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The death of a beautiful mind
John Forbes Nash, Jr. (Photo: Berit Roald ©NTB Scanpix.)
John Nash was not just one of the most original and significant mathematicians of the 20th century, he was certainly the one best known to the public. His life, with its brilliant beginning, its long, desperate middle and its glorious later years turned out to make an irresistible story: Sylvia Nasar's biography A Beautiful Mind was a bestseller, and the movie went on to make his personal saga familiar to millions of people who otherwise might never have heard his name. So when he and his wife Alicia died in a crash on the New Jersey Turnpike on May 23 (in an airport taxi, returning from his Abel Prize ceremony in Oslo) it was frontpage news worldwide. Most valuable are the pieces where journalists contacted sources with personal knowledge of John and Alicia.

The author of 'A Beautiful Mind' on the life and death of John Nash  for the Washington Post, Zachary Goldfarb interviews Sylvia Nasar. " ...very few lives have a third act, and it was the third act to me that made this story so unique. Most biographies of geniuses are of a meteoric rise and then the gradual or sudden fall, but Nash's third act starting with aging out of schizophrenia and the Nobel was 20 years long."

The Wisdom of a Beautiful Mind  The New York Times gathered a set of recent quotes from Nash. "I can see there's a connection between not following normal thinking and doing creative thinking. I wouldn't have had good scientific ideas if I had thought more normally" (from The Irish Times), "... rationality of thought imposes a limit on a person's concept of his relation to the cosmos." (from Les Prix Nobel: The Nobel Prizes 1994).

'Brilliant' mathematician John Nash recalled fondly  The Boston Herald spoke with Isadore Singer, once Nash's colleague at MIT. "It was a pleasure to be a colleague of his. I had a great deal of admiration for him. ... He was off base often enough and knew it. We all tried to take care of him at various times in his life. ... He was not tolerant of most people, he was so brilliant. I'm lucky to have gotten to know him very well."

John Nash: The 60 Minutes Interview  On CBSNews.com, Peter Klein tells how he and Mike Wallace arranged for Nash to be interviewed on 60 Minutes. The original 2002 interview is linked to this page.

What John Nash taught us.  on the Fortune.com website, a Time article by Robbert Dijkgraaf. "One consistent element of Nash's work was that he was always going in directions that were either thought to be impossible, or actively discouraged. It's amazing the problems he was thinking of. They were really the biggest problems in mathematics. People think that there are these very big problems that everyone's working on, but people simply cannot find the internal courage to address the bigger issues. Nash suffered for that; he was really a mathematician that pushed his mind to go far, far beyond where other peoples' would dare to go."
Mathematicians and Blue Crabs
Manil Suri is a mathematician, a novelist and an occasional OpEd contributor to the New York Times. On May 2, 2015 they ran "Mathematicians and Blue Crabs," his report on the art and science of mathematical modeling of populations, and how this has played out recently in regulating the harvest of blue crabs, "the most valuable commodity" in the waters of Chesapeake Bay. (Suri teaches at the University of Maryland, Baltimore County). He asks: "how much can formulas tell about these creatures' unpredictable lives?" He starts at the beginning: "One of the simplest population formulas specifies that the output is some number $R$ times the input" and explains how $R>1$ leads to exponential growth, like compound interest, and $R<1$ to a population that would "decrease at each step and eventually die out." The next more complicated model: "By setting $R$ to decrease as population increased, the 19thcentury mathematician PierreFrançois Verhulst formulated a model in which the population first grew almost exponentially, but eventually stabilized at the maximum carrying capacity of the environment." Models now take many more factors into account. "The math behind these formulas may be elegant, but applying them is more complicated." A big problem is the quality of the data fed into the formula. "For instance, it was long believed that a blue crab's maximum life expectancy was eight years." But "this estimate .. turned out to be much too high." And since the estimate had been used in calculating crab mortality from fishing, it had led to unjustified restrictions on the harvest. So "what chance is there to find an accurate quantitative formula?" Suri answers: "In some sense, that might be the wrong goal anyway. Randomness is built into biological processes, so predicting a population is never going to be like calculating the interest on a bank account. The best we can do is use available science to make educated guesses about various outcomes."
"What Einstein Should Have Known"
is the title of a May 13, 2015 posting by John Farrell on the Forbes magazine website. Farrell covers science and technology for their "Pharma & Healthcare" blog, and he's sharing with us insights gleaned from John Gribbin's recently published Einstein's Masterwork: 1915 and the General Theory of Relativity (Icon Books, London, 2015). Part of Gribbin's story, as retold by Farrell, is that "it took Einstein a decade to formulate and publish his theory of gravitationbetween 1905 and 1915. But if he'd been a little more acquainted with the history of mathematics, he could've saved himself a few years and a whole lot of stress ... . Once his intuition told him that gravity could be described as a property of space and time ... Einstein knew he would need a very special branch of geometry to model it. What he didn't knowand should have ... is that this branch of mathematics had already been invented long before he was born." Gribbin mentions Gauss but focuses on Riemann, in this passage quoted by Farrell:

Although Riemann's extension of geometry into many dimensions was the most important feature of his lecture [presumably for his 1854 Habilitation TP], the most astonishing, with hindsight, was his suggestion that space might be curved into a closed ball. ... 'Everybody knows' that Einstein was the first person to describe the curvature of space in this way  and 'everybody' is wrong.
The story continues with William Clifford; another quote from Gribbin:

But Clifford realised that there might be more to space curvature than this gradual bending encompassing the whole Universe. In 1870, he ... described the possibility of 'variation in the curvature of space' from place to place, and suggested that: 'Small portions of space are in fact of nature analogous to little hills on the surface [of the Earth] which is on the average flat; namely, that the ordinary laws of geometry are not valid in them.' In other words, still seven years before Einstein was born, Clifford was contemplating local distortions in the structure of space  although he had not got around to suggesting how such distortions might arise, nor what the observable consequences of their existence might be, and the General Theory of Relativity, as we shall see, actually portrays the Sun and stars as making dents, rather than hills, in spacetime, not just in space.
"Einstein was unaware of his forebears in nonEuclidean geometry. And from 1907, when he first began work in earnest on his new gravitation theory, until 1912, Einstein went down many blind alleys before he realized he would need a set of field equations based on Riemann's and Clifford's work in order to finalize a testable theory. The rest is history ..."
[This is not the place for an analysis of Gribbin's book, but the distinction between "dents" and "hills" is not auspicious. TP]
Tony Phillips
Stony Brook University
tony at math.sunysb.edu

Math Digest includes posts throughout each month, with summaries of math stories and unique insights (and occasionally videos, interviews and podcasts) on mathrelated topics recently covered by the media.
Recently posted:
On using math to analyze leads in sports, by Allyn Jackson
Want to know what size lead a basketball team needs in order to have a 90 percent chance of winning in the remaining seconds of the game? Just take the square root of the number of remaining seconds and multiply by 0.4602. That's the conclusion of work by Aaron Clauset, a computer scientist at the University of Colorado at Boulder, and his collaborators Marina Kogan and Sidney Redner. After analyzing a huge amount of data from basketball, football, and hockey games, they formulated "a simple model in which the score difference randomly moves up or down over time," the New Scientist says. The model is surprisingly accurate, considering that it incorporates no features of the games. It works well for games like basketball, where the scores are fairly large numbers, but is not very reliable for games like soccer, where scores are small. "[S]o you probably shouldn't use it when betting on the English Premier League," the magazine says.
See "Winning formula reveals if your team is too far ahead to lose," by Gilead Amit. New Scientist, 11 July 2015.
 Allyn Jackson
Also now on Math Digest: Media coverage of Mathcounts, finding a shipwreck using Bayesian search theory, mathematician and musician Sitan Chen ...
Citations for reviews of books, plays, movies and television shows that are related to mathematics (but are not aimed solely at the professional mathematician). The alphabetical list includes links to the sources of reviews posted online, and covers reviews published in magazines, science journals and newspapers since 1996.
