# Math Digest

## On Media Coverage of Math

Edited by Mike Breen and Annette Emerson, AMS Public Awareness Officers
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Samantha Faria (AMS), and Allyn Jackson (Deputy Editor, Notices of the AMS)

### May 2015

On an interview with Martin Groetschel, by Allyn Jackson

Martin Groetschel is a mathematician at the Technical University of Berlin and general secretary of the International Mathematical Union. On the occasion of his appointment as president-designate of the Berlin-Brandenburg Academy of Sciences, the Welt am Sonntag published this interview with him. In it he responds to a variety of questions about mathematics, how it is perceived, and how it is taught. Lossau asks Groetschel whether someone who is weak in arithmetic could become a good mathematician. Absolutely, Groetschel replies, explaining that mathematicians rarely do arithmetic calculations and instead think mainly about abstract structures. They can then discover new phenomena and connections between them without having to do any calculations. "I know some mathematicians who have problems handling numbers fluently," he said. "But I'm not naming names."

See "Mathematiker rechnen nicht [Mathematicians don't do arithmetic]": Interview with Martin Groetschel, by Norbert Lossau. Welt am Sonntag, 31 May 2015.

--- Allyn Jackson

On media coverage of John Nash, by Annette Emerson

Immediately after John Forbes Nash, Jr., 86, and his wife, Alicia, 82, were killed in a traffic accident in New Jersey on May 23, the media worldwide exploded with articles about Nash, his life, his mathematics and his impact on the mathematics community. In this month's Math in the Media Tony Phillips points to articles on reminiscences of Nash by his biographer Sylvia Nasar and by his colleague at MIT, Isadore Singer; recent quotes from Nash; and recollections by Peter Klein on the interview Mike Wallace did with Nash for 60 Minutes. Other pieces offer insights on Nash. Peter Brown, a journalist for Science, had just seen Nash at the Abel Prize Ceremonies in Oslo earlier that week, and wrote about Nash's appearance and responses after the award ceremony ("John Nash's memorable final appearances," by Peter Brown, Science, 29 May 2015). Ron Howard, director of A Beautiful Mind, the movie about Nash, recalls when he met Nash. "I couldn’t understand much about the Nash Equilibrium or anything else he was explaining that day, but I could recognize a spark of creative energy and vision that I could recognize and relate to. That day I began to see John as an artist." ("The Beauty of John Nash," by Ron Howard, Time, 27 May 2015) In another piece, writer John Cassidy notes Nash's "game-theoretical methods he pioneered became widely used in the social sciences, and especially in economics," and provides some background on economics, including, "In the nineteen-sixties, seventies, and eighties, economic theorists worked on extending Nash’s approach. At the same time, however, it became clear that his concept of equilibrium has some serious drawbacks that limit its usefulness....These days, political scientists, evolutionary biologists, and even government regulators are obliged to grasp best-response equilibria and other aspects of game theory." ("The Triumph (and Failure) of John Nash's Game Theory," by John Cassidy, The New Yorker, 27 May 2015) Articles, tributes and condolences continue to appear in the news and social media. See a brief biography of Nash.

--- Annette Emerson

On the math of how wrinkles form, by Lisa DeKeukelaere

Using experimental data from tests aimed at examining how aerodynamics change when air is removed from balls of silicone, scientists have developed a new set of equations for describing how wrinkles form on a sphere. The scientists discovered that the wrinkle patterns depend only on the curvature of the base (non-wrinkling) layer and the amount of stress applied to the outer layer, and the model works on spheres ranging from the size of ping-pong balls to the tiny hemispheres of a silicone polymer. Understanding development of wrinkles and dimples has applications ranging from planetary surfaces to the human small intestine, and the new equations offer hope that similarly simple formulas exist for other elastic systems which at present are calculated only with large, complex computer models. According to one of the researchers, the new development is significant for the collaboration between experimentalists--who shared their intriguing wrinkled spheres with mathematicians--and the theorists, who developed the equations that form the basis for new questions and experiments.

(Image: Under pressure, curved surfaces transition from a regular, dimpled pattern to one with irregular wrinkles. Norbert Stoop.)

See "The Fascinating Math of How Wrinkles Form," by Sarah Lewin, Quanta Magazine, 17 May 2015.

--- Lisa DeKeukelaere

On guitars and the defense and medical industries, by Claudia Clark

Paul Reed Smith did not have any particular interest in mathematics when he founded the company PRS Guitars in 1985. But his father, Jack Smith—an applied mathematician for the U.S. Air Force and Navy—helped him to see the relationship between mathematical formulas and the sounds being produced by his guitars. "We first thought we were working on just a guitar thing," Smith says, "but it turns out we were working on any kind of measuring and data extraction." Now, Dent writes, "Smith is developing a mathematically-based way of extracting undetected data from those waveforms, as well as unseen data from digital images." He is forming a new company—Digital Harmonic—to focus on this. So far, the U.S. Navy and John Hopkins "have formed partnerships with him, to try and apply his algorithms in both the defense and medical industries." Such applications could include improvements in underwater images for the U.S. Navy or in medical imaging for medicine. "All of these images are made up of the waveforms Smith proposes to clear of noise," notes Dent. Smith's algorithm might also be applied to DNA sequencing, where it "could possibly allow for longer, more reliable and less expensive 'read lengths' of a DNA sequence," she writes.

(Photo: By chascar (originally posted to Flickr as Paul Reed Smith) [CC BY 2.0 (http://creativecommons.org/licenses/by/2.0)], via Wikimedia Commons.)

See "Mathematics of the Ultimate Rock & Roll Guitar Could Help U.S. Navy And DNA Sequencing," by Millie Dent, Forbes, 14 May 2015.

--- Claudia Clark

On finding a shipwreck using Bayesian search theory, by Samantha Faria

Don’t call Tommy Thompson a treasure hunter. At the forefront of deep water searching, he was a cross between Indiana Jones and Nikola Tesla, always methodical, meticulous and careful.

In the hey-day of the California gold rush, ships laden with riches made their way to the East Coast. On September 12, 1857 the S.S. Central America sank in the deep ocean carrying with it one of the greatest lost treasures in United States history. In 1985, Thompson was determined to find this wreck. He recruited scientist Bob Evans, who went through old boxes of microfilm, read about the storm and the 153 survivors’ testimonies. He looked for things like the strength of the storm, condition of the vessel, and how the storm was affecting it. All of this research became a data correlation matrix; laid out it was a humongous 12 feet by 12 feet. Next Bayesian search theory was employed. Dr. Kathryn Laskey described it as "taking a whole mess of different kinds of data and putting them into a common framework that we can actually then use to search…each of those pieces of information on its own might be very weak but when you put them all together you get more powerful information than any one of them individually and you apply a mathematical formula called Bayes Rule..."

Taking a systematic approach to the search, Thompson brought in Dr. Larry Stone, and asked him if he could create algorithms to find something that was lost at sea. "Bayesian modelling could take large sets of data sometimes with conflicting information in it to create a collective whole understanding of where the truth probably lay. That's why we collected every piece of data that we possibly could." said Evans. Stone created a Bayesian model of all of the factors that could help figure out where the ship was resting. He then organized the information in to three scenarios to figure out a position of some sort. "The probability map covered an area about the size of Rhode Island," explained Stone. Using high-tech sonar, the team started in the high probability area and worked its way outward in a rectangular spiral, like a lawn mower moving back and forth through the water rather than grass. They tried to move efficiently through the probability map. Sure enough, they found a wreck in the high probability area! After spending the summer combing through it and recovering artifacts, but not gold, the team realized it was not the right ship. Although some members of the group were mad, frustrated and felt that they had wasted their time, Thompson wanted to make sure he had searched the entire probability map. The following winter Evans poured over the sonar pictures taken throughout the map. One spot intrigued him. In an effort to be thorough, the crew went back and dropped the sonar down in the area that Evans had highlighted. In the control booth they watched the submersible in real-time video; suddenly the S.S. Central America came into view. The wreck was on the very edge of the probability map, 200 miles off the coast of South Carolina about 8000 feet below on the Atlantic floor. Finally the shipwreck had been found.

Unfortunately, 39 insurance companies filed suit against Thompson and his company, claiming rights to the gold because of damages they paid in the 19th century. The lawsuits dragged on in federal court for 10 years. By this point Thompson had millions tied up in legal fees as well as outstanding loans. Thompson’s group sold the gold for $48 million. Soon after, Thompson disappeared. This past January Thompson was captured in West Boca Raton, Florida and later extradited to Columbus, Ohio where he pled guilty to the charge of criminal contempt. (Image: photo reproduction of painting of the sinking of the Central America, 1857. J. Childs (engraver & publisher), National Maritime Museum, London. Public domain via Wikimedia Commons, licensed under the Creative Commons Attribution 2.5 Australia license. PD-1996|Australia|public domain-copyright has expired.) See "How Data Nerds Found A 131-Year-Old Sunken Treasure." FiveThirtyEight.com, 13 May 2015. ---Samantha Faria (Posted 5/27/15) On Sitan Chen, student mathematician and musician, by Lisa DeKeukelaere Sitan Chen Garners Top Oral Award at CEE's 28th Research Science Institute. In an interview with US News & World Report, Harvard student Sitan Chen explains his view that there are no hard problems, just a lack of understanding and a lack of the right framework for approaching the question. Chen, a 20-year-old junior majoring in mathematics and computer science, won third prize in the 2011 Siemens Competition in Math, Science, and Technology, and has given piano performances at Carnegie Hall six times. Chen notes that he initially was inspired by math competitions in middle school and a program for students to partner with math professors during high school, but he advises other students to focus on hard, interesting problems and self-improvement, rather than competitions and comparing oneself to others. He briefly explains his 2011 Siemens Competition entry, which used graph theory to optimize circuit design, and he describes his interest in future work in algebraic geometry, algebraic topology, and the P vs. NP problem in computer science. See "Theoretical Mathematician Says There Are No Hard Problems," by Mary Cirincione, U.S. News & World Report, 12 May 2015. --- Lisa DeKeukelaere John Urschel, on his interests, by Mike Breen John Urschel, an offensive lineman for the Baltimore Ravens and a published mathematician, talks about some of his many interests in a short interview in Download, a weekly feature of The New York Times Sunday Review. As if playing professional football weren't enough to keep a person busy, Urshchel reveals that he is also a blues and jazz guitarist and recently competed in his first chess tournament. Urschel also says that he loves horror films and Dinosaur Comics, a comic that uses the same images each day, but with different text. See "John Urschel," by Kate Murphy for Download. The New York Times, 10 May 2015, page SR2. --- Mike Breen (Posted 5/18/15) On MathCounts, by Claudia Clark The Raytheon MATHCOUNTS Competition Series is a series of math contests offered for Grade 6, 7, and 8 students around the United States and the world. Each year, local and state contests culminate in a national competition, with 4 students from each state, U.S. territory, and other locations competing for scholarships and prizes. In this article, Baker describes a few highlights—focusing in particular on the 4 Massachusetts finalists—from the annual Raytheon MATHCOUNTS National Competition, which was held in Boston, Massachusetts earlier this month. In the end, Massachusetts' competitors Nathan Ramesh and Jeffrey Chang made it through the morning's written exam to the "Countdown" segment of the competition, but the winner was Kevin Liu, last year's runner-up, from Indiana. (Photo, courtesy of Raytheon: Kevin Liu, left, the 2015 Raytheon MATHCOUNTS National Champion, shakes the hand of runner-up Andy Xu after the final question of the Countdown Round.) See "You Can Count on Them," by Billy Baker. The Boston Globe, 9 May 2015, page 1; "Math Challenge," Mathcounts champ Liu on LIVE with Kelly and Michael, 11 May 2015; and "14-year-old math champ’s winning answer," USA Today, 11 May 2015. --- Claudia Clark On mathematicians and blue crabs, by Lisa DeKeukelaere See "Mathematicians and Blue Crabs," Op-ed by Manil Suri, The New York Times, 2 May 2015. Mathematicians are trying to help the State of Maryland maintain a sustainable population of blue crabs by setting harvesting limits based on mathematical models?with mixed results. As columnist Manil Suri explains, population numbers often depend on a wide range of factors and assumptions that can be difficult to verify, resulting in models whose predictive capabilities are more like estimated weather forecasts than set-in-stone laws of physics. Suri highlights the statistic R, used to denote the growth rate of a population, and highlights Maryland?s efforts to keep R from falling below one?which would mean a decline in the population?by focusing on limits for specific types of crabs, such as egg-bearing females. Suri notes that although the mathematicians have yet to adapt a model that ensures sustainability year after year, the accumulation of additional data as years go by could lead to success in the future. --- Lisa DeKeukelaere On mathematician and musician James Stewart, by Claudia Clark "Integral House" in the Rosedale neighborhood of Toronto is on the market. Commissioned by the late Canadian mathematician and musician James Stewart, writer of a series of high school and college calculus textbooks, the name of the house alludes to Stewart's love of curves. Why curves? In the trailer for a documentary film currently being made about him, Stewart explained, "I'm a mathematician. All straight lines have the same shape so they are not so interesting to me, whereas there's an infinite variety of curves." The 18,000 square-foot home was designed by the Toronto husband-and-wife team Brigitte Shim and Howard Sutcliffe. The 5-story house took 6 years, and cost an estimated$24m, to build. It has won several design awards and includes a pool, planted roofs, geothermal heating and cooling, and a performance space that can seat 150 people. Stewart died in December of last year after an 18-month battle with multiple myeloma.

See interior and exterior pictures of "Integral House.” A documentary about Stewart, The Integral Man: The math and music behind the house, is currently being filmed and is due to be completed next year.

See "The \$23m house built by mathematics: Toronto home that doubles as concert venue was designed by professor with 'science of curves'," by Sara Malm, Daily Mail, 1 May 2015.

--- Claudia Clark

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