math

Conrad Wolfram argues that the part of math taught in schools, hand calculation, is tedious and mostly irrelevant to real mathematics. He proposes teaching math through computer programming so students can tackle real problems.

Matt Parker's Royal Institution talk based on his book Humble Pi, covering everyday mathematical mistakes and spurious patterns that went wrong in engineering and software. It mixes stand-up comedy with stories of coincidence and error.

Mathematician 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.

Matt Parker gives a hands-on Royal Institution talk on how four-dimensional shapes appear in a 3D world, with props like straw frames, Mobius strips and a knitted hat. It is a playful general-audience tour of the fourth dimension.

Mathematician Hannah Fry's TED talk on patterns in dating and mate-seeking, including optimal stopping and three math-backed tips for finding a partner.

Ruben Meerman presents a TEDx talk on the stoichiometry of weight loss, showing with lab demonstrations where fat goes when it is lost. He argues that most of it is exhaled as carbon dioxide.

A UCTV panel with endocrinologist Robert Lustig, dentist Cristen Kearns and health policy expert Laura Schmidt on how the US food system and sugar industry influence diet and health, including industry efforts to shape the science.

Cambridge Analytica CEO Alexander Nix keynotes the OMR 2017 marketing festival on big data and personality-based targeting in political campaigns. It was given before the company's scandal broke.

Gerald Jay Sussman speaks at Dan Friedman's 60th birthday celebration about how programming helps formulate and clarify ideas. He argues that ambiguous mathematical notation hinders understanding.

Steven 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.

Freya 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.

Eugenia 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.

Tom 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.

Erik Meijer argues that category theory is the mathematicians' version of interface-based design. He shows that Java 8 lambdas and method references form a Cartesian closed category.

Jiahao 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.

Conal 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.

Adam Neely's Ableton Loop 2017 talk links rhythm, pitch and synaesthesia. He shows that polyrhythms sped up become chords, so tempo and pitch are related by ratios.

A 95-minute recorded debate at the ARITH23 computer arithmetic conference between John Gustafson, proponent of unums/posits, and William Kahan, architect of IEEE 754 floating point. They argue the merits of the new number formats versus conventional floats and interval arithmetic.

Gernot Heiser presents seL4, a microkernel with a mathematical proof connecting security properties to the binary code, and explains what its open-sourcing means for users. It covers its roles as a microkernel, separation kernel and hypervisor.

Meredith 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.

Philip 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.

Leslie Lamport argues that programmers, like architects, should write rigorous specifications before coding, especially for concurrent and distributed systems. The talk introduces the case for writing specs (the TLA+ mindset) as a way of thinking above the code.

Jay Parlar's Strange Loop talk shows how model checkers such as Alloy can find complex bugs in a system's design without running or reading any code. He walks through modeling architectures and checking every possible sequence of operations, including a real security bug and a UI feature-interaction bug.

Edwin Brady, creator of Idris, presents Idris 2 and demonstrates type-driven development, where the compiler assists by filling holes and suggesting implementations from types.

Guy Steele's PPoPP 2017 keynote surveying the history of computer science metanotation, including BNF, inference rules, and overline notation. He argues the field's notations are inconsistent and fragmented.

Edwin Brady presents Idris 2, a rewrite of the Idris dependently typed language, and shows type-driven development in practice. The demos show the compiler filling in whole functions from their types.

Aditya Siram introduces ATS, a statically typed ML-like language that compiles to C and offers type-safe pointer arithmetic and a full proof language. The Strange Loop talk shows off C interop, concurrency and verification features with non-trivial examples.

Hillel Wayne's PyCon 2018 talk on testing beyond pytest and mypy. It introduces property-based testing with the Hypothesis library and design-by-contract with dpcontracts, and shows how to combine them with an existing test suite.

Hillel 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.

Philip Wadler's Lambda Days talk on propositions as types, the link between logic and computation that underlies theorem provers and programming language design.

A Clojure/conj 2016 talk demoing Barliman, a prototype smart editor that does program synthesis. Given a partial program and tests, it completes the program using a relational interpreter written in miniKanren.

Nadia Polikarpova's Strange Loop talk on program synthesis driven by refinement types, as in Synquid. It shows how rich type specifications can be turned into verified, executable code.

David Christiansen gives a Strange Loop 2018 introduction to dependent types, where one language serves for both compile-time and run-time code and programs unite with proofs. It draws on his book The Little Typer.

Tikhon Jelvis's Compose Conference talk on using the Z3 SMT solver to analyze and verify programs, including checking invariants with bounded loops. He demonstrates verifying programs in a small language by compiling them to Z3.

Robert Moss's JuliaCon 2015 talk describes using Julia as a specification language for ACAS X, the next-generation airborne collision avoidance system that succeeds TCAS.

An AdaCore webinar in which NVIDIA engineers explain why and how they adopted Ada and SPARK for security-critical firmware. It covers the business case and the engineering experience of the transition.

Edwin Brady, creator of Idris, introduces type-driven development in a dependently typed language. He shows types being written first and programs derived with interactive editing, then extends beyond simple examples to programs that interact with users and networks.

John Kitchin shows how Emacs org-mode with Python lets researchers combine narrative, math, figures and executable code in one document. It exports to LaTeX, HTML and PDF, and he used it for papers and e-books.

Damian Conway's hour-long keynote at the Perl conference, On the Shoulders of Giants, showing off Perl 6 (Raku) features with history, algorithms and a quantum math operator built with grammars. It is delivered with comic flair.

Felienne Hermans argues that Excel is the world's most popular programming language and shows how spreadsheets work as a pure functional language. She implements a few mathematical problems in spreadsheet formulas to illustrate why they are so powerful and approachable.