math visualization

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.

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.

Christopher Domas presents his Cantor Dust tool at Derbycon 2012, a 3D visual approach to reverse engineering binaries by visualizing their structure dynamically.

Christopher Domas's REcon 2013 talk on dynamic binary visualization for reverse engineering. He shows how rendering binary data as interactive visual maps and trigraphs reveals structure that hex dumps hide, leading to his Cantor.dust tool.

Bret Victor's talk on Drawing Dynamic Visualizations. It argues that visualization tools offer either the directness of hand drawing or the dynamics of programmed graphics, and shows a tool that combines both.

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.

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.

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.

Steven Wittens' JSConf US 2013 talk on drawing with WebGL, using animated visuals to walk through vectors, matrices and the rendering pipeline. Despite the title, it works as a visual primer on the linear algebra behind 3D graphics.

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.

A three-minute capture of SORTDEMO.BAS, the sorting visualization that shipped with QBasic. It animates insertion, bubble, heap, exchange, shell and quick sort with chiptune-like sound.

A Computer History Museum oral history with Avie Tevanian covering his math talent, work on the Mach microkernel at CMU, joining NeXT, leading NEXTSTEP development and the 1996 Apple acquisition.

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.

Gerald Jay Sussman speaks at Dan Friedman's 60th birthday celebration about how programming helps formulate and clarify ideas. He argues that ambiguous mathematical notation hinders understanding.

A four-minute tour of the TeXmacs scientific editor, showing math typing, figures, citations, a drawing tool, document styles, HTML export, presentations and animations.

Gary Garrett's stop-motion animation of his song Flying Dream, with notes arranged on a lattice of fifths and major thirds. It shows how harmony looks in just intonation, inspired by Harmonic Experience.

Bret Victor's talk proposing a new kind of maker space built for seeing and understanding a project's behavior: inside it, across time and across possibilities. It argues for scientific understanding over recipes and rules of thumb.

Richard Hamming's 1995 lecture on n-dimensional space, showing how geometric intuition about spheres and cubes breaks down in high dimensions. It is part of his course on learning to learn.

Tom LaGatta's talk on category theory at a 2014 LispNYC meetup, covering objects, morphisms and the basic ideas in an informal, conversational style. It runs about 97 minutes.

A Foresight Institute workshop video with two talks: Shawn Douglas on nanoscale instruments for visualizing small proteins, and Bret Victor on Dynamicland. Victor's part shows biomolecular design built in his Realtalk system with physical objects.

A short clip of Venetian Snares' track 'Look' from Songs About My Cats (2001), shown as a spectrogram. The audio encodes an image in its frequency content.

John Kitchin shows how Emacs org-mode with Python lets researchers combine narrative, math, figures and executable code in one document. It exports to LaTeX, HTML and PDF, and he used it for papers and e-books.

Damian Conway's hour-long keynote at the Perl conference, On the Shoulders of Giants, showing off Perl 6 (Raku) features with history, algorithms and a quantum math operator built with grammars. It is delivered with comic flair.

Donald Knuth's 2017 Christmas Tree Lecture at Stanford about a combinatorial geometry problem whose computed numbers matched a striking formula. He tells the story of the conjecture and its sequel.

Felienne Hermans argues that Excel is the world's most popular programming language and shows how spreadsheets work as a pure functional language. She implements a few mathematical problems in spreadsheet formulas to illustrate why they are so powerful and approachable.

Physicist Geoffrey West speaks at an FQXi conference on time about complexity and scaling laws. He covers how metabolism, growth and lifespan scale across organisms and how the same mathematics applies to cities and companies.

Dan Abramov's talk on the wet codebase, using visualizations to show how removing all duplication too early produces wrong abstractions that are hard to unwind.

Jon Purdy's Stanford EE380 seminar giving an overview of concatenative programming, from function composition theory and history down to low-level implementation and correctness benefits.

Huygens Optics shows how DIY photon sieves shape a laser's wave front, explaining how they differ from zone plates and how aperture count affects the focal point, with time-resolved visualizations of the diffraction.

Nassim Taleb argues that evidence on terrorism risk presented in media is statistically naive, using extreme value theory without math to separate fat-tailed risks like Ebola and terrorism from thin-tailed ones.

Curtis Poe's FOSDEM talk arguing that day-to-day Perl 6 is far simpler than its enthusiasts' talk of exotic features suggests. He compares basic math and string handling across languages.

Erik Meijer argues that category theory is the mathematicians' version of interface-based design. He shows that Java 8 lambdas and method references form a Cartesian closed category.

A one-minute visualization of a simulated ant colony in which ants follow pheromone trails, with the source code on GitHub. It shows emergent behavior arising from simple rules.

A PyData London 2018 talk on how JPMorgan scaled its Athena Python platform over ten years to about 35 million lines of code and thousands of developers. It covers infrastructure, tooling and culture for analytics and visualization at that scale.

Find the Longest Path is a comedic song by Daniel J. Barrett, a Billy Joel parody that describes the NP-hard longest path problem in informal terms.

Adam Tornhill's GOTO Copenhagen 2019 talk on how to prioritize technical debt in large codebases. It argues for combining code complexity with change frequency (hotspots) from version control data, rather than trying to quantify debt in the abstract.

Gernot Heiser presents seL4, a microkernel with a mathematical proof connecting security properties to the binary code, and explains what its open-sourcing means for users. It covers its roles as a microkernel, separation kernel and hypervisor.

Second half of a demonstration of the 1982 Xerox Star user interface. It shows how the Star differed from the later Lisa and Mac interfaces, with strengths in networking and printing and little direct manipulation.