# Math Digest

## Summaries of Articles about Math in the Popular Press

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (Brown University), Annette Emerson (AMS)

### July 2005

"Life Cycles," by Brian Hayes. American Scientist, July-August 2005, pages 299-303.

 Brian Hayes investigates whether there is a periodicity in the creation and die-offs of species. He uses curve-fitting and Fourier analysis on data from paleontologist John Sepkoski. That data gives the youngest and oldest geological layers in which a species appeared, which means that sub-stages, stages, and periods must be translated to years. Hayes translates in a way that is different from the method chosen by authors of a recent article on the subject. Despite the different methods, the results both show a 62 million year period. Yet to get that result, Hayes had to throw out data from a period from which data were sparse, so he wonders if the evidence for periodicity is unmistakable. --- Mike Breen

 "Football by the Numbers" is about Aaron Schatz, who "has developed something football has historically lacked: a statistical method for judging individual players and plays that accounts for such contextual factors as down, field position, and strength of opponent." Some NFL franchises have sought his insights, but for now Schatz and colleagues run FootballOutsiders.com. "A Home for Wayward Math Problems" describes The Open Problems Project--the brainchild of Joseph O'Rourke (Smith College), Joseph S.B. Mitchell (State University of New York, Stonybrook), and Erik D. Demaine (Massachusetts Institute of Technology). The three mathematicians have collected and published online (to date) 59 unsolved math problems, each with a concise description, history, citations to related results, "and in some cases a cash reward." The article includes a brief overview of the nature of mathematical problem solving and provides the link to the the Open Problems Project. --- Annette Emerson

"Flawed Statistics in Murder Trial May Cost Expert His Medical License," by Eliot Marshall. Science, 22 July 2005, page 543.

The concept of the independence of two events is a central tenet in many statistics classes, and a British doctor may soon lose his license due to his misapplication of this principle. In the 1999 trial of a woman accused of killing her infant son, child abuse expert Roy Meadow presented an inaccurately small probability that two infants in the same family will die suddenly of unexplained natural causes. Meadow derived the statistic himself using the death probability of a single infant, but he incorrectly assumed that two inter-familial infant deaths would be independent of one another. The woman was convicted and spent three years in prison before the decision was reversed. While some fault Meadow for abusing his position as a doctor and delivering evidence outside his field of expertise, others think his current role in the case is simply that of a scapegoat.

---Lisa DeKeukelaere

"Harvard Researchers Discuss Systems Biology," by John Russell. Bio-IT World, 21 July 2005.

Bio-IT World experiments with posting an entire interview with two scientists to follow up on a shorter report. The topic is the efforts by Harvard Medical School researchers Jeremy Gunawardena and Aneil Mallavarapu to create a new modeling language for systems biology. Gunawardena, a "self-professed mathematician (Ph.D. in algebraic topology)," is director of The Virtual Cell Program in the School's Department of Systems Biology, and in the interview he explains that they are "focusing on biochemical modeling, and we're using it to build fairly simple models called ODE (ordinary differential equations). You represent species as concentration or the amount of species as variables. We want to expand and use the language to describe other types of models like partial differential equations, and we're working on what it will take to write stochastic models. Right now we're just doing biochemistry, but there's nothing in the language that limits it to that."

--- Annette Emerson

"U math institute bugs its way to record grant," by Mary Jane Smetanka. Star Tribune, 20 July 2005.

The occasion for this article is the awarding by the National Science Foundation (NSF) of a nearly $20-million grant to the Institute for Mathematics and its Applications (IMA) at the University of Minnesota. The renewal grant constitutes a 77 percent increase in NSF funding for the IMA. The IMA is one of six US-based mathematics research institutes funded by the NSF; the foundation also contributes funding to a math institute in Canada. The IMA specializes in bringing together mathematicians with researchers from other areas of science and engineering and also with people from industry. Throughout its 25-year history, the IMA has shown how mathematics can make substantial contributions towards the solution of practical problems in science, engineering, and technology. The article discusses an IMA "success story" in which mathematicians, biologists, and engineers began a collaboration that has led to the development of a six-legged robot whose gait is based on that of insects. The hope is that such robots might be able to assist on, for example, future space missions. In other media coverage, IMA director Douglas Arnold was interviewed on Minnesota Public Radio's "All Things Considered" program on 21 July 2005. --- Allyn Jackson Return to Top "The professor's days are numbered," by Keith O'Brien. The Boston Globe, 18 July 2005. O'Brien writes about Dan Rockmore, professor of mathematics at Dartmouth College. Some of the article is about Rockmore's teaching: He tries to keep math interesting and he says "I think it's a tragedy when people get turned off by mathematics or quantitative kinds of approaches very early in life," and part deals with numbers, especially prime numbers. Rockmore has written a recently published book Stalking the Riemann Hypothesis: The Quest to Find the Hidden Law of Prime Numbers. --- Mike Breen Return to Top "Geheimnisse, die sich in Zahlen verbergen", by George Szpiro. Neue Zürcher Zeitung, 17 July 2005. This installment of Szpiro's monthly column on mathematics discusses a recent article from the Ramanujan Journal. How large can the numerator of a fraction become if a selection of the fractions 1/2, 2/3 ... N/(N+1) are multiplied or divided by one another? --- Allyn Jackson Return to Top  Students at Bates College can study the design of roller coasters in the course Roller Coasters: Theory, Design, and Properties. The course itself was designed by two faculty in the Bates mathematics department, Meredith L. Greer and Chip Ross, and by two students, "to appeal to people who might normally shy away from math courses." The most recent course ended with a trip to Cedar Point, an amusement park with 16 roller coasters including the first to top 400 feet and 120 mph. --- Mike Breen Return to Top "Data-Point: Steady strides." Random Samples-People, Science, 15 July 2005, page 379. This short item reports that 333 women received doctorates in mathematics in the U.S. in 2003-04, which is an all-time high. The number represents one-third of all U.S. math doctorates---almost double the fraction from 25 years ago. To those who say that women aren't suited for higher mathematics, Ellen Kirkman, a mathematics professor at Wake Forest and lead author of the survey on which the article is based, says, "We would not be seeing this increase if women did not have the ability or the stamina to pursue math degrees." The survey is in the August issue of Notices. --- Mike Breen Return to Top "9-Year-Olds Said Better in Math, Reading," by Darlene Superville. Guardian Unlimited, 14 July 2005. The performance on a 2004 national math test improved for many age groups and for minorities. Nine-year olds scored 241 in mathematics (out of 500) compared to 232 in 1999. Nine- and thirteen-year old minority students earned their highest marks in the history of the exam. The test, given by the National Assessment of Educational Progress, is voluntary. It was taken by 28,000 students during the 2003-04 school year. --- Mike Breen Return to Top "Floating ideas," by Marc Abrahams. The Guardian UK, 12 July 2005.  Marc Abrahams, co-founder of the Annals of Improbable Research, writes about Japanese mathematician Shizuo Kakutani. At the outbreak of World War II, Kakutani was a visiting professor at the Institute for Advanced Study in Princeton. He was given the option of staying there or returning to Japan, and Kakutani chose to return home. While shipboard he apparently spent his time proving theorems, then inserting them in bottles and throwing them overboard with the instruction that, if found, the mathematical messages should be returned to Princeton. Abraham reports that to date none of the theorem-filled bottles has been found. --- Annette Emerson Return to Top "Take it to the limit," by Dana Mackenzie. New Scientist, 9 July 2005. This article discusses a revolution that has taken place in the science and engineering of communication codes. These codes "have nothing to do with spies or security," the article explains. Rather, the codes are used to ensure efficient and reliable transmission of information over communication channels; communication between spacecraft and the Earth is cited as a prime area where such codes play a vital role. Communication channels always have some amount of noise, which causes errors in the information transmitted. There are ways of correcting these errors, but they add to the cost of the transmission. In the 1940s, Claude Shannon developed a notion that is now known as the "Shannon limit", which, as the article describes it, is "a formula for how much information you can send with essentially perfect fidelity at a given signal-to-noise ratio." The problem was, Shannon's work gave no indication of how to create codes that give results close to the Shannon limit. For decades engineers struggled along with codes that gave far less than optimal results. It was only in the 1990s that some little-known research was rediscovered that allowed the creation of new codes, called turbo codes and low-density parity check (LDPC) codes, which operate essentially at the Shannon limit. --- Allyn Jackson Return to Top "Teaching Qubits New Tricks," by Charles Seife. Science, 8 July 2005, page 238. Quantum computers would revolutionize computing: For example they could quickly factor the large numbers that current encryption methods are based on. A trait they share with traditional computers is the need for error correction. Physicist Ray Laflamme and colleagues have shown mathematically that quantum error correction techniques that had appeared to be different are actually the same. This could make quantum error correction more efficient and help people understand the limits of quantum information. Peter Shor said that the result is very nice but, "Whether it's a giant leap or just a substantial step forward remains to be seen." The research is published in the Physical Review Letters. --- Mike Breen Return to Top  This epsiode includes actual interviews interspersed with dramatizations of the story about MIT math professor Ed Thorp, who in the 1960s was enlisted by gambler Manny Kimmel to make a fortune in blackjack at the major casinos. Thorp's 1962 book, Beat the Dealer: A Winning Strategy for the Game of Twenty-One and scholarly reviews of the book were reported in The Boston Globe, which in turn generated about 20,000 letters from readers to the MIT math department asking for expert explanations on how to win at blackjack. Thorp describes how he learned to program what was at the time a high-speed computer and tested his theory on counting cards and predicting the odds as hands are played out. --- Annette Emerson Return to Top "A Book With a Theory of Everything?," by John Allen Paulos. ABC News, 3 July 2005. Paulos reviews a new book, The Road to Reality: A Complete Guide to the Laws of the Universe, by Roger Penrose. He describes the 1,100-page, detail-packed tome as more like a mathematical physics text than a book of popular science, as the author focuses "on the facts and theories of modern physics and the mathematical techniques needed to arrive at them" in the attempt to explain the laws governing our universe. In the end Paulos describes the book as "truly magisterial" but one which will be best appreciated by those who have considerable background in the subjects. --- Annette Emerson Return to Top "You Are What Your Record Is (Except When You're Not)," by Alan Schwarz. The New York Times, 3 July 2005, Sports, page 8.  If you are interested in how Major League baseball teams will fare in the remainder of the season, you might want to examine the Pythagorean Theorem of Baseball. The theorem, so-called because it involves squaring some numbers, uses runs scored and allowed by a team to determine a team's performance. This performance can then be compared with the team's actual won-lost record to see if the team is doing better or worse than the theorem would indicate. According to this article, at the halfway point of the season the Washington Nationals were the biggest over-performers, being in first place despite allowing more runs than they've scored. The article also examines teams' performance in games decided by one run. Fans often think that winning a high percentage of such games indicates a strong team, but Schwarz writes that one-run victories are more attributable to chance than others, so that a winning percentage in these games which exceeds a team's overall winning percentage may be a sign of bad things to come (presuming that the team's luck won't continue). For this statistic, the San Diego Padres may have the most to lose: At the time of the article, the Padres, first place in their division with a record of 43-36, had won 18 of 25 one-run games. --- Mike Breen Return to Top "Gender Divide: Educators worrying more than in the past about shortage of women in such hard-science fields as engineering," by Laura Giovanelli. Winston-Salem Journal, 3 July 2005. "Summer camps geared toward girls have been set up all over North Carolina and the country as educators work to attract more women to engineering and other math-related fields," this article reports. One of these camps is the setting for the article, which discusses the phenomenon of low representation of women in mathematics and science. One of the teachers in the camp noted that even when girls display mathematical ability, they often lack confidence in that ability. "Even at 12, some girls have already decided what they're not good at," the article says. The camps are dedicated to building up girls' confidence in mathematics so that they continue to study the subject throughout high school and beyond. --- Allyn Jackson Return to Top "Renaissance's Man: James Simons Does The Math on Fund," by Gregory Zuckerman. Wall Street Journal, 1 July 2005, page C1; "Seeking the secrets of a `black box' investor," by Joseph Nocera. International Herald Tribune, 19-20 November 2005, page 14. "Mr. Simons, a world-class mathematician who runs Renaissance Technologies Corp., is creating a buzz in the hedge-fund world because he is about to launch a fund that he claims could handle US$100 billion---about 10 percent of all assets managed by hedge funds today. It will have a minimum investment of US\$20 million, and is aimed at institutional investors, according to early marketing materials," writes Zuckerman. The article discusses Simons' wildly successful company, which he built after an outstanding but brief career as a mathematician. Together with mathematician S-S Chern, Simons developed the so-called Chern-Simons invariants, which have been important in theoretical physics. For his work in geometry Simons received the AMS Veblen Prize in 1976. He taught at MIT, Harvard, and SUNY Stony Brook and also served as a codebreaker during the Vietnam War before switching to money management. Simons' company closely guards the secrets to his success. Of the new hedge fund, Zuckerman writes: "The fund will use complex quantitative models, developed by the 60 or so mathematics and physics Ph.D.s on staff". Although Simons rarely talks with reporters, he did talk with Joseph Nocera for the IHT article (which originally ran in the New York Times.

--- Allyn Jackson

"What Don't We Know?" Science, 1 July 2005, pages 75-102.

In celebration of its 125th year of publication, Science has published 125 unanswered scientific questions. Included in the questions are the seven Millennium Problems (the solution of each earns the solver one million dollars). Charles Seife writes about the P = NP? problem on page 96 in "What Are the Limits of Conventional Computing?". The other six problems are listed at the bottom of pages 101 and 102. There is an error in the description of the Riemann Hypothesis, however.

--- Mike Breen

"Tilt! If High-rise Buildings Were Designed More Like Ships, Would They Float Upright During An Earthquake?," by Dana Mackenzie. Discover, July 2005, pages 36-37.

If an earthquake causes the ground to behave like a fluid, could "buoyant" buildings survive the melee without capsizing like a ship in a storm? Using computer models of floatation principles spelled out by Archimedes in the third century, mathematician Chris Rorres is developing answers to this question. By testing the angle at which different shapes will tilt in liquid, Rorres obtained a measure that can predict whether an object will collapse following an earthquake. Other scientists point out that Rorres' model may not be directly applicable: Post-earthquake soil may not act like a true liquid and constructing buildings according to the requisite ratio may present other risks. Still, Rorres' work represents a promising idea in preventing earthquake destruction.

--- Lisa DeKeukelaere

 Chaos theory, whose most famous example traces the cause of an earthquake to the flapping of butterfly wings, lurks behind unforeseen changes in the behavior of a waterslide system. In steep slides, the water flows fast enough to create swirling, unstable currents that can be disrupted by variables such as the fabric of a rider's bathing suit or even the amount of dust in the air. This unpredictability provides an interesting challenge for designing the slides, which requires not only mathematics, but also a keen sense of visual proportion and material behavior. Cold, clear water carrying a screaming, spandex-clad body through a fiberglass tube is not as simple as it sounds, after all. --- Lisa DeKeukelaere