Shinichi Mochizuki and the impenetrable proof - "Fesenko has studied Mochizuki's work in detail over the past year, visited him at RIMS again in the autumn of 2014 and says that he has now verified the proof. (The other three mathematicians who say they have corroborated it have also spent considerable time working alongside Mochizuki in Japan.) The overarching theme of inter-universal geometry, as Fesenko describes it, is that one must look at whole numbers in a different light — leaving addition aside and seeing the multiplication structure as something malleable and deformable. Standard multiplication would then be just one particular case of a family of structures, just as a circle is a special case of an ellipse." (previously: 1,2; via) [more inside]
Lesser-Known Trolley Problem Variations There’s an out of control trolley speeding towards Immanuel Kant. You have the ability to pull a lever and change the trolley’s path so it hits Jeremy Bentham instead. Jeremy Bentham clutches the only existing copy of Kant’s Groundwork of the Metaphysic of Morals. Kant holds the only existing copy of Bentham’s The Principles of Morals and Legislation. Both of them are shouting at you that they have recently started to reconsider their ethical stances. [more inside]
What do the words "safety," ''chaotic" and "problem" have in common? They're all on General Motors' list of banned words for employees who were documenting potential safety issues. The revelation of the 68-word list is one of the odder twists in GM's ongoing recall of 2.6 million older-model small cars for defective ignition switches. Last Week Tonight with John Oliver weighs in.
Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)
"Systems thinking (PDF) is the process of understanding how things influence one another within a whole...Systems Thinking has been defined as an approach to problem solving, by viewing 'problems' as parts of an overall system, rather than reacting to specific part, outcomes or events and potentially contributing to further development of unintended consequences." -Wikipedia [more inside]
The Angel Problem. The Angel and the Devil play a game on an infinite chess board...
Kathryn Joyce looks at unregulated Christian homes for troubled children.
Inducement Prizes -- Best known for the Ansari X Prize, the DARPA Grand Challenge and the Clay Mathematics Millennium Problems, inducement prizes have a long history, but their recent successes have led to increased government interest, viz. challenge.gov, and resulted in the development of vaccines, thanks in large part to the work of Michael Kremer.* [more inside]
If a train leaves Chicago at noon carrying 20 passengers, 5 of whom smoke, in 4 cars, what is the name of the conductor's dog?
A nearly impossible logic puzzle. Other mindtwisting puzzles. More puzzles of varying difficulty (don't scroll down too far!). XKCD's take. (previously epic post Also: 1, 2)
“Do not do what I do; rather, take whatever I have to offer and do with it what I could never imagine doing and then come back and tell me about it.”
Mark C. Taylor, the chairman of the religion department at Columbia, offers a radical proposal in The New York Times for the restructuring of the American university system. Two key components of the proposal entail ending tenure and shuttering academic departments—replacing disciplines with problems, and then tackling them with a cooperative and multidisciplinary approach, e.g. The Department of the Future of Water made up of geologists, anthropologists, political scientists, and ethicists. Should we End the University as We Know It?
The Italian Job: Problem Solved