# Math Digest

## Summaries of Media Coverage of Math

Edited by Allyn Jackson, AMS
Contributors:
Mike Breen (AMS), Claudia Clark (freelance science writer), Lisa DeKeukelaere (2004 AMS Media Fellow), Annette Emerson (AMS), Brie Finegold (University of California, Santa Barbara)

### January 2007

"When Averages Hide Individual Differences in Clinical Trials," by David Kent and Rodney Hayward. American Scientist, January-February 2007, pages 60-68.

The randomized controlled clinical trial is a fairly recent invention, according to researchers and physicians David Kent and Rodney Hayward. It was devised as "a means of determining a treatment's effect when many other factors, including unknown ones, might affect patient outcomes." But in an article in this issue of American Scientist, Kent and Hayward write that "because many factors other than the treatment affect a patient's outcome, determining the best treatment for a particular patient is fundamentally different from determining which treatment is best on average."

They then describe two specific studies, as well as their reanalysis of each using risk models, to demonstrate how summarizing the overall results of a trial---expressed through the values of absolute risk reduction and relative risk reduction---can hide risks or benefits to some patients. Kent and Hayward then discuss and illustrate, using the results of a computer simulation of a hypothetical trial, how using "one variable at a time" subgroup analysis is also not likely to identify subgroups that differ greatly in response to therapy. They also present some of the reasons that risk-based subgroup analyses have rarely been done, but conclude that "analyzing and presenting clinical trial results across dimensions of risk can provide us with a more flexible, multi-dimensional evidence base for treating actual, not average, patients."

--- Claudia Clark

"Math circles primed for idol's 300th birthday," by Susan Snyder. Philadelphia Inquirer, 29 January 2007.

"Move over, Ben Franklin. Your 300th anniversary celebration has passed. It's Leonhard Euler's turn." So begins this article about the mathematical community's year-long celebration of Euler's 300th birthday, actually April 15. He is described as one of the most prolific mathematicians, an "intellectual ancestor" of Sudoku, who "discovered how water flows, designed the perfect shape for teeth on a gear, developed the equations needed to make accurate lunar tables to determine longitude at sea, and calculated the moment of inertia." The Mathematical Association of America and mathematics departments in colleges and universities around the world are planning special events and publications to celebrate Euler's 300th.

--- Annette Emerson

"The Thinkers: He brings higher mathematics to bear on high finance," by Mark Roth. Pittsburgh Post-Gazette, 29 January 2007.

 In this issue of the Pittsburgh Post-Gazette, as part of a series on innovative thinkers in Western Pennsylvania, writer Mark Roth profiles Carnegie Mellon University mathematics professor Steven E. Shreve. Shreve oversees the Carnegie Mellon computational finance program, begun in 1994. Roth notes that the growth of enrollment in such programs is a sign of how "the growing power of computers and an explosion of new formulas have turned the world of high finance into a field that depends on high-level mathematics." Roth then discusses the application of mathematics to finance, including Shreve's work in the area of convertible bonds, as well as Shreve's work on solving problems related to the transmission of video clips over the Internet. --- Claudia Clark

"Den kleinsten Kreis um sehr viele Punkte finden (The smallest circle to find many points)," by George Szpiro. Neue Zürcher Zeitung, 28 January 2007

It is not so simple to find the smallest circle that encompasses many---say millions----of points in the plane, but there exist�some algorithmic procedures, as Szpiro explains

--- Allyn Jackson

"Viel Mathematik ganz kurz (Much mathematics all at once)": Review of Fünf Minuten Mathematik (Five Minutes of Mathematics), by Ehrhard Behrends. Reviewed by George Szpiro. Neue Zürcher Zeitung, 28 January 2007.

Szpiro liked very much this book, which discusses a wide swath of classical and modern mathematics.

--- Allyn Jackson

"The Geometry of Music," by Michael D. Lemonick. Time, 26 January 2007.

This issue of Time included a short article discussing a paper published in Science in July 2006. Princeton University composer Dmitri Tymoczko has shown that chords correspond to points in orbifolds (referred to in the article as "weird multi-dimensional spaces"), and pleasing sequences of notes can be thought of as paths through this musical space. The tone of the piece gave the composer's analysis of songs like those of Deep Purple a mystical-magical aura. According to the Science article, we most often use the chords at the center of the orbifold, and counterpoint corresponds to connecting nearby points along non-intersecting paths in the space. At Tymoczko's site, one can dowload ChordGeometries, a program for visualizing chords, and watch a movie of Chopin's notes running through the Möbius strip.

--- Brie Finegold

"Professor Files Lawsuit, Then Wins Tenure," by Piper Fogg. The Chronicle of Higher Education, 26 January 2007, page A10.

In 2005 Gregg H. Turner was fired from his job as a math professor at New Mexico Highlands University. He said that the firing was because he had criticized the university president, Manny M. Aragon. The American Association of University Professors (AAUP) censured the university for the firing and for other actions. Turner sued the university and settled this summer for US$170,000 and another chance at obtaining tenure. He now has tenure. The university said, "It's clear that the university thinks that Dr. Turner can and will make valuable contributions to our students, and this was demonstrated by the granting of tenure." The AAUP is encouraged but will not reconsider its censure until other issues at the university are resolved. --- Mike Breen Return to Top "Figure studies: Missouri sculptor melds art and mathematics in his world-renowned work," by James A. Fussell. The Kansas City Star, 20 January 2007.  Toroidally Warped Sherk Surface Conception by Brent Collins, image created with software by Carlo Sequin Missouri sculptor Brent Collins uses geometry in his work. Although he has no formal training in art, his sculptures have been praised by many, including those in mathematics and science. People in Kansas City can now see a "1200 pound curling ribbon of bronze traveling over the surface of an imaginary sphere" in front of the city's new H&R Block building. Collins has collaborated with Carlo Sequin, a computer science professor at the University of California, Berkeley, who created software to enlarge Collins' handmade works. The sculpture in Kansas City is one result of their collaboration. In this article, Collins says, "The idea that mathematics is antithetical to artistic expression is wrong." (Collins has other pictures of his sculptures online.) --- Mike Breen Return to Top "Math Play," by Ira Flatow. Talk of the Nation: Science Friday, National Public Radio, 19 January 2007; "The Math Rookie Is a Girl, A Big Problem for the Geeks," by Neil Genzlinger. The New York Times, 25 January 2007, page B8. Host Ira Flatow talks with playwright Kathryn Walat about her off-Broadway production, Victoria Martin: Math Team Queen. Flatow says that the play asks the question: Can a popular girl who knows Pi to 53 decimal places be on a math team and still be popular? Victoria, third-most popular in her class, at first lies to her popular cheerleader friends about being on the high school math team, but finally cares less about what her friends think and more about being true to herself. She also transforms the members of the school's all-male math team when she joins. Walat herself liked math and science in high school and college, but wound up majoring in writing. In the writing of this play, she was inspired by math camps for gifted children, and when it was time to "pitch" the project she says that she found many "closet mathletes." The play will run at the Julia Miles Theater until 11 February 2007. After that, Walat hopes that other companies across the country will produce the play. She adds that high school students and adults love the play. Genzlinger is not one of those adults. In his review in The New York Times, he writes that the play "ends up being surprisingly oppressive," and that it lacks momentum. He also labels the characters in the play "cardboard." --- Mike Breen Return to Top "Conviction by Numbers," by Mark Buchanan. Nature, 18 January 2007, pages 254-255. A jury tries a defendant using evidence that can include statistics, but who tries the veracity of the statistics? The 2003 murder trial of Lucia de Berk, a Dutch nurse accused of killing patients who died under suspicious circumstances while in her care, highlighted this important question. A statistical expert at her trial testified that there was only a 1 in 342 million chance that her affiliation with the patients was coincidental---a number that weighed heavily on the jurors' decision to convict---but several Dutch mathematicians are claiming not only the number but also the court's interpretation of it are incorrect. An advisory judicial committee is reassessing de Berk's case, but even the statistical expert at the trial now admits that non-statistical evidence---instead of his numbers---should be the main deciding point. --- Lisa DeKeukelaere Return to Top "Math Panel Issues Its First Report, But Holds Off on Policy Proposals," by Sean Cavanagh. Education Week, 17 January 2007. The National Mathematics Advisory Panel has issued its interim report, which describes the panel's organization into subcommittees and its progress so far, but offers no conclusions or advice. Panel member Francis "Skip" Fennell, president of the National Council of Teachers of Mathematics, explains that "All of the groups need more time to write and flesh things out." The panel met in New Orleans right after the Joint Mathematics Meetings. Its final report is due by 28 February 2008. --- Mike Breen Return to Top "Pitt math professor took best shot at cannonball conjecture," by David Templeton. Pittsburgh Post-Gazette, 16 January 2007. The article reports that in July 2006 University of Pittsburgh mathematician Thomas C. Hales, and his former graduate student Samuel P. Ferguson, now at the National Security Agency, published their proof of the 400-year old Kepler Conjecture. The conjecture states that the most efficient way to stack cannonballs or equal-sized spheres is in a pyramid. Their 300-page proof, completed in 1998, was controversial because of its extensive use of computer code. Although a panel of 12 mathematician referees was never able to confirm the proof with complete certainty even after several years of review, the journal Annals of Mathematics nevertheless accepted the paper for publication. The accomplishment was reported in the article because Hales and Ferguson received the first David P. Robbins Award of the AMS in January 2007 at the annual Joint Mathematics Meetings. The Robbins Prize recognizes an outstanding research paper in mathematics. The Post-Gazette article explains a bit about the conjecture, how Hales and Ferguson approached the problem, and the award. --- Annette Emerson Return to Top "Israeli, American share Wolf Prize in Mathematics," by Judy Siegel-Iztkovich. The Jerusalem Post, 15 January 2007; "Wolf Prize in Mathematics Awarded to HU's Harry Furstenberg," IsraelNationalNews.com, 16 January 2007; "Wolf Foundation recognizes achievements in math, physics," Associated Press, 18 January 2007. "Awards: Wolf Prizes." Newsmakers, Science, 26 January 2007, page 443. Harry Furstenberg (Hebrew University of Jerusalem) and Stephen Smale (University of California, Berkeley, and Toyota Technological Institute, University of Chicago) will share the 2006-7 Wolf Prize in Mathematics. The president of Israel will award the prizes to the two mathematicians on 13 May 2007. Furstenberg will receive the prize "for his profound contributions to ergodic theory, probability, topological dynamics, analysis on symmetric spaces and homogeneous flows." Smale was honored for his "ground-breaking contributions that have played a fundamental role in shaping differential topology, dynamical systems, mathematical economics, and other subjects in mathematics." The prize, worth US$100,000, is given by the Wolf Foundation.

--- Mike Breen

"When Number Proofs Are Done by Computer, Mightn't Some Err?," by Sharon Begley. The Wall Street Journal, 12 January 2007, page B1.

Begley uses two talks from the January 2007 Joint Mathematics Meetings to discuss the nature of proof. One talk was by Doron Zeilberger (Rutgers University) who used gambler's ruin to study "the limits of proof and of machine proofs." In the other talk, Michael Filaseta (University of South Carolina) and his student, Mark Kozek, discussed composite numbers that remain composite when any digit is inserted in their decimal expansion. The smallest such odd number that doesn't end in 5 is 25,011. Begley uses this talk as an example that humans can still discover secrets about the natural numbers. She also quotes Brian Davies of King's College London who wrote on the nature of proof in "Whither Mathematics?" in the December 2005 issue of the Notices of the AMS.

--- Mike Breen

"A New Standard for Measuring Doctoral Programs," by Piper Fogg. The Chronicle of Higher Education, 12 January 2007, pages A8-A13.

 The Faculty Scholarly Productivity Index, produced by Academic Analytics (a for-profit company) has ranked the top 10 doctoral institutions in 104 disciplines. The rankings incorporate journal and book publications, citations, grants, honors, and awards. These numbers are assigned various weights depending on the discipline to arrive at a single index (the signed number of standard deviations above or below the mean). The Chronicle obtained the indices and published many of them in this article. Academic Analytics ranked New York University number one in mathematics, the University of Michigan number one in applied mathematics, and Duke University number one in the aggregated field of math and statistics. [The Digest is merely reporting these findings, and makes no claim as to their validity.] As with most rankings, the findings are controversial. One criticism is that the company finds faculty via the universities' websites, which may not be up-to-date. --- Mike Breen

"Math Convention," by Keith Devlin and Linda Wertheimer. Week end Edition, National Public Radio, 6 January 2007.

 Participants at the 2007 Joint Mathematics Meetings. Photo by Wayne Catalano. Mathematician Keith Devlin (Stanford University) talks with Wertheimer about the Joint Mathematics Meetings in New Orleans (which took place 5-8 January 2007). He explains to her what happens at the meeting and gives titles of two talks presented during the meeting. The two also talk about whether math is a science. Devlin, who did the interview from WWNO in New Orleans, tells Wertheimer that he is "having a ball" at the meeting, explaining that it is "One of those times in the year when I'm surrounded by 5000 people who don't think I'm unusual." (See highlights of the Joint Mathematics Meetings.) --- Mike Breen

"Martin Kruskal, pre-eminent applied mathematician, at 81," by Kitta MacPherson. The Star-Ledger, 5 January 2007;
"M. Kruskal, 81, mathematician's wave research rippled through sciences," by Thomas H. Maugh II. The Los Angeles Times, 6 January 2007.

Martin Kruskal died 26 December 2006. He was on the Princeton University faculty for 38 years before moving to Rutgers University in 1989. In 2006 he received the AMS Steele Prize for Seminal Contribution to Research along with Clifford Gardner, John Greene, and Robert M. Miura for their "fundamental paper in the theory of solitons, inverse scattering transforms, and nonlinear completely integrable systems" ("KortewegdeVries equation and generalizations. VI. Methods for exact solution," Comm. Pure Appl. Math. 27 (1974), 97–133). Solitons have many applications, including fiber optic communication. Kruskal was also known for a clever card trick called the Kruskal Count. He had two prominent brothers: William, his older brother, a statistician, and Joseph, his younger brother, a computer scientist. Kruskal is survived by his wife, Laura, a daughter, two sons, and five grandchildren.

--- Mike Breen

Recent columns by "The Numbers Guy" Carl Bialik. The Wall Street Journal Online, January 2007.

 Bialik's columns enlighten readers on the uses, reporting, and sometimes misrepresentations of statistics: "Counting Internet Users," 5 January 2007; "Rethinking Mileage Estimates," 12 January 2007; and "Another Look at Murder Stats," 19 January 2007. --- Annette Emerson

"Top 100 Science Stories of 2006. Number 8 Mathematics: Fundamental Problem Solved After 100 Years," by Keith Devlin. Discover, January 2007.

After briefly explaining Perelman's accomplishment and the Poincaré conjecture about the structure of space, Devlin says that the new result will no doubt have an impact on everyday life "although that impact will most likely come from the methods Perlman developed to solve the problem rather than from the result itself... powerful methods to handle potential singularities in the equations of space." Devlin speculates that "If, in the year 2100, Discover runs a feature on the top advances in science in the 21st century, the proof of the Poincaré conjecture is still likely to be the number-one story in mathematics."

--- Annette Emerson