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.

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.

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.

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.

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.

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.

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.

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.

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.

Stated Clearly explains the RNA world hypothesis, which resolves the chicken-or-egg problem of genes versus enzymes by proposing that RNA once did both jobs. It outlines how evolution could begin with RNA chains alone.

Scott Manley surveys the research on whether people can adapt to rotating artificial gravity, from early Soviet centrifuge tests to modern studies. He concludes it is an engineering problem and discusses Coriolis effects and station radius.

A five-minute BicycleDutch episode showing how Dutch junctions are designed so cyclists and pedestrians can cross safely. It explains the layout choices that separate and protect them.

A Design Club episode that analyzes how Super Mario Bros. level 1-1 teaches players to play through level design alone, without text tutorials.

Tom Scott tours the rotating room artificial gravity facility at Brandeis University's Graybiel lab. It shows how humans cope with rotation-based gravity and the odd effects such as Coriolis forces.

Robert Miles covers a paper where researchers ran real versions of his earlier mesa-optimizer thought experiments. They show inner misalignment, where an AI learns the wrong goal in training and misbehaves when deployed.

Practical Engineering explains how continuous welded rail copes with thermal expansion by restraining it, using the relationship between temperature, stress and strain. The video is part of a series on railways.

A short BicycleDutch episode showing how Dutch junctions with protected cycle paths are laid out. It argues these are proven, non-experimental designs that make intersections safer for cyclists.

Half as Interesting explains why the Eiffel Tower's night-time lighting is under copyright, which makes publishing photos of it at night legally problematic.

CityNerd explains why traffic congestion grows nonlinearly as more cars use a road network, and why adding road capacity tends not to fix it. It covers the consequences for drivers, bus riders, cyclists and pedestrians, and discusses alternatives such as true bus rapid transit.