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In briefHuygens Optics explains the Fourier transform and shows how a lens performs one optically. A DLP projector is used as a Fourier filter to do simple pattern recognition on lithographic character patterns.
In briefGabriel Lebec's Fullstack Academy talk introduces lambda calculus syntax, the history of mathematical logic, and the essence of functional programming using JavaScript. It also covers combinators, currying and Church encodings.
In briefMike Pound explains the discrete cosine transform and how it underpins JPEG compression. It is part two of Computerphile's JPEG series.
In briefA Golden Balls episode in which one contestant announces he will steal, leading to an unexpected outcome in the split-or-steal prisoner's dilemma.
In briefThe 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.
In briefNumberphile talks with mathematician Ron Graham about the magnitude of Graham's number, building up from arrow notation to show how impossibly large it is. It is part of a series of videos on this number.
In brief3Blue1Brown 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.
In briefDavid Kriesel's 31C3 talk, in German, on the discovery that Xerox scanner-copiers silently replace digits and letters in scanned documents. He explains how the bug stayed unnoticed in the wild for years.
In briefTom Scott-style absurdist tour by Tom7 of SIGBOVIK chess projects: a tournament of 30 weird chess algorithms used to rate a color- and piece-blind chess program. Topics include mirrors, arithmetic encoding, perverted game tree search and a diluted Stockfish.
In brief3Blue1Brown shows how the uncertainty principle arises from Fourier transforms. A wave packet cannot be narrow in both position and frequency, so the principle is a property of waves rather than of measurement.
In briefA Vsauce video exploring whether chairs exist, through metaphysics, mereology and the philosophy of categorizing objects. It runs about 38 minutes and cites academic work on ontology.
In briefDave Ackley demonstrates the Demon Horde Sort, an inherently robust sorting machine running in his Movable Feast Machine simulator. This is the uncut version with all details and side thoughts.
In briefMathologer 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.
In briefA 2007 Google Tech Talk in which Cliff Click of Azul Systems presents a lock-free concurrent hash table that scales to 768 CPUs. He explains why it is correct by reasoning in a different way than usual happens-before and memory-order arguments.
In briefAn 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.
In briefJiahao Chen's JuliaCon 2017 talk argues that vector transposes should be taken seriously in type systems and linear algebra libraries. It explains why treating vectors as matrices causes trouble in languages.
In briefPhysicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.
In brief3Blue1Brown visualizes the Riemann zeta function and the analytic continuation that extends it beyond where its series converges, building toward the Riemann hypothesis.
In briefDonald 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.
In briefA Dyalog demonstration of developing a Sudoku solver in APL, using an algorithm by Arthur Whitney with performance work by John Scholes. The narration steps through the array-oriented solution.
In brief3Blue1Brown builds toy SIR models to simulate how an epidemic spreads and tests scenarios like social distancing, travel restrictions, central gathering places and quarantine. It was made during the early COVID-19 outbreak.
In brief3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.
In briefMatt Parker analyzes the Minecraft speedrunning controversy in which Dream was accused of cheating via improbably lucky drops. He walks through the probability and the statistical arguments in the original accusation and the reply.
In briefSteven 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.
