rational numbers

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.

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.

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.

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.

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 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.

Scott Galloway's TED talk uses data to argue that young Americans are financially worse off than earlier generations, calling it a great intergenerational theft. He covers root causes and what could change it.

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.

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

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.

In a TED talk, behavioral economist Dan Ariely uses visual illusions and his research to show that people are less rational in their decisions than they think. He covers defaults, such as organ donation rates, and how choice framing steers decisions.

Erik Meijer gives a provocative talk presenting what he calls a rational alternative to Agile, arguing against Scrum-style practice. He also touches on the tenth-man concept.

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.

Catherine West's RustConf 2018 closing keynote on building a game in Rust and organizing a large codebase. It builds up an entity component system and generational indices step by step.

Martin Kleppmann's GOTO Berlin 2016 talk on how collaborative editors, offline apps, and multi-datacenter databases handle concurrent updates. It covers conflict resolution approaches including operational transformation and CRDTs, with a worked look at text CRDTs.

The Grugq's Hack In The Box 2012 talk on operational security for hackers, drawing on hacker indictments and counter-intelligence research. It reviews OPSEC goals and methods for avoiding detection and arrest, with case studies of how hackers got caught.

Psychologist Melanie Joy's TEDxMunchen talk introduces carnism, the invisible belief system that conditions people to eat some animals but not others, and how it shapes reactions to food choices.

Adam Conover's talk at a millennial marketing conference argues that generations are an unscientific, condescending idea and that millennials do not exist as a real category. The description notes that researcher Jean Twenge later said he misrepresented some of her work.

Zoz's DEF CON 22 talk on operational security in the age of pervasive surveillance. He shows how hard it is to avoid mistakes even for people who should know better.

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.

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.

Lord David Willetts argues at the Royal Institution that the post-war baby boomers gained wealth and security at the expense of younger generations. He draws on his book The Pinch, covering housing, wealth and social policy in the UK.

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.

Neil Fraser of Google presents Differential Synchronization, the algorithm behind MobWrite, for keeping multiple copies of a document in sync in real time. The talk argues the approach is robust, convergent and efficient.

Matthew Cole's Black Hat 2013 talk on operational security failures by CIA operatives. It covers the Abu Omar case and how sloppy tradecraft with cell phones exposed officers through call records and metadata.

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