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In briefThe first chapter of 3Blue1Brown's Essence of Linear Algebra series, introducing vectors with animated geometric visuals. It begins a series that builds intuition for linear algebra from the basics.
In briefJim Weirich's RubyConf 2012 talk derives the Y combinator step by step, live-coding in Ruby lambdas. It builds up an understanding of functional programming and lambda calculus from first principles.
In brief3Blue1Brown's animated visual introduction to the Fourier Transform, showing how a signal breaks into frequency components.
What you’ll learnWhat a neural network actually is (neurons, layers, weights and biases), pictured through a network that learns to read handwritten digits.
8:38How layers could pick out edges and shapes
In briefFreya Holmer explains how Bezier curves work, from the helper-line construction to their uses in animation, text rendering and shapes. It uses visuals from her Unity Shapes plugin and was a SoME1 contest winner.
In briefMonty Montgomery of Xiph.org gives real-time demonstrations of sampling, quantization, bit depth and dither using real audio equipment, including both digital analysis tools and vintage analog bench gear. It shows that sampled audio is not stair-stepped and corrects common misconceptions about digital audio.
In briefFreya Holmer's 74-minute video essay on splines, covering Bezier curves, B-splines, derivatives and the different levels of continuity (C0, C1, C2), built with custom animation tools. She notes she did not cover non-uniform splines.
In briefThe full-length Numberphile interview with mathematician and hedge fund founder Jim Simons. He discusses his path from mathematics and codebreaking to founding Renaissance Technologies, his use of algorithms in markets, and his philanthropy.
In briefAn 88-minute Microsoft Research talk that explains how quantum computers beat classical ones using basic linear algebra, qubits, superposition and gates. It works through the Deutsch oracle problem and ends with entanglement, teleportation and a live demo.
In briefThe first lecture of Gilbert Strang's MIT 18.06 Linear Algebra course, covering the geometry of linear equations. It opens a full 35-lecture university course.
In brief3Blue1Brown explains the math and mechanics behind Bitcoin visually: ledgers, digital signatures, proof of work and the blockchain, building up a decentralized payment system from first principles.
In briefA short Dyalog demonstration building Conway's Game of Life in a single line of APL, step by step. It shows how array operations replace loops.
In briefMatt Kulukundis explains how Google designed SwissTable, a fast, cache-friendly hash table, step by step from std::unordered_map. The talk covers open addressing, SIMD probing and the tradeoffs of changing a fundamental data structure.
In briefPart 1 of a lecture by physicist Albert Bartlett on the exponential function and its consequences for population growth, resource use and energy. It argues that steady growth rates quickly lead to enormous quantities.
In briefMicrosoft's Brian Beckman gives an hour-long, whiteboard-style walk through monads, building from function composition and monoids using school-level math. It is aimed at practicing programmers rather than category theorists.
In briefA SIGGRAPH 2019 course on geometric algebra. Charles Gunn gives an intro, then Steven De Keninck gives a programmer-focused course with live examples in ganja.js.
In briefVeritasium examines the role of luck in success, with simulations and examples showing how small advantages and chance can compound. It argues that top outcomes are disproportionately luck-driven while still crediting effort.
In briefReducible's visual walkthrough of the Fast Fourier Transform, motivated by polynomial multiplication. It shows how the FFT's key ideas can be discovered by asking the right questions.
In briefThe first video of 3Blue1Brown's Essence of Calculus series, which builds toward integrals, derivatives, and the fundamental theorem of calculus from a simple geometry question. It aims to make viewers feel they could have invented calculus themselves.
In briefPython core developer Raymond Hettinger explains how Python's dictionary implementation evolved into the compact, ordered dict in Python 3.6. He uses pictures and small bits of pure Python, and covers key-sharing, compaction and versioning.
In briefCGP Grey explains first-past-the-post voting and why it pushes elections toward two dominant parties. It is the first in his series on electoral systems.
In briefPhilip Wadler's Strange Loop talk on Propositions as Types, the link between logic and computation (the Curry-Howard correspondence). He traces its history through Church, Godel and Turing and shows how it shaped theorem provers and programming languages.
In briefMeredith Patterson and Sergey Bratus argue that networked software stays insecure because protocols and inputs are too complex to recognize safely. They propose using formal language theory and grammars to build secure, verifiable input handling.
In briefThe first lecture in Bartosz Milewski's category theory series for programmers. It covers the motivation and philosophy behind category theory and why composition matters for handling complexity.
