Reynolds Number - Numberphile
In briefNumberphile with Tom Crawford of Oxford explains the Reynolds number, the second of three videos on Navier-Stokes and fluid flow, with demonstrations of laminar versus turbulent behavior.
Math & Theory
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Infinite Mario AI - Long Level
In briefA bot built by Robin Baumgarten plays Infinite Mario using A* path-finding, shown as a red planned path that updates as new obstacles appear. It won the Mario AI competitions and uses only on-screen information.
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Lec 1 | MIT 6.042J Mathematics for Computer Science, Fall 2010
In briefThe 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.
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Why It's Impossible to Tune a Piano
In briefA minutephysics video explaining why a piano cannot be perfectly tuned, comparing equal temperament with just intonation and the math of harmonics.
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A Million Dollars vs A Billion Dollars, Visualized: A Road Trip
In briefTom Scott makes the difference between a million and a billion dollars tangible by using distance on a road trip instead of volume. The drive makes the scale of a billion intuitively felt.
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Infinite fractions and the most irrational number
In briefMathologer 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.
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Category Theory in Life - Eugenia Cheng
In briefEugenia Cheng gives the opening keynote at Lambda World 2017, presenting category theory as very abstract algebra whose abstraction gives it broad applicability. She applies it to everyday questions including privilege and prejudice.
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I Built a COMPUTER in Magic: The Gathering
In briefKyle Hill of Because Science explains and demonstrates, using real cards, how Magic: The Gathering can be used to build a Turing machine, a computer inside the card game.
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17. Succinct Structures I
In briefErik Demaine's MIT 6.851 Advanced Data Structures lecture introducing succinct data structures, covering rank, select and tries. It is part of the Spring 2012 course.
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Ptolemy and Homer (Simpson)
In briefA short animation reconstructing a planet's looping orbit using Ptolemy's epicycles and deferents, with the epicycles tracing out the face of Homer Simpson. It shows how enough circles can reproduce nearly any shape.
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Differential Synchronization
In briefNeil Fraser of Google presents Differential Synchronization, the algorithm behind MobWrite, for keeping multiple copies of a document in sync in real time. The talk argues the approach is robust, convergent and efficient.
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"Tackling Concurrency Bugs with TLA+" by Hillel Wayne
In briefHillel Wayne's Strange Loop talk introducing TLA+ as a specification language for finding concurrency bugs in designs. It covers stalling, race conditions and dropped messages, with PlusCal examples.
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MIT Godel Escher Bach Lecture 1
In briefThe first lecture of an MIT course on Douglas Hofstadter's Godel, Escher, Bach, covering themes like self-reference, recursion and incompleteness. The full lecture series is on YouTube.
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Spherical Geometry Is Stranger Than Hyperbolic - Hyperbolica Devlog #2
In briefCodeParade's short devlog on how spherical geometry looks in 2D and 3D and why it feels so unusual, part of the Hyperbolica series on a non-Euclidean game.
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The Best (and Worst) Ways to Shuffle Cards - Numberphile
In briefPersi Diaconis explains on Numberphile the mathematics of card shuffling, including why seven riffle shuffles are needed to randomize a deck and how different shuffles compare.
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What if Current Foundations of Mathematics are Inconsistent? | Vladimir Voevodsky
In briefVladimir 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.
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Does "land area" assume a country is perfectly flat?
In briefMatt 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.
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I Solved Klotski
In brief2swap explains how he solved the Klotski sliding-block puzzle by mapping its full state space as a graph and visualizing it. The video includes footage of the Guinness world-record solve and links to an interactive graph.
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Category Theory by Tom LaGatta
In briefTom 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.
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A4 Paper Is Too Perfect
In briefCGP Grey explains the elegant ratio of A4 and the metric paper sizes, then zooms out across scales from the Planck length to the observable universe.
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Surreal Numbers (writing the first book) - Numberphile
In briefA Numberphile interview with Donald Knuth about how he came to write the first book on surreal numbers after a lunch with John Conway. He tells the story casually in about 14 minutes.
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Lecture 1 | Convex Optimization I (Stanford)
In briefThe introductory lecture of Stephen Boyd's Stanford Convex Optimization I course (EE 364A). It outlines convex sets, functions and problems, and the course's coverage of least-squares, linear and semidefinite programming, duality and interior-point methods.
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Cambridge Ideas - Professor Risk
In briefDavid Spiegelhalter, Professor of the Public Understanding of Risk, uses statistics to weigh everyday risks such as bacon sandwiches and cycling. The six-minute piece introduces micromorts as a way to compare the risk of dying.
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Why is this number everywhere?
In briefVeritasium explores why the number 37 turns up so often, drawing on Tom Magliery's collection of 37 sightings and a poll of about 200,000 people asked to pick a random number. It covers how humans choose numbers and why 37 stands out.
