complex 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.

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

Mathologer explains epicycles and complex Fourier series, inspired by an animation of Homer Simpson drawn with epicycles. It covers the shape of the Moon's orbit around the Sun and how to make your own epicycle drawings.

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 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.

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.

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 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.

WonderWhy surveys complex international borders, including enclaves like Vatican City, San Marino and Lesotho, the enclave-within-enclave town of Baarle, and the India-Bangladesh Cooch Behar region.

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.

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 short Healthcare Triage episode by Aaron Carroll arguing that milk gets an undeserved pass in efforts to improve diets. It examines claims about calcium and bone strength and concludes you don't need to drink milk.

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.

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

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.

3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.

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.

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.

3Blue1Brown illustrates how enormous the 256-bit search space is, showing how infeasible it is to find a hash or key by guessing and checking.

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 short Globe and Mail animated explainer on why renting can leave you as well off as buying a home. It walks through a rent-versus-buy comparison using Toronto numbers and the opportunity cost of a down payment. The video notes it dates from 2015 and the housing market has changed since.

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.

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.

A short infographic video on the distribution of wealth in America, contrasting what people believe, what they consider ideal, and the actual numbers. It highlights how top-heavy US wealth is.

NASA's animated explanation of the Curiosity rover's Mars landing, which relied on a complex automated sequence taking about seven minutes. It features NASA engineers discussing the risks before the 2012 landing.

Scott Manley explains the plumbing of rocket engines, including pressure-fed, gas generator, expander and staged combustion cycles. He shows why more complex designs exist and what they gain.

Military History Visualized charts ship production by the United States and Japan from December 1941 to September 1945. The growing numbers show why Japan, despite a stronger starting navy, could not win a long war.

PBS Space Time, together with It's Okay to be Smart and PBS Eons, asks how a universe drifting toward disorder produced something as complex as life. It presents the idea that the laws of physics, through thermodynamics, may actually favor the emergence of life.

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.

A two-minute clip in which Milton Friedman uses a humble pencil to show how thousands of strangers across many countries cooperate, without central direction, to make a simple product. It is a short visual version of the 'I, Pencil' essay's argument about free markets and dispersed knowledge.

Numberphile explains the long and short scales for naming large numbers, covering millions, billions, trillions, milliards and the Greek myriad, with James Grime and Tony Padilla.

A video arguing that exercise matters for the brain as much as the body, linking movement, the nervous system and BDNF to learning and memory. It draws on research connecting complex movement to brain development.

Destin Sandlin of Smarter Every Day investigates manipulation on Facebook, interviewing the company's team about content moderation. It is the third video in his series on social media manipulation.

Tom Scott explains YouTube's 11-character video IDs, which are base-64 encoded 64-bit numbers, and whether YouTube could ever run out of them. It covers counting systems and base 64 briefly.