calculus

Tom Stuart's Ruby Manor 3 talk builds FizzBuzz using nothing but Ruby lambdas, working through Church encodings of numbers, booleans and data structures. It is a hands-on introduction to lambda calculus.

Jim 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.

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.

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.

Christopher 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.

A 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.

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.

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.

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.

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.

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.

Matt 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.

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.

A panel with Tony Hoare, Joe Armstrong and Carl Hewitt, hosted by Francesco Cesarini, on the history and future of concurrency. The three creators of CSP, Erlang and the actor model discuss their differing approaches.

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.

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.

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