halting problem

A Computerphile video in which Mark Jago of the University of Nottingham explains Turing's halting problem and how it led to the blueprint for the modern computer.

Numberphile with Daniel Erman on the Josephus problem, where people in a circle are eliminated in turn. It shows how the survivor's position follows a neat pattern tied to powers of two and binary.

3Blue1Brown walks through a very hard Putnam competition problem and its elegant solution, emphasizing the visual intuition and the thought process behind solving it.

Veritasium'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.

Robert Miles introduces the first of several videos on the paper 'Concrete Problems in AI Safety', focusing on how AI systems can cause accidental negative side effects. It explains the problem in accessible terms.

Tom Scott visits Penistone to explain the Scunthorpe problem, showing why naive web and profanity filters block innocent words.

Tom Scott explains phatic expressions such as hello, thank you and how are you, which carry social meaning rather than information, and why replies like no problem can seem rude to some people.

Engineering Explained argues that internal combustion engines are far from dead, and discusses the continued development of ICEs and the problems facing electric vehicles.

Numberphile with Tim Browning on the sum-of-three-cubes problem and why 33 was the lowest unsolved case. The description notes a later solution for 33.

Polylog explains how algorithms can be turned into circuits and encoded as satisfiability problems, which lets you effectively run them backwards. It uses this to motivate breaking RSA, general reductions to SAT, and what P vs NP is really asking.

Tom Scott explains for Computerphile why handling time and timezones in code is so hard, walking through a simple web app that computes how long ago something happened. It covers the quirks of timezones and calendars and ends in an exasperated rant.

Veritasium's Derek Muller argues that Facebook's business model works against pages and creators, because it charges them to reach the audiences they built. He explains how filtering and paid promotion undermine the value of likes.

CGP Grey explains how traffic jams come from human driving behavior such as tailgating and reaction delays, and how leaving gaps and smoothing speed would reduce congestion. It also touches on self-driving cars.

Wendover Productions examines why carbon offsets so often fail to reduce emissions, covering specific examples and the perverse incentives in offset schemes.

Real Engineering looks at why Africa's abundant solar potential is hard to turn into usable power, especially for Europe. It covers the transmission, infrastructure and economic obstacles, and the pivot from concentrated solar to photovoltaics.

Real Engineering looks at the numbers for running California on renewables, focusing on the large energy storage needed. It argues about the cost of batteries and the role of other sources.

Rob Miles explains on Computerphile why implementing an off switch for a general AI is hard. A capable agent would resist being stopped because shutdown prevents it from achieving its goal.

Food YouTuber Adam Ragusea argues that gas stovetops are weaker than electric burners, dirty to clean, and a health risk from indoor air pollution. He cites Consumer Reports ratings and a literature review on gas stove health effects.

Real Engineering explains why biofuels, especially corn ethanol, are a poor energy source, looking at energy inputs, efficiency and carbon cost.

Matt 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.

An 11-minute animated introduction to P vs. NP and the wider landscape of complexity classes, inspired by the Complexity Zoo wiki. It assumes no background in computer science.

The first video in a series on extremely large numbers, introducing the topic with examples. Later parts go deep into the fast-growing hierarchy.

2swap explores lambda calculus using John Tromp's lambda diagrams, with animated beta-reductions, asking what PLUS times PLUS gives. It touches on Church encodings and the equivalence of Turing machines and lambda calculus.

A short Art of the Problem clip explaining Diffie-Hellman key exchange, using a paint mixing analogy for one-way functions and touching on modular arithmetic and discrete logarithms.

An older 3Blue1Brown video on why topology matters, built around the inscribed rectangle problem. It walks through how tori and Mobius strips appear in the solution. The channel later replaced it with an updated version.

Kyle Hill explains what nuclear waste actually is and how it is stored, arguing that the problem was effectively solved decades ago. It covers solid shielded waste and deep geological storage.

Cleo Abram's explainer on whether nuclear waste is really the intractable problem it is portrayed as, looking at how spent fuel can be recycled and used. It features a collaboration with Johnny Harris.

A short explainer on the history and mechanics of public key cryptography and the Diffie-Hellman key exchange. It uses a mixing-paint-colors analogy to show how two parties can agree on a shared secret in public.

Asianometry explains the EUV light source inside ASML's lithography machines, where lasers hit falling tin droplets twice to produce 13.5 nm light. It walks through the engineering of the droplet generator, the pre-pulse and main laser, and the plasma that results.

Kurzgesagt's animated take on climate change argues that, despite alarming headlines, there are real reasons for hope as technology, policy and public attitudes shift. It surveys trends and solutions while acknowledging the scale of the problem.

Bill Hammack of engineerguy explains how medieval engineers designed stone cathedrals using rules of thumb, with no science, mathematics or literacy. He uses it to define the engineering method.

MinutePhysics, with 3Blue1Brown, explains Bell's theorem using a Venn diagram paradox and polarizing filters. It shows why no local hidden variable theory can reproduce quantum correlations.

CGP Grey argues that aging and death are a problem worth defeating, using a short animated essay. It is part of a pair with a follow-up from Kurzgesagt.

Benn Jordan explains how Flock Safety's license plate cameras log and share vehicle locations, and explores how adversarial AI can defeat them. It covers weak security and the surveillance risks of private police-camera networks.

CGP Grey explains that postal codes are routing instructions for mail rather than geographic regions. He looks at the quirks and problems this causes.

Real Engineering's Brian McManus explains Helion's approach to nuclear fusion: colliding two plasma rings, compressing them magnetically, and capturing energy directly from the changing magnetic flux rather than boiling water. It covers why this pulsed design sidesteps problems of tokamaks and laser fusion.

Ward Cunningham explains the history and intent of the debt metaphor, which he coined while refactoring the WyCash product. He says debt means code reflecting an incomplete understanding of the problem, not sloppy programming.

Engineering Explained examines Toyota's hydrogen-burning V8 engine built with Yamaha and explains the practical problems of hydrogen combustion vehicles. It covers efficiency, storage and distribution issues.

An Economics Explained video on the different kinds of billionaires, from founders to oligarchs. It explains how wealth is held in illiquid stock and why diversification is a problem for some.

The Center for Election Science explains favorite betrayal in instant-runoff voting: in some elections, ranking your favorite first can cause your least favorite to win. It contrasts this with plurality voting's spoiler problem.