problem statements

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.

A BBC Earth clip from Inside the Animal Mind in which a crow named 007 solves an eight-step puzzle to get a reward. It showcases crow problem-solving.

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.

A short excerpt of Jon Stewart interviewing former Treasury Secretary Larry Summers about the causes of inflation and whether workers or corporate profits are to blame. It comes from an episode of The Problem With Jon Stewart.

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.

Dave Jones of EEVblog investigates why a 4K BenQ monitor switches itself off, tracing it to static discharge from an office chair. He uses an oscilloscope to examine the static impulses.

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.

Dan Pink's TED talk argues that traditional carrot-and-stick rewards often fail for creative work, drawing on the candle problem and social science research. He points to autonomy, mastery and purpose as better motivators.

Tantacrul examines sonification, the practice of turning data into sound or music, and critiques how scientists and musicians, including NASA and CERN projects, use it well and poorly.

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.

Sabine Hossenfelder explains why she left academia, criticizing its incentives, funding and career structure. She gives a personal account of the social problems in science.

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

Big Clive tears down a smart meter with a wireless modem found among fly-tipped materials. He examines its internals and checks conspiracy claims about microphones, cameras and 5G.

Steve Yegge's OSCON Data 2011 talk imagines what you could do with Google-scale storage and compute a decade later. He argues smart people should work on hard problems such as biology rather than cat pictures, and the talk ends with a moment many took as him quitting Google.

A JRE clip in which Bret Weinstein explains his concern that most American lab mice descend from a single lab lineage. He argues this undermines how well mouse research translates to humans.

A short, humorous critique of Helion Energy's fusion approach, framed as a response to a Real Engineering video. It covers low reactivity, neutron production, bremsstrahlung losses and diagnostics.

Dave2D reviews the Lenovo Legion Go S running Valve's SteamOS instead of Windows, calling it the first true competitor to the Steam Deck. He compares handheld gaming performance and experience across the two operating systems.

A WSJ investigation by Joanna Stern into iPhone thieves who watch victims enter their passcode, then use it to lock them out of Apple accounts and drain bank and payment apps. It explains how the thefts work and how to protect yourself.

A scene from Moneyball in which Brad Pitt's character argues with scouts who pick players on intangible impressions instead of performance data. It is a four-minute clip.

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.

Sabine Hossenfelder reads a confidential email and uses it to explain her worries about academia and incentives in theoretical physics research. She ties it to her earlier Nature Physics comment on research quality.

An excerpt from Russell Barkley's lecture on ADHD, focusing on inhibition, impulsivity and emotional regulation. It explains ADHD as a problem of response inhibition and emotional impulsivity.

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 Last Week Tonight segment in which John Oliver explains the US nuclear waste storage problem, including the Yucca Mountain politics. It argues the country needs a safe place to store waste.

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.

James Mickens of Harvard gives a funny lecture at HBS's Future Assembly arguing that blockchains are a very bad idea. He covers their trust, legal and practical shortcomings for real-world problems.

A short clip of Dr. Robert Zubrin, author of The Case for Mars, answering why humanity should go to Mars. He argues that societies grow by challenging themselves and that exploration inspires young people.

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.