math

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.

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.

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.

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 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.

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.

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.

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

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.

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.

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.

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.

A 3Blue1Brown live lockdown math episode asking what Euler's formula e^(pi i) is actually saying. It builds intuition through exponentials, rotation and vectors landing on the unit circle.

The first of an eight-part ScienceClic series building general relativity, covering worldlines, proper time and coordinate systems with animated visualizations.

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 explains why no voting system can be perfectly fair, drawing on Arrow's theorem and the work of Eric Maskin. It looks at problems with systems like first-past-the-post and ranked-choice voting.

Scott Aaronson's Harvard CMSA talk traces what mathematical truths are knowable, from Godel and Turing to the Busy Beaver function. He covers recent work on Busy Beaver values.

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.

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 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.

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.

Inigo Quilez live-codes a cartoon character painting entirely from math, using signed distance fields in a Shadertoy shader. He explains each step of building the image from formulas.

Inigo Quilez live-paints a mountain landscape using only math in a shader, building up from a basic polynomial noise surface through fractal terrain, lighting and atmosphere. The code runs in real time on Shadertoy so viewers can edit it as they follow along.