random numbers

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.

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.

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.

Veritasium explores why the number 37 turns up so often, drawing on Tom Magliery's collection of 37 sightings and a poll of about 200,000 people asked to pick a random number. It covers how humans choose numbers and why 37 stands out.

Matt Parker's LMS popular lecture on how seemingly incredible results can be meaningless random patterns. He ranges from ancient Woolworths civilisations to shoelaces and DNA.

Tom Scott visits Cloudflare's San Francisco office to show the wall of lava lamps whose camera feed is used as a source of entropy for random number generation. It is a short explainer on how this helps secure internet encryption.

Numberphile with Simon Pampena on how humans misunderstand randomness, including coin-flip sequences, run lengths and the gambler's fallacy.

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.

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.

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.

Stephan T. Lavavej's GoingNative 2013 talk explaining why calling rand() and using rand() % 100 is bad in C++, and how the C++11 <random> header does the job properly.

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.

Civilization creator Sid Meier's GDC 2010 talk on applying psychology to game design. He discusses player perception, randomness, and win states, and why designers must account for how players experience events.

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.

Numberphile interviews Grant Sanderson of 3blue1brown about Bertrand's paradox, where different reasonable ways of picking a random chord of a circle give different probabilities.

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.

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.

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.

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

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 PBS Infinite Series episode explaining the mathematics of quantum computers, including how qubits store complex numbers and how quantum computation differs from classical computation. Hosted by Kelsey Houston-Edwards.

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.

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.

David MacKay, scientific advisor to the UK energy department, gives a Harvard talk on sustainable energy at macro and micro scale, drawn from his book Sustainable Energy Without the Hot Air. It stresses the land area renewables require.

Tom Scott makes the difference between a million and a billion dollars tangible by using distance on a road trip instead of volume. The drive makes the scale of a billion intuitively felt.

Persi Diaconis explains on Numberphile the mathematics of card shuffling, including why seven riffle shuffles are needed to randomize a deck and how different shuffles compare.

Vsauce explores math through card tricks and big numbers, including an animation of how enormous 52 factorial, the number of deck orderings, really is.

Steven Pinker's TED talk presents data on homicide, war, poverty and pollution to argue that the world has improved over the past decades. He frames progress as problem-solving, not inevitability.

Dr Mike Pound explains the suspected backdoor in the Dual_EC_DRBG random number generator and how elliptic curve constants could let someone predict its output.

A clip from Mr. Show season 3 in which characters insist that 24 is the highest number. It is a short absurdist sketch about counting.

CGP Grey explains the history of the US Social Security card and number, and why they became a de facto national ID despite never being meant for it. He also covers why America resists a proper identity card.

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.