prime 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.

3Blue1Brown explains why plotting primes in polar coordinates produces spiral patterns, using modular arithmetic, Dirichlet's theorem and rational approximations of pi.

Numberphile with Tadashi Tokieda on the Trinity Hall Prime, a prime number whose digits form a picture of the college's coat of arms, left as a gift by a departing mathematician.

The first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions. It covers the history and the math with strong visuals.

Matt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.

Veritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.

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

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.

A Numberphile interview with Donald Knuth about how he came to write the first book on surreal numbers after a lunch with John Conway. He tells the story casually in about 14 minutes.

The first lecture of Francis Su's Harvey Mudd real analysis course, covering the construction of the rational numbers. It begins a full lecture series that follows a standard analysis text.

John Bird and John Fortune satirize the investment banking mindset in a mock interview about the subprime mortgage crisis. The sketch lampoons structured credit products and the banks' reassurances shortly before the crash.

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.

A clip from Yes Prime Minister in which Sir Humphrey shows how leading questions can make a survey support or oppose national service. It is a short satirical scene.

The first video in a series on extremely large numbers, introducing the topic with examples. Later parts go deep into the fast-growing hierarchy.

Tom Scott explains for Computerphile how floating point numbers work, why moving the binary point is fast, and why it handles money badly.

A short clip from the BBC sitcom Yes, Prime Minister in which Jim Hacker explains which kind of person reads which British newspaper. It is a satirical take on press readership and bias.

A clip from the 2015 film The Big Short in which FrontPoint Partners investigate mortgage lending in Florida and place their first trade. It shows brokers and a stripper-adjacent loan scene illustrating subprime lending to unverified borrowers.

A two-minute Yes Prime Minister scene in which Sir Humphrey persuades Jim Hacker to buy Trident, using tortured logic about nuclear deterrence.

A short scene from the British sitcom Yes Prime Minister in which officials describe 'salami tactics' for invading a country slice by slice. Each small step is too minor to justify a major response.

A sketch from the British sitcom Yes, Prime Minister in which Jim Hacker and the chief scientific advisor discuss the logic of the nuclear deterrent.

A Yes, Prime Minister scene in which Sir Humphrey shows how leading questions can make a poll produce either answer on national service.

3Blue1Brown builds visual intuition for quaternions, showing how to think about this four-dimensional number system using stereographic projection and rotations in 3D space. It is part one of a two-part series with an interactive companion site.

Numberphile talks with mathematician Ron Graham about the magnitude of Graham's number, building up from arrow notation to show how impossibly large it is. It is part of a series of videos on this number.

Freya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.

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.

Numberphile's James Grime introduces quaternions, a type of number beyond the complex numbers, building up from real and complex numbers and explaining why they are useful.

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.

Primer simulates green beard altruism, where individuals recognize and help others carrying a shared marker, and shows how imposters affect its evolution. It is an animated evolution simulation based on published papers.

Numberphile's Ben Sparks shows why the golden ratio is the most irrational number, using seeds, continued fractions and rational approximations. He also explains why plants use it for spacing leaves and seeds.

A short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.

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.

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 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.

Roy Beck's short gumball presentation using World Bank and Census data to argue that letting people immigrate to the US cannot solve world poverty because the numbers are so large. It is made by NumbersUSA, an immigration-restriction advocacy group.

John Oliver's Last Week Tonight segment on auto lending, showing how lenders steer vulnerable buyers into subprime loans and crushing debt. It uses comedy sketches to explain the practices.

CityNerd's Ray Delahanty tallies the personal costs of driving and then the externalities that car dependency imposes on everyone else, with numbers for each. It is an urbanist case that driving is heavily subsidized and costs society far more than drivers pay.

Steven Wittens' JSConf US 2013 talk on drawing with WebGL, using animated visuals to walk through vectors, matrices and the rendering pipeline. Despite the title, it works as a visual primer on the linear algebra behind 3D graphics.

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.

Episode 4 of James Burke's Connections series, tracing how commercialism, climate change and the Black Death shaped the move to the Renaissance. It follows threads through waterpower, the printing press, the Jacquard loom and the Hollerith punch card toward modern computing.