Page 2 of 15
In briefNumberphile visits Cliff Stoll, the man behind ACME Klein Bottles, and sees how he stores a thousand glass Klein bottles in a crawlspace under his house. A remote-controlled forklift fetches them.
In briefA five-minute preview of 3Blue1Brown's Essence of Linear Algebra series, which uses animation to build geometric intuition for topics from a standard linear algebra course.
In briefVeritasium explores the Prisoner's Dilemma and Axelrod's tournaments, showing why tit-for-tat and forgiving strategies win in repeated games. It extends the ideas to cooperation in evolution and conflict.
In brief3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.
In briefThe first part of Welch Labs' series on imaginary numbers, presenting them as the natural extension of the number line into two dimensions. It covers the history and the math with strong visuals.
In briefAn animated introduction to geometric algebra, presented as a language that can describe most of physics. It was made with manim and covers multivectors and how they generalize familiar tools like cross products and quaternions.
In briefChristopher Domas's Derbycon 2015 talk on the M/o/Vfuscator, a compiler that emits only x86 mov instructions, showing mov is Turing complete. It explains how a full machine is built from mov and why the output is a nightmare to reverse engineer.
In briefA 10-minute 3Blue1Brown chapter explaining the determinant as the factor by which a linear transformation scales area or volume. It builds the idea geometrically with animations before any formulas.
In briefChandler Carruth's CppCon 2014 talk on writing fast C++, explaining why data structure choice and memory layout matter more than clever algorithms. It covers why standard containers like unordered_map perform poorly on modern CPUs.
In briefA short CGP Grey explainer on the alternative vote (instant runoff voting) versus first past the post, made around the 2011 UK referendum. It shows how ranked ballots are tallied and why they avoid spoiler effects.
In brief3Blue1Brown explains fractal dimension and shows why many fractals are not strictly self-similar. Self-similarity turns out to be a special case of the broader idea of fractional dimension.
In briefVsauce's roughly 24 minute explainer on the Banach-Tarski paradox, building from infinity and set theory to the decomposition of a sphere into pieces that form two spheres.
In briefVeritasium's explainer on Godel's incompleteness theorems and the limits of mathematical proof, tracing set theory, Hilbert's program and the road to Turing and modern computing.
In brief3Blue1Brown visualizes high-dimensional spheres to explain a surprising puzzle about how a sphere fits in a box as dimensions grow. It builds geometric intuition for counterintuitive properties of high-dimensional space.
In briefA short SIGBOVIK 2017 presentation by Tom Wildenhain showing that PowerPoint animations are Turing complete, with a working Turing machine built in slides. The talk is delivered deadpan as a serious research result.
In briefJuan Pedro Bolivar Puente explains immutable and persistent data structures in C++ and how they support value semantics. He presents the Immer library, rrb-trees, and a prototype text editor that opens a huge file instantly.
In briefAndrei Alexandrescu's CppCon 2019 talk revisits sorting, showing how branchless tricks, hybrid strategies and a cost metric can speed up std::sort-style algorithms on modern hardware.
In briefMathematician Kevin Buzzard explains why he believes the Lean theorem prover will shape the future of mathematics, and describes digitizing his university curriculum in Lean with undergraduates, plus the cultural challenges.
In briefCGP Grey compares airplane boarding methods, based on an arXiv paper, and shows why the intuitive back-to-front approach is slow while random or outside-in boarding does better.
In briefA two-minute video of Conway's Game of Life running inside Conway's Game of Life, built from OTCA metapixels and Golly. It zooms smoothly between scales.
In briefThe first of four short videos from Bill Hammack (engineerguy) introducing and giving the history of a 100-year-old mechanical computer, Michelson's harmonic analyzer. The series goes on to explain Fourier synthesis, analysis and operation of the machine.
In brief3Blue1Brown's chapter on eigenvectors and eigenvalues in the Essence of Linear Algebra series. It builds a visual intuition for what they mean, why an eigenbasis is useful, and ends with a puzzle.
In briefFreya Holmer's Dutch Game Day 2023 talk asking why vectors can't be multiplied, building from complex numbers to a single axiom and arriving at geometric algebra, quaternions and multivectors.
In briefMatt Parker talks Numberphile through the different kinds of numbers: algebraic, transcendental, computable, normal, and beyond. It shows how few numbers we can actually name or describe.
