normal numbers

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.

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.

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.

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.

A 30-minute edit of a conversation between Adam Curtis and Russell Brand in which Curtis explains HyperNormalisation and his ideas on individualism, power and real change.

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.

Astronaut Mike Mullane explains normalisation of deviance, where teams gradually come to accept violations of their own safety standards. He uses the Challenger shuttle disaster as the main case, drawing on NASA's ignored warnings before the launch. It is the first part of a talk given to a fire-fighters' association.

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.

Adam Curtis's 2016 BBC documentary arguing that politicians, financiers and technologists retreated into a simplified, fake version of the world because reality became too complex. It ranges across Trump, Brexit, Syria, Surkov's Russia and more.

Adam Curtis's 2016 BBC documentary argues that since the 1970s governments, financiers and technologists have retreated into a simplified fake world. It ranges from Syria and Libya to the road to Trump.

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.

Adam Curtis's 2016 BBC documentary HyperNormalisation, about 160 minutes long. It cuts together roughly forty years of politics, finance and technology to argue that people have retreated into a simplified fake world.

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.

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.

Richard Cook's short Velocity 2013 talk on resilience in complex adaptive systems, arguing systems operate near the edge of failure and that the surprise is how rarely they fail. He presents a model of how pressures push systems toward failure boundaries.

Alan Kay's 2009 UIUC talk arguing that computing is more a pop culture than a science and that ignoring history and fundamentals leads to inferior solutions. He touches on the history of interactive environments and what the web should have been.

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.

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

An animated xtranormal explainer on quantitative easing, what the Federal Reserve was doing and how things got there. It was made by Omid Malekan.

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.

A short xtranormal-animated comedy sketch comparing the iPhone 4 and the HTC Evo. It dates from the 2010 smartphone wars.

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.