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.

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 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.

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.

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.

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.

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.

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.

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.

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.

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.

3Blue1Brown, in collaboration with minutephysics, introduces the math of superposition and quantum states using polarized light. It builds up the quantum behavior of photons as a simple counting and probability problem.

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.

A short video explaining the Intel Management Engine, a hidden embedded computer inside Intel machines with deep access to hardware. It is presented from an insider's perspective and raises backdoor and NSA concerns.

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.

Forgotten Weapons examines the Heckler & Koch G11, a West German experimental rifle built around a caseless cartridge. The video covers the G11K2 and its unusual technology before its cancellation for political and economic reasons.