problem solving

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

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.

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.

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.

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.

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.

Martin Donald explains the Wave Function Collapse algorithm using Sudoku-like constraint solving and shows how he implemented it with Blender and Godot. It links demos and reference articles.

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.

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.

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.

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.

2swap explains how he solved the Klotski sliding-block puzzle by mapping its full state space as a graph and visualizing it. The video includes footage of the Guinness world-record solve and links to an interactive graph.

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.

PBS Space Time explains how general relativity permits warp drive in principle and covers recent theoretical advances toward solving the negative energy problem.

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.

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.

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

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.

A Kurzgesagt animated explainer on whether aging could be cured within our lifetimes, made with Lifespan.io and the LEAF foundation. It introduces the idea of treating aging as a medical problem.

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.

A Kurzgesagt video arguing that social media's problem is information flooding and tribal polarization. It suggests a return to smaller online communities and more in-person interaction.

Comedian Dominic Frisby gives a ten-minute explanation of land value tax. He argues it would fix problems of rent-seeking and the economics of land ownership.

Technology Connections explains why the superheterodyne radio has its name and how mixing frequencies lets it tune stations well. It walks through the underlying wave phenomena and algebra and why the design solved a hard tuning problem.

A short RepresentUs explainer on how money corrupts American politics and what an anti-corruption act could do about it. It covers lobbying, super PACs and campaign finance, and pitches the group's proposed reforms. The video was later superseded by an updated version.

About Here looks at the housing crisis and argues for non-market solutions such as co-op and social housing, drawing on Vancouver's situation. It discusses how public supply can hold down rents.

Scott Manley looks at SpinLaunch, which aims to throw launch vehicles out of a spinning launcher at hypersonic speed. He covers its recent Mach 1 test of a one-third scale launcher and the engineering problems that remain.

A PBS Space Time episode asking whether the universe's information can ever truly be lost, tying quantum mechanics, determinism and black holes together. It sets up the black hole information paradox.

A PBS Space Time episode explaining why faster-than-light travel is equivalent to travelling back in time, using relativity and Minkowski diagrams for different observers.