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In briefThe preface to Herb Gross's MIT OpenCourseWare 'Calculus Revisited: Single Variable Calculus', an older black-and-white lecture series. It introduces his approach to teaching calculus from the basics.
In briefMatt Might's Curry On talk on ending errors in code, both software and the human genome. He covers conservative approximation of the halting problem via static analysis and a computational approach to precision medicine.
In briefMatt Parker explains the history behind NTSC television running at 29.97 frames per second rather than 30, tracing it to the backward-compatible addition of color. He walks through the arithmetic behind the odd ratio.
In briefA 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.
In briefAn animated simulation comparing single-winner voting methods such as plurality, instant runoff and STAR. Colored regions show which candidate wins as a randomized electorate shifts across a two-dimensional political space, building on Ka-Ping Yee's earlier diagrams.
In briefVeritasium explains how Penrose tilings and quasicrystals overturned the belief that 5-fold symmetry and non-periodic crystals were impossible, including an interview with Paul Steinhardt.
In briefJames Long's dotJS 2019 talk on how CRDTs enable local-first apps and how simple they can be to implement. He shows how to use them to build robust offline-capable frontends.
In briefNumberphile's James Grime explains Cantor's result that some infinities are bigger than others, including why the reals outnumber the integers. It is a short, accessible introduction to countable and uncountable infinity.
In brief3Blue1Brown explains why positive results on accurate medical tests are often false positives, and reframes Bayes' rule using likelihood ratios (Bayes factors) to update odds. It uses visual examples to make the reasoning intuitive.
In briefMartin Kleppmann's QCon London 2018 talk on keeping data consistent in distributed systems without a central leader. It surveys CRDT algorithms for syncing devices and collaborative editing over peer-to-peer networks.
In briefGuy Steele presents a small geometric problem and compares four computational approaches: a classic sequential solution and three parallel-friendly ones. Each is illustrated pictorially and with working code, weighing total work against time to solution.
In briefConal Elliott presents his paper on automatic differentiation, deriving a simple, generalized AD algorithm from a natural specification. Varying the representation of derivatives yields forward and reverse mode algorithms that avoid the complexity and statefulness of backpropagation.
In briefEdwin Brady, creator of Idris, presents Idris 2 and demonstrates type-driven development, where the compiler assists by filling holes and suggesting implementations from types.
In brief3Blue1Brown's discovery-oriented introduction to error correction codes, building up Hamming codes from the puzzle of locating a flipped bit. It explains the parity-check idea and why it is so efficient.
In briefA short clip from Carl Sagan's Cosmos in which he explains how Eratosthenes measured the circumference of the Earth using shadows in two Egyptian cities. It is a clear, visual account of an ancient scientific feat.
In brief3Blue1Brown 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.
In briefJohn Scholes builds a depth-first tree-search operator step by step in a Dyalog APL session. It covers higher-order functions and runs the search on the N-Queens problem.
In briefTim Hutton's demonstration of SmoothLifeL, a continuous version of Conway's Game of Life using floating point values. It shows gliders traveling in any direction, rotating pairs, and elastic cord-like structures, with config details to run it yourself.
In briefVeritasium tells the history of how imaginary numbers arose from the quest for a general solution to the cubic equation, including the duels and secrecy among Renaissance mathematicians. It argues math had to give up the requirement that it mirror reality.
In briefLex Fridman interviews Stephen Wolfram for about three hours on cellular automata, computation, the Wolfram Physics Project and his career with Mathematica and Wolfram Alpha.
In briefA short 3Blue1Brown video explaining Euler's formula e^(i*pi) = -1 through dynamics, treating velocity as the thing that moves a point to a new position. It builds geometric intuition for why an exponent with i produces rotation.
In briefRobert Miles examines whether the case for AI safety is a Pascal's mugging, a tiny probability of an enormous payoff. He argues it is not, because AI risk does not depend on vanishingly small probabilities.
In briefNumberphile with Simon Pampena on how humans misunderstand randomness, including coin-flip sequences, run lengths and the gambler's fallacy.
In briefThe Center for Election Science explains favorite betrayal in instant-runoff voting: in some elections, ranking your favorite first can cause your least favorite to win. It contrasts this with plurality voting's spoiler problem.
