finite fields

Christof Paar's university lecture introducing Galois fields and finite-field arithmetic as used in AES. It covers the mathematics behind the AES S-box.

A 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.

PBS Infinite Series explains how Shor's algorithm lets a quantum computer break RSA encryption, building on earlier episodes about cryptography and the math of quantum computers. It works through the idea step by step.

David Tong, a Cambridge theoretical physicist, explains at the Royal Institution that the fundamental building blocks of nature are quantum fields rather than particles. He covers what we know about these fields and how they fit into the Standard Model.

Sean Carroll's 2013 Fermilab Users Meeting lecture on particles, fields and the future of particle physics. He explains that particles are vibrations in underlying quantum fields and touches on the Higgs, neutrinos and dark matter.

The first lecture of Michael Sipser's MIT 18.404J Theory of Computation course, covering course mechanics, finite automata, regular languages and regular expressions. It proves closure of regular languages under union and begins concatenation.

Veritasium argues that electric energy is carried by fields around the wires rather than by electrons moving through them, using a thought experiment with a large circuit.

3Blue1Brown explores infinite sums from convergent to divergent, with an introduction to the 2-adic metric, themed on the cycle between discovering and inventing mathematics.

Pro Magic player Luis Scott-Vargas triggers a mandatory-action infinite loop on Magic Online, and the game stalls in a non-terminating state.

3Blue1Brown 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.

A bot built by Robin Baumgarten plays Infinite Mario using A* path-finding, shown as a red planned path that updates as new obstacles appear. It won the Mario AI competitions and uses only on-screen information.

Veritasium shows how Hilbert's infinite hotel can still run out of room, using infinite buses of guests. It explains the surprising answer in a short animated segment.

Inigo Quilez live-codes a cartoon character painting entirely from math, using signed distance fields in a Shadertoy shader. He explains each step of building the image from formulas.

Mathologer examines how identities like 1+2+3+... = -1/12 arise in Ramanujan's work, starting from his 1913 letter to Hardy. The video explains the rules for summing infinite series and why such results are meaningful but not naive sums.

Vsauce's Michael Stevens takes viewers past infinity using transfinite numbers, ordinals and cardinals, with input from mathematician Hugh Woodin. It is a fast-paced, mind-bending tour of different sizes of infinity.

Veritasium 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.

Veritasium explores how electrical energy actually travels in a circuit, arguing that it flows through electromagnetic fields around the wires rather than through the electrons. It builds a long-cable experiment with Caltech to test when a distant bulb lights.

Mathologer uses continued fractions to show why the golden ratio is the most irrational number, comparing it with root 2, e and pi and pointing to where this shows up in nature.

Lex Fridman interviews physicist Roger Penrose on consciousness, the limits of computation, quantum mechanics and his cyclic cosmology. It covers his views on AI and the big bang.

Dave Ackley presents robust-first computing and the ULAM programming language for the Movable Feast Machine, a cellular-automata-like architecture. It was a short video for the Future Programming Workshop 2015.

Stand-up Maths explains why the perimeter of an ellipse has no simple closed-form equation, showing the infinite series and presenting approximation formulas.

A tour of Christian Schallert's 24 square meter apartment in Barcelona, designed so that it looks like an empty cube until he builds the furniture he needs. Kirsten Dirksen shows how the space is transformed for cooking, sleeping and dressing.

A SIGGRAPH 2013 demo from Douglas Lanman and NVIDIA of near-eye light field displays, which allow much thinner head-mounted displays that still show accurate focus and depth cues.

Footage of Richard Box's art installation in which fluorescent tubes light up in the ground under high voltage power lines, showing the electric fields they produce.

Disney Research's demo of quasistatic cavity resonance, which uses a purpose-built room or cabinet to generate magnetic fields that deliver kilowatts of power wirelessly to mobile receivers inside.

Stanford physicist Leonard Susskind explains what the Higgs mechanism is and what it means to give mass to particles. He also covers what is at stake for physics and cosmology.

Dave Ackley gives a high-level introduction to robust-first computing, which prioritizes robustness over efficiency in computer architecture. A sorting demo illustrates the idea.

Inigo Quilez live-codes the "Happy Jumping" animated scene in a Shadertoy GLSL shader over about six hours. He builds the raymarched character step by step, explaining the math and procedural techniques, with checkpoints linked for each stage.

A Numberphile video in which physicists Tony Padilla and Ed Copeland show a seemingly astounding result that 1+2+3+4+... equals -1/12. The argument is informal and has drawn criticism for glossing over what the result actually means.

ScienceClic gives a 15-minute animated introduction to quantum field theory, covering fields, spin, conserved quantities, the standard model and interactions.

The full unedited 2003 ZDF television interview with David Foster Wallace, running about an hour and a half. He talks about literature, boredom, silence, television and what stories do.

Microsoft engineers Chiara Mooney and Shiven Mian describe the journey and challenges of building and consuming React Native for Windows inside Microsoft. It was given at Chain React 2023.

Christian Schafmeister's Google Tech Talk on designing spiroligomer molecules and building Clasp, a Common Lisp on LLVM that interoperates with C++, to program molecular design. It covers the chemistry, automatic differentiation for force fields, and how the compiler is built.

A lecture by Richard Feynman on how computers work, using the analogy of a filing clerk that becomes progressively dumber and faster. It also covers heuristics and how computers handle data and solve problems in finite time.

Veritasium explains magnetism as a consequence of special relativity. Length contraction of moving charges makes a current in a wire attract or repel a nearby moving charge.

Physicist Al Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population, energy consumption and resource depletion. He argues that steady percentage growth cannot be sustained on a finite planet and that most public discussion ignores this.

Utah State plant scientist Bruce Bugbee presents his analysis of the energy and environmental costs of vertical and indoor farming. He argues artificial lighting cannot compete with sunlight in fields or greenhouses.

A recording of physicist Albert Bartlett's well-known lecture on the arithmetic of exponential growth, applied to population and energy use. He argues that steady percentage growth in a finite world cannot continue and sneaks up suddenly.

An animated 11-minute tour of the whole field of mathematics as a single map, showing how pure and applied math and their sub-fields relate to each other.

A PBS clip in which Richard Feynman explains the strange nature of light and electromagnetic radiation. He conveys how little of it we actually see and how radio waves are present everywhere.