A Math Puzzle Worthy of Freeman Dyson

Thomas Lin in Quanta:

Freeman Dyson — the world-renowned mathematical physicist who helped found quantum electrodynamics with the bongo-playing, Nobel Prize-winning physicist Richard Feynman and others, devised numerous mathematical techniques, led the team that designed a low-power nuclear reactor that produces medical isotopes for research hospitals, dreamed of exploring the solar system in spaceships propelled by nuclear bombs, wrote technical and popular science books, penned dozens of reviews for The New York Review of Books, and turned 90 in December — is pondering a new math problem.

“There’s a class of problem that Freeman just lights up on,” said the physicist and computational biologist William Press, a longtime colleague and friend. “It has to be unsolved and well-posed and have something in it that admits to his particular kind of genius.” That genius, he said, represents a kind of “ingenuity and a spark” that most physicists lack: “The ability to see further in the mathematical world of concepts and instantly grasp a path to the distant horizon that’s the solution.”

Press said he’s posed a number of problems to Dyson that didn’t “measure up.” Months and years went by, with no response. But when Press asked a question about the “iterated prisoner’s dilemma,” a variation of the classic game theory scenario pitting cooperation against betrayal, Dyson replied the next day. “It probably only took him a minute to grasp the solution,” Press said, “and half an hour to write it out.”

Together, they published a much-cited 2012 paper in the Proceedings of the National Academy of Sciences.

More here.