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 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.

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.

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.

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.

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.

3Blue1Brown uses Wordle as an excuse to teach information theory and entropy, building a solver that picks guesses by expected information and incorporating word frequencies.

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.

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.

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.

A design essay on why products designed in Western contexts often fail when deployed in developing countries. It covers expert blindness and cultural assumptions, with examples such as malaria nets and the One Laptop Per Child project.

Numberphile talks with Grant Sanderson of 3Blue1Brown about a darts puzzle with a shrinking bullseye. Solving it takes the volumes of high-dimensional spheres, and the answer turns up Euler's number.

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.

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.

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.

AlphaPhoenix uses Monte Carlo simulation and annealing-style methods to draw North Carolina congressional district maps, both gerrymandered and fair. He focuses on the fascinating computational problem rather than the politics.

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.