math history

A Veritasium video on how a feud between Russian mathematicians led to Markov chains and the modern prediction algorithms built on them. It covers the history and the math behind them.

An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.

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.

Mathologer examines the infamous Numberphile claim that 1+2+3+... equals -1/12, explaining what is wrong with the calculation and how it connects to real math like the zeta function and analytic continuation.

Mathologer shows how times table diagrams on a circle produce cardioids and other curves connected to the Mandelbrot set. He explains the patterns and links to a tool for making your own diagrams.

The first episode of Crash Course World History, in which John Green covers the shift from hunting and gathering to agriculture and how it shaped civilization. It is delivered fast and with jokes.

Matt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.

Veritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.

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 space-filling curves and the Hilbert curve, and how infinite mathematical constructions connect to finite, practical approximations. It touches on mapping between dimensions and sensory ideas.

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

Posy gives a short history of the computer mouse cursor, from early straight pointers to the tilted arrow, comparing Apple and Windows designs. He then explains why he designed his own cursor set and offers it as a free download.

A fast, absurdist 19-minute animated run through the history of the whole world, narrated and scored by Bill Wurtz in his distinctive style. It compresses millennia of events into jokes, songs and quick visuals.

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.

Matt Parker of Stand-up Maths explains single-pile Nim and the trick that wins it, using Dr NIM, a 1960s mechanical plastic computer that plays perfectly. He teaches the strategy so viewers can beat friends.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

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 first part of Extra History's animated miniseries on the South Sea Bubble. It explains how England's government debt led Robert Harley to turn to financier John Blunt, whose schemes began inflating artificial demand for shares.

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

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.

Matt Parker of Stand-up Maths asks whether a country's reported land area accounts for hills and mountains, working through how surface area depends on the resolution of elevation data. It follows up on a question from a viewer and work by researchers who measured it.

Matt Parker of Stand-up Maths demonstrates MENACE, Donald Michie's 1961 machine made of matchboxes that learns to play noughts and crosses through reinforcement. He builds and trains a physical version.

Stand-up Maths explains why the perimeter of an ellipse has no simple closed-form equation, showing the infinite series and presenting approximation formulas.

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.

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.

Veritasium tells the story of Thomas Midgley Jr., who introduced leaded gasoline and CFCs, and covers the science behind lead exposure and ozone damage. It also touches on isotope geochemistry used to uncover the history.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.

Kurzgesagt explains the Holocene or Human Era calendar, which adds 10,000 years to the current year to anchor dates to the start of human civilization. It argues this gives a more sensible frame for human history.

jan Misali traces the history of the letter W, including why it is called double u. The video is part of a series of deep dives into individual letters.

Phil Vischer of VeggieTales and Holy Post gives an 18-minute history of racial injustice in America, covering why anger persists despite civil rights laws. It is told from an evangelical Christian perspective and adapted from a class he co-taught.

Lindybeige gives an hour-long history of English coinage and the problems of maintaining a trustworthy currency. It ends with an explanation of why the pounds, shillings and pence system worked so well.

Kurzgesagt's animated overview of human origins and the vast prehistory before recorded history. It covers how modern humans emerged and spread.

Freya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.

Numberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.

A minutephysics video explaining why a piano cannot be perfectly tuned, comparing equal temperament with just intonation and the math of harmonics.

Terence Tao and Grant Sanderson of 3Blue1Brown walk through the cosmic distance ladder, showing how humans measured distances from the Earth to the Moon, Sun, planets and beyond. It includes animations and the history behind each step.

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.

3Blue1Brown introduces group theory and abstract groups, then builds toward classification of finite simple groups and the enormous Monster group with its 196,883 dimensions.

A 21-minute animation showing how a sphere can be turned inside out without creases or tears, known as sphere eversion.

Matt Parker of Stand-up Maths examines the Texas Supreme Court filing claiming Biden's 2020 win had a one-in-a-quadrillion chance. He walks through why the statistical argument is flawed.