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See also: Blog on Math Blogs: Two mathematicians tour the mathematical blogosphere. Editors Brie Finegold and Evelyn Lamb, both PhD mathematicians, blog on blogs --on topics related to mathematics research, applied mathematics, mathematicians, math in the news, mathematics education, math and the arts and more.
"The Twin Prime Hero," by Michael Segal. Nautilus (Issue 005, Fame), 26 September 2013;
The past April, the pure mathematics community was taken by surprise when a proof of a variant of the Twin Prime Conjecture was published in the Annals of Mathematics. The proof showed, for the first time, that a fixed number--greater than two and less than 70 million--separates infinitely many pairs of consecutive prime numbers. But no one may have been more surprised by the world-wide attention paid to this news than the person who proved it, mathematician Yitang "Tom" Zhang--a man who not only worked "in relative secrecy, but…was also a complete unknown" in the mathematical community. Zhang has been a lecturer at the University of New Hampshire since he was hired in 1999, eight years after receiving his PhD. Segal's article contains an interview with Zhang, whom the interviewer describes as "soft-spoken" and "simultaneously driven and calm, with an ambition centered around a love of math." Zhang answers questions about how he became interested in the conjecture, when he first tried to solve it, why he worked alone, why he thought he was able to solve it, how he and his wife felt after he solved the problem, how it feels to be famous and speak in public, and what advice he would give to a student who wanted to solve a problem. Zhang was later featured in an article in the Sunday Union Leader. (Photo: Tom Zhang, lecturer in mathematics at the University of New Hampshire Credit: Lisa Nugent, UNH Photographic Services.) See the UNH press release.
--- Claudia Clark
"Still a beautiful mind--and an inspiring West Virginian," by Jean Snedegar with Suzanne Higgins. West Virginia Public Broadcasting, 23 September 2013.
You may be able to tell from the title that this is an interview with John Nash. He doesn't do many interviews but he agreed to be part of this series called "Inspiring West Virginians." Nash and his sister, Martha Nash Legg, grew up in Bluefield, WV and the two begin by talking about Nash's boyhood. He says that he was influenced by E.T. Bell's Men of Mathematics while Legg says, "I guess today we'd call him nerdy!" Nash also reflects on his adulthood, "The return to sanity was a gradual process, but I did gradually reject listening to voices internally ... I was able to put it aside after a while." Legg recalls hearing that her brother had won the 1994 Nobel Prize: "The radio was on in the bedroom. And I heard them say something about a Nobel Prize Award in Economics, and I thought they said, 'John Nash in game theory,'... And it brought tears to my eyes thinking how much my parents would have loved to have heard that." The segment concludes with Nash saying that he is still active: "Well, it's not unusual to work to 70, maybe 75, but now I'm 84. I could go to 90!"
--- Mike Breen
"The Simpsons' secret formula: it's written by maths geeks," by Simon Singh. The Observer, 21 September 2013;
Singh met with writers of the television show The Simpsons, which he calls "the most mathematically sophisticated show in the history of primetime broadcasting." In his articles he describes some of the math that has appeared on the series as well as the people behind the references. One example (in The Observer) occurs in an episode involving a baseball team. Fans at the team's stadium are asked to guess the attendance and are given these choices: 8128, 8208, 8191, and "No way to tell." The numeric choices, in order, are a perfect number (the proper factors of 8128 sum to 8128), a narcissistic number (8208 has four digits and 84+ 24+ 04 + 84 = 8208), and a Mersenne prime (8191 is a prime number equal to 213 - 1). That reference was easy to spot but others aren't so easy, being so-called visual freeze-frame gags that only become obvious when the show is paused. In addition to the gags, the article also has profiles of some of the writers with math backgrounds. Singh also alludes to Futurama, another animated show, which had even more math jokes (see an earlier Digest) and wrote more about the show in an article for the BBC News Magazine. Singh and David X. Cohen, writer for The Simpsons, talked about the math on the show on the December 6th edition of Science Friday. Image: Last Exit to Springfield.
--- Mike Breen
"Alan Turing's story could be rebooted by calls to pardon late computer legend," by Anthony Faiola. The Washington Post, 19 September 2013.
In 1954, at the age of 41, Alan Turing was found dead of cyanide poisoning. One of the 20th century's most brilliant mathematicians and a founder of modern computers, Turing had been convicted of homosexuality under a British law dating from 1885 and sentenced to "chemical castration." Whether his death was a suicide is unclear; what is clear is the persecution he endured as a gay man in an intolerant society. "More than half a century after his apparent suicide and following global strides in gay rights," Faiola writes, "a movement is cresting to reboot the record of the British mathematician's short but luminous life." In addition to his seminal theoretical contributions, Turing had a significant practical impact: He led a team that cracked German codes during World War II. "As Hitler's blitz began raining fire on British cities [in 1940], Turing and others worked round the clock to turn the tide of the war by cracking Nazi messages encoded by the infamous Enigma machines," Faiola writes. One of Turing's colleagues once said that if Turing's homosexuality had been discovered earlier, he would have been fired from the codebreaking work and the Germans would have won the war. Although the notion of pardoning Turing has much support, some are concerned that the pardon would unleash a torrent of pardon requests from families of now-deceased gay individuals who were convicted under the 1885 law. The law was repealed in 1967 in England and Wales, and in 1980 in Scotland.
--- Allyn Jackson
The first article is an editorial addressing revelations about the National Security Agency (NSA) compromising Internet encryption techniques. The editorial acknowledges the work NSA mathematicians have done in encryption and in protecting the security of the Internet but says that recent allegations, based on documents provided by whistleblower Edward Snowden, are that the NSA "has also worked to weaken or create vulnerabilities in encryption standards." The news prompted action from the National Institute of Standards and Technology, which has opened a review of two of its standards, and the Internet Engineering Task Force, which is looking into strengthening protocols for Internet security and privacy. The editorial concludes with this assessment: "The balance between security and civil liberties has gone off the charts in the wrong direction." The more recent article tries to piece together the amount of research that the NSA funds and quotes researchers who are concerned by the NSA's actions and those who aren't. The tag line under the article title is: "Cryptographers condemn US National Security Agency’s tapping and tampering, but mathematicians shrug."
--- Mike Breen
"The Math-Supercomputing Connection," by Tiffany Trader. HPCWire, 17 September 2013.
This is an excerpt of an interview with David Brown, director of the Computational Research Division at Berkeley Lab, who earned his PhD in applied math from CalTech. He says that math in the "language of science," and is often used to make it possible to use computers to solve difficult problems. Here is his response about how math applies to supercomputers: "The scientific performance of big applications on supercomputers is as much a result of better mathematical models and algorithms as it is of increases in computer performance. In fact, the increases in performance of many scientific applications resulting from these better models and algorithms has often exceeded the performance increases due to Moore's Law."
--- Mike Breen
"How to Fall in Love With Math," by Manil Suri. The New York Times, 16 September 2013.
Last month The New York Times published an inspiring op-ed about how to fall in love with math, written by Manil Suri, a mathematics professor at the University of Maryland Baltimore County. He starts by grumbling over how most people identify mathematics with mundane things like addition or multiplication and how little awareness there is about the breadth and scope of mathematics. In his view mathematics is about ideas above anything else, ideas that inform our existence and that permeate our universe. He then talks about how many profound mathematical ideas don't require advanced skills to appreciate, in the same way you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. He demonstrates his point by walking the reader through mathematical concepts such as the origin of numbers and fractal images. Suri concludes by reflecting on the importance of changing the negative attitudes toward mathematics since students are known to have a better chance of succeeding in a subject that they perceive as playful and stimulating. Suri's peice generated over 360 online comments and these Letters to the Editor.
--- Baldur Hedinsson
"UW prof helps solve 40-year-old math problem," by Greg Mercer. The Record (Waterloo, Ontario), 16 September 2013.
After 15 years of intense work, University of Waterloo professor Jim Geelen (left) and colleagues Bert Gerards (center) of Maastricht University (Netherlands) and Geoff Whittle (right) of Victoria University of Wellington (New Zealand) have found a solution to Rota's Conjecture, a theory that involves embedding abstract geometric structures called matroids into concrete geometric frameworks. In order to find the solution, Geelen spent over a year learning about graph minor theory, which eventually proved to be essential to solving the conjecture. Geelen notes that the first few years of efforts to prove the conjecture were the most difficult, but the long hours and close collaboration among the international team resulted in mathematical success as well as strong friendships. In January, more than 40 years after the conjecture first was presented in 1970, Geelen, Gerards, and Whittle found a proof while working together in Waterloo. They anticipate that writing up their work will require three years.
--- Lisa DeKeukeleare
"The mathematics of murder," by Adeline Lo and James H. Fowler. Nature, 12 September 2013, page 170.
"Gun-control advocates believe that widespread gun ownership increases the rate of gun-related crime, whereas critics argue that gun availability actually decreases gun violence because potential assailants are less likely to commit such cries if they believe citizens are armed. But who is right?" The authors summarize recent scientific literature covering many factors and variables--legal, statistical, social, and economic--and find that "many of these correlations are difficult to interpret." This article concentrates on one study by Wodarz and Komarova published in PLos ONE in which "the key insight is that there are essentially two perfect worlds, one in which no one owns a gun (meaning no one is able to attack) and one in which everyone owns a gun (meaning no one is willing to attack)"--and that there is a big in between where "there's the worst of both worlds." Ultimately "their model implies that stricter laws are the best way to reduce gun deaths," but that they offer the important contribution of "highlighting key parameters that require further empirical investigation."
--- Annette Emerson
"How Math's Most Famous Prize Affects The Productivity Of The Geniuses Who Win It," by Max Nisen. Business Insider, 10 September 2013.
The Business Insider's strategy section has this piece on how winning awards can alter the recipient's behavior. According to a new study-- "Prizes and Productivity: How Winning the Fields Medal Affects Scientific Output"--by two economists, Harvard's George Borjas and Notre Dame's Kirk Doran--receiving a big award actually kills productivity. The authors followed recipients of the Fields Medal, the most prestigious prize in mathematics, and found that mathematicians who win it publish far less in the years afterwards than their peers. The Fields Medal is meant to reward great achievement, but it may also have the unintended side effect of creating complacency. The researchers explain this in part by citing what economists call the "wealth effect." The award being equivalent to "wealth" in terms of prestige and job security, making Fields Medalists less productive. The authors also found a surprising positive effect of winning the award. Though the winners publish less, they take more risks in the future and tackle more challenging problems. Receiving the Fields Medal offers the medalists the opportunity and safety to do truly innovative work.
--- Baldur Hedinsson
"Why Do I Panic When It Comes to Math?", by Marilyn vos Savant. Parade, 8 September 2013.
In response to a reader's question asking why an otherwise intelligent adult would find the prospect of a math problem to be panic-inducing, columnist Marilyn vos Savant postulates that the system of math education in America is responsible for such a phobia. Vos Savant argues that although children are able to pick up logic-based math more easily than reading at an early age, our educational construct focuses on reading, and teaches math in terms of operations rather than concepts. At the other end of the scale, vos Savant posits that math education continues too long into high school and college, and includes topics unnecessary for most professions. Taken together, she argues, the missed opportunities in early education, and the fast pace and overly demanding approach taken later have resulted in cases of "math anxiety" in America.
--- Lisa DeKeukeleare
"Ratio for a good life exposed as 'nonsense'," by Bruce Bower. Science News, 7 September 2013, pages 5-6.
It turns out psychologists can do math, and other psychologists can catch and expose their egregious errors. In another take from physicist Alan Sokal's blooper reel, Sokal and psychology master's student Nicholas Brown have discredited a math-heavy October 2005 American Psychologist article on the "critical positivity ratio"--the balance of positive and negative emotions leading to optimal "life success." The 2005 paper, written by psychologists Barbara Fredrickson of UNC Chapel Hill and Marcial Losada of Losada Line Consulting in Brazil, applied Lorenz's classic equations--a simplified three-dimensional model of atmospheric convection which led to some of the seminal discoveries in chaos theory--to 28 days of emotion data collected from volunteers. They found that the volunteers who seemed to be "flourishing," exhibiting traits such as helpfulness to others and high creativity, displayed a ratio of positive to negative emotions between about 3:1 and 12:1. The 3:1 lower bound has, itself, flourished, becoming widely cited as the threshold emotional balance required for prosperity.
But there were problems--not the least of which was that the Lorenz equations were involved in drawing such a seemingly straightforward conclusion. For one thing, Sokal points out, Fredrickson and Losada made no attempt to justify treating their emotional variables as continuously changing, fluid-like quantities. For another, they made no attempt to fit the parameters of the Lorenz equations to their data--thus treating emotions exactly like a simplified two-dimensional fluid, heated from below and cooled from above. Amazingly, these errors went unnoticed until Brown, who has no post-secondary mathematics training, read the paper for one of his classes at the University of East London. After struggling through Lorenz's landmark 1963 paper, Brown realized that Fredrickson and Losada had unwittingly stumbled upon an invariant: no matter what their volunteers' emotional data was, their calculations would always churn out the same set of meaningless ratios. He then called the attentions of Sokal and psychologist Harris Friedman, of the University of Florida in Gainesville, to this discovery. The three published their, er, findings, in American Psychologist in July, joining other psychologists' recent calls for a cleaning of the discipline's theoretical house. For her part, Fredrickson has published a commentary on the take-down, admitting to the error of her math, but supporting the critical positivity ratio with--who'd have guessed--experimental evidence.
--- Ben Polletta
"Ideas for Improving Science Education," by Claudia Dreifus. The New York Times, 2 September 2013.
In this article, Dreifus asks 19 people, including the following four mathematicians, what change they would make if they could do one thing to improve science education in this country.
--- Claudia Clark
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