math invention

The first lecture of N J Wildberger's History of Mathematics course, starting with Pythagoras' theorem and following Stillwell's text. It emphasizes the flow of ideas over proofs.

Mathematician Colin Wright demonstrates juggling and explains the mathematics of juggling patterns, including notation that led to new throwing patterns. It is a public presentation at the Museum of Mathematics aimed at a general audience.

Thomas Garrity discusses mathematical maturity, a concept mathematicians use for professional development, and how it can inform teaching, mentoring and careers. It was given at the IAS/PCMI Park City Mathematics Institute.

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.

The first lecture of MIT 6.042J Mathematics for Computer Science, taught by Tom Leighton, introducing mathematical proofs. It covers propositions, implication and basic proof methods.

Conrad Wolfram argues that the part of math taught in schools, hand calculation, is tedious and mostly irrelevant to real mathematics. He proposes teaching math through computer programming so students can tackle real problems.

Matt Parker's Royal Institution talk based on his book Humble Pi, covering everyday mathematical mistakes and spurious patterns that went wrong in engineering and software. It mixes stand-up comedy with stories of coincidence and error.

A ten-minute clip of Richard Feynman describing how mathematicians and physicists differ in their interests and customs. He argues physics rests on visualizing and applying math rather than pure abstraction.

Gregory Chaitin is interviewed on Closer To Truth about whether mathematics is invented or discovered. He gives a nuanced view that ties the question to the nature of reality.

A short Great Big Story piece about Hagoromo, a Japanese chalk brand so prized that mathematicians stockpiled it, with some reportedly dealing it on the side. It tells the quirky tale of a writing tool whose supply became scarce.

A clip of Richard Feynman contrasting the Greek and Babylonian traditions of mathematical reasoning. It compares the axiomatic approach of mathematicians with how physicists use mathematics.

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.

An amateur animation of Tom Lehrer's satirical song New Math, which pokes fun at 1960s math teaching and subtraction in base 8. The animation illustrates the old and new subtraction methods.

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.

Mathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.

Andrej Bauer's IAS talk introduces constructive mathematics and what it feels like to do mathematics without excluded middle. It is framed as a tour for classical mathematicians.

Chamath Palihapitiya talks with Jason Calacanis about how he bought into the mythology of Silicon Valley, which he calls a Ponzi scheme, and about rebuilding Social Capital. He urges founders to grow slowly and build what matters.

A clip of Australian Prime Minister Malcolm Turnbull saying the laws of Australia prevail over the laws of mathematics, regarding encryption. The audio is quiet in the second half.

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 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.

Vladimir Voevodsky's IAS lecture starts from Godel's second incompleteness theorem to explore whether first-order arithmetic could be inconsistent. It motivates his vision of univalent foundations and computer-checked proofs.

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

Inigo Quilez shows step by step how to build a simple heart shape from mathematics and shaders, with code on Shadertoy. It is an introduction to procedural graphics and signed distance functions.

Part 2 of Richard Feynman's Messenger Lectures at Cornell, The Character of Physical Law, on the relation of mathematics to physics. He explains why understanding nature requires mathematics.

Mathematician Hannah Fry's TED talk on patterns in dating and mate-seeking, including optimal stopping and three math-backed tips for finding a partner.

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.

A 13-minute clip from This Week in Startups in which Chamath Palihapitiya describes venture capital as a Ponzi-like scheme driven by fees and inflated valuations among VCs.

Chamath Palihapitiya's Stanford GSB View From The Top talk on money as an instrument of change. HN mostly knows it for his remarks on social media's dopamine-driven feedback loops and regrets about Facebook.

A TED interview in which Chris Anderson talks with Jim Simons about his life: code-breaking, math, founding Renaissance Technologies, and his philanthropy in math education and origins-of-life research.

An original recording of a Verizon customer service call in which the rep fails to understand the difference between cents and dollars, known as Verizon Math.

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.

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.

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

Matt Parker gives a hands-on Royal Institution talk on how four-dimensional shapes appear in a 3D world, with props like straw frames, Mobius strips and a knitted hat. It is a playful general-audience tour of the fourth dimension.

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.

Timothy Gowers thinks aloud, in real time, as he tries to understand why Pascal's determinant equals 1. He does not fully solve it in this episode, but shows his exploratory process.

Lex Fridman interviews mathematician and economist Eric Weinstein about science, mathematics, and society. The conversation ranges across physics, academia, AI and job displacement.

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.