large numbers

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

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.

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.

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.

Andrej Karpathy gives a one-hour general-audience introduction to large language models, covering what they are, how they are trained, comparisons to operating systems, and security challenges such as jailbreaks.

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.

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.

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.

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

Hyrum Wright shares lessons from five years of mass code migrations in Google's huge C++ codebase. He covers why to migrate, how hard it really is, and how Google updates core libraries and their users continually.

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.

A short cartoon explaining how language models like ChatGPT work, from autocomplete and conditional probabilities to neural networks, gradient descent and backpropagation. It shows how networks act as universal function approximators.

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

Matt Parker of Stand-up Maths explains why people keep making the same mistake with millions and billions, using a Bloomberg cash calculator example. He looks at the unit slip behind the repeated arithmetic error.

Footage from the Chasing Ice project of the largest glacier calving event ever filmed, at Greenland's Ilulissat Glacier in 2008. A 75-minute event is condensed to a few minutes of cameras watching ice collapse.

Timothy Daly, an original author of the Axiom computer algebra system, talks about turning a large Common Lisp codebase into a literate program. He argues code should be written as readable manuals, and the talk was given at Write the Docs 2013.

A timelapse compilation of the night sky above the Very Large Telescope at Paranal, Chile, using ESO photographers' footage set to music. It shows the stars wheeling overhead and the observatory at work.

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.

The official tour video of Miniatur Wunderland in Hamburg, the world's largest model railway. It shows the 1,300 square meter layout with trains, aircraft, cars and ships moving around.

John McCall of Apple's Swift team presents at CppNow 2023 on introducing a memory-safe successor language into large C++ code bases. He argues incremental improvement of C++ hits hard limits and explains Swift's C++ interoperability for gradual migration.

Tom Scott visits Dinorwig Power Station in Wales, a pumped-storage hydro plant often called Britain's largest battery. He explains how it works and how its role has shifted from TV pickup spikes to balancing wind and solar.

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.

A Discovery Channel computer simulation of a large asteroid impact on Earth, showing the scale of the devastation. It sits in a broader context of early Earth impacts and the moon-forming collision.

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.

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.

Practical Engineering explains pumped storage hydropower, which makes up most grid-scale electricity storage. It covers how it works and why it fits only certain geographies.

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.

Jeff Dean of Google describes his experiences building Google's systems and how its infrastructure evolved over time. The Stanford talk covers search, scaling tipping points and lessons from building large-scale software.

Real Engineering looks at the numbers for running California on renewables, focusing on the large energy storage needed. It argues about the cost of batteries and the role of other sources.

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.