares airplane boarding methods, based on an arXiv paper, and shows why the intuitive back-to-front approach is slow while random or outside-in boarding does better.

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.

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

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.

Robert Miles examines whether the case for AI safety is a Pascal's mugging, a tiny probability of an enormous payoff. He argues it is not, because AI risk does not depend on vanishingly small probabilities.

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.

CGP Grey, adapting The Dictator's Handbook, explains how rulers keep power and why succession causes trouble when they die. It is the sequel to his video on the rules for rulers.

A minutephysics video explaining why a piano cannot be perfectly tuned, comparing equal temperament with just intonation and the math of harmonics.

Musician Adam Neely examines whether certain keys sound sadder than others, looking at the history of tuning systems and temperaments and at how instrument timbre shapes the emotional character we hear. It draws on historical aesthetics writing and audio examples.

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.

WIRED's 5 Levels format with Jacob Collier explaining harmony to a child, a teen, a college student, a professional and Herbie Hancock.

A five-minute animated explainer of liquid democracy, in which voters can delegate their vote to trusted people. It starts from the origins of democracy and contrasts direct and representative models.

A Computerphile video in which Mark Jago of the University of Nottingham explains Turing's halting problem and how it led to the blueprint for the modern computer.

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.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

Technology Connections explains how RGB light and color work, from hue and saturation to color vision and how objects appear under different lighting. It uses a studio setup with colored lights to demonstrate the effects.

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.

Vsauce asks whether music will ever run out of new melodies. It counts the possible note combinations and discusses how common chord progressions and remixing affect originality.

MinutePhysics, with 3Blue1Brown, explains Bell's theorem using a Venn diagram paradox and polarizing filters. It shows why no local hidden variable theory can reproduce quantum correlations.

Veritasium explores why time seems to speed up as we age, covering chronoception and several competing explanations beyond the common proportional-theory argument.

MinutePhysics explains Shor's algorithm, showing how a quantum computer factors large integers by finding the period of a number modulo N. It walks through the modular arithmetic and number theory that give the exponential speedup over classical factoring, and why this threatens encryption.

Veritasium presents David Sinclair's information theory of aging, which says aging is a loss of epigenetic information, and the evidence that aging can be slowed or reversed. It touches on stressors like fasting, exercise and cold exposure.