# Math Digest

## Summaries of Media Coverage of Math

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

### February 2006

"Algorithms cut job to shape." Fairfax New Zealand Limited and Dominion Post, 27 February 2006.

 Mathematician Hamish Dean has developed software that may "cut" by 1 or 2 percent (and up to 5 pecent in some cases) the amount of fabric manufacturers need to make clothes. His algorithms can minimize wasted material used to cut multiple shapes from a single piece of fabric. Software companies for the clothing industry are currently negotiating with Dean to license his program, "ShapeShifter," which, the article reports, could have applications for companies that produce window-tinting film and diamond-cutting equipment. --- Annette Emerson

"The Galois Story," by Ivars Peterson. Science News Online, 25 February 2006.

 The intrigue associated with mathematician Evariste Galois stems from not only the depth of his algebraic theories, but also from the circumstances of his death by duel at the age of 20. Peterson presents claims about Galois' death from a variety of popular books, the most well known being Genius and Stupidity, by Eric Temple Bell. While Bell portrayed Galois as a brilliant, persecuted soul, other authors say his fate resulted from his arrogance and self-destructive tendencies. Most believe that Galois' duel involved a woman, but a variety of published theories have him caught in a love triangle, punished for offending a girl, self-sacrificed as a martyr, or silenced by police for his radical views. --- Lisa DeKeukelaere

"Math Clears Up an Inner-Ear Mystery: Spiral Shape Pumps Up the Bass," by Adrian Cho. Science, 24 February 2006, page 1087;
"Shape of Cochlea Found to Be Important to Hearing," by Robert Roy Britt. FoxNews.com, 10 May 2006.

The mystery is why the cochlea, a part of the ear that perceives sound, is coiled like a spiral. Applied mathematician Daphne Manoussaki (Vanderbilt University) is part of a team that conluded that the spiral shape increases sensitivity to low frequencies. The increasing curvature directs energy toward the outer wall of the spiral, increasing sensitivity to low-frequency sound by as much as 20 decibels. The paper presenting the research will be published in Physical Review Letters.

--- Mike Breen

"Implementing a Quantum Computation by Free Falling," by Jonathan Oppenheim. Science, 24 February 2006.

"Quantum computers," mathematician Jonathan Oppenheim writes, "can efficiently solve problems that are believed to be unfeasible on a classical computer, as they would need to run exponentially longer." But other than a few quantum algorithms, Oppenheim notes that "finding more problems that can be solved faster on a quantum computer ... has proven to be a difficult task."

Enter the team of mathematicians Michael Nielson, Mark Dowling, Mile Gu, and Andrew Doherty. After defining some quantum computing terminology, Oppenheim explains for the more general reader how these mathematicians have "linked a problem in Riemannian geometry---namely, finding the shortest path between two points---to the problem of deciding whether a unitary can be implemented efficiently." (A unitary is a mapping a quantum computer makes from initial to final quantum states.) For further reading, see "Quantum Computation as Geometry," by Nielson et al, appearing in this same issue of Science.

--- Claudia Clark

"Math gets its due as field enjoys rise in status, pay," by Eric Hand. St. Louis Post-Dispatch, 19 February 2006, page C4.

Changing the public perception of mathematics was the topic of one of the symposia at the annual meeting of the American Association for the Advancement of Science, held in St. Louis in February. Hand talked to mathematicians at the meeting and at Washington University in St. Louis to see if, and how, perceptions had changed, and found that the many applications of mathematics have indeed changed perceptions. Popular culture has also noticed, as evidenced by the CBS television show NUMB3RS. Hand also cites data from the 2005 Annual Survey of the Mathematical Sciences. Washington University mathematics faculty Ravindra Girivaru and Steven Krantz, as well as graduate students Brad Henry and Aaron Wiechmann, are quoted in the article.

--- Mike Breen

"Mathematik in hohen Dimensionen (Mathematics in high dimensions)", by George Szpiro. Neue Zürcher Zeitung, 19 February 2006.

This article discusses a mathematics project, entitled "Phenomena in High Dimensions," that encompasses 13 teams with 150 mathematicians from Europe and Israel and that is supported by 2 million euros from the European Union.

--- Allyn Jackson

"Women turn math insult into aptitude adjustment," by Sue Hutchison. San Jose Mercury News, 15 February 2006.

Columnist Sue Hutchison discusses an event organized by Stanford University's Institute for Research on Women and Gender. The event took as its starting point the remarks last year by former Harvard president Lawrence Summers about whether women lack innate ability in mathematics. The column notes that although women receive half of all bachelor's degrees in mathematics, they comprise only 10 percent of all mathematics professors. "Getting more women into the highest echelons of math-science research shouldn't be dismissed as an exercise in political correctness," Hutchison writes. "It's about the bottom line. That means creating more diverse applications, and, yes, selling more technology."

--- Allyn Jackson

"Panning for Terrorists." Reading File, New York Times, 12 February 2006, Week in Review, page 5.

The Reading File prints excerpts from other sources. In this case, it has printed an excerpt from John Allen Paulos's February column on electronic surveillance. In addition to his philosophical objections to US government snooping, Paulos objects on statistical grounds: There are so many "false positives" generated that it is impossible to sift through all of them to find the guilty.

--- Mike Breen

"Danica McKellar's Mathematical Theorem": Interview with Scott Simon and Ketih Devlin. Weekend Edition, National Public Radio, 11 February 2006.

In addition to being an actress (on TV's The Wonder Years and The West Wing), McKellar is also a mathematician who recently proved her own theorem. This radio interview was held just after she participated in "Proof and Prejudice: Women in Mathematics", a special event at the Institute for Research on Women and Gender at Stanford University on 7 February 2006. See past coverage about McKellar.

--- Annette Emerson

"FAU prof, class honor E day,' a little letter that means a lot to mathematicians," by Jennifer Peltz. South Florida Sun-Sentinel, 8 February 2006.

Florida Atlantic University mechanical engineering professor Isaac Elishakoff and his students celebrated the number e on February 7, 2006 (the one-place decimal approximation to e is 2.7). The class sang a song about e and ate e-shaped cookies. The number may not be as famous as another irrational constant, pi, but it has many uses, for example in continuously compounded interest. Elishakoff says that "E is the beef of engineering."

--- Mike Breen

"It's the geometry, stupid: Ontario's debate over high-school calculus misses the point," by Kenneth Kidd. Toronto Star, 5 February 2006.

In this article, Canadian mathematicians lament the disappearance of geometry from high school mathematics curricula in North America. The article notes that in Canada, when grade 13 was eliminated, four years of high school mathematics were squeezed into three, and geometry lost out. In addition, geometry "has been smothered by the sheer variety and tonnage of other mathematical tools and disciplines that have been crammed into high school curricula across North America." University math professors say that students burdened with this "tonnage" have trouble learning calculus. If the students instead learned some geometry, which would help them visualize problems, calculus would come much easier. "In the absence of that ability to see' a calculus problem in the same way you'd look on a geometry puzzle, calculus becomes just a series of messy formulas to be memorized and applied," the article states. Bill Casselman, a mathematician at the University of British Columbia who is quoted in the article, pointed out that when students just memorize formulas, they don't understand the reasoning behind what they are doing. And, he said, "Without the reasoning, it's no fun."

--- Allyn Jackson

"X = Karin (Johnny) > 95%," by Karin Klein. The Los Angeles Times, 4 February 2006.

Klein, an editorial writer for the Los Angeles Times, reflects on her experience tutoring a student, Johnny Patrello, in algebra when they were both in high school. She says that Patrello's problem then was the same as many students' problems with mathematics now: not knowing arithmetic. She calls for a revamp of the U.S. educational system so that students are grouped by their skills in a subject and aren't promoted until they're ready. Klein writes in a touching way about Johnny passing algebra, graduating, and raising a family of successful children.

--- Mike Breen

"Ever More Relevant, Prime Number Proofs Chalk Up More Successes," by Sharon Begley. The Wall Street Journal, 3 February 2006.

Proofs involving primes are a hot topic in the mathematical community: they initiate key advances in cryptography, they dwell in the legacy of mathematicians like Euclid and Fermat, and their hypotheses are often easily explainable to the general public. One current question centers on the prevalence of prime numbers separated by a certain distance: the twin primes conjecture posits that there are infinitely many pairs of prime numbers whose difference is 2. Researchers are chipping away at the problem by examining the number of primes separated by larger distances, such as 6 and 16. By amassing these building blocks and working together to strengthen proofs, these researchers are fostering an impressive millennium for prime number puzzles.

--- Lisa DeKeukelaere

"Forensic software traces tweaks to images," by Helen Pearson. Nature, 2 February 2006, page 520.

This brief article is part of a larger piece, "Should journals police scientific fraud?", and suggests that editors of scientific journals might use the same computer tools being developed for law enforcement to detect when photographs and graphics have been digitally altered. Programs like Photoshop, for example, can be used to cut and paste---replicate or "clone"---or to erase a portion of an image. Computer scientists claim that "computer algorithms could automatically scan digital images and ferret out signs of manipulation." Such systems are also of interest to lawyers, police, and news organizations, all of whom need to detect faked photo documentation. The article reports that Hany Farid (Dartmouth College) and his colleagues "have designed a suite of ten mathematical techniques to scan images for the hallmarks of manipulation" which may eventually be distributed and packaged as part of various image-processing programs.

--- Annette Emerson

"History by numbers": Review of God Created the Integers: The Mathematical Breakthroughs that Changed History, edited by Stephen Hawking. Reviewed by Jeremy Gray. Nature, 2 February 2006, page 536.

 Gray reports that the breakthroughs of the book's subtitle---mathematical yardsticks that changed history---were well chosen and "an interesting mix of the well known and the unexpected," covering a range of topics and periods. Gray does find it annoying that new translations were not done for more of the works covered, as some have dated style and commentaries, and he suggests that even some of the modern introductions and comments "are generally accurate but the origin of the information is not stated, so readers have no chance to catch up with contemporary scholarship in the history of mathematics." However, he does note that "Hawking's comments have an infectious enthusiasm for their subject and the book contains some great works." --- Annette Emerson

"The Dean of Debunkers" by Susan Kruglinski. Discover, February 2006, pages 18-19.

In this month's issue of Discover, Columbia University mathematics department lecturer Peter Woit is interviewed on the subject of string theory, which, in his words, is "really an approximation of a theory." He describes what he finds wrong with the theory, the reasons for its influence, and the positive effects it has had on mathematics. Woit also discusses his hopes that new experimental results from the Large Hadron Collider, due to come online next year, will "start telling us what direction to go in." For more information, and a lively discussion, go to Woit's blog, "Not Even Wrong."

--- Claudia Clark

"Definition of art? Try painting by numbers," by Chuck Haga. Minneapolis Star-Tribune, 11 February 2006;
"Computer Analysis Suggests Paintings Are Not Pollocks," by Randy Kennedy. New York Times, 9 February 2006;
"In the Hands of a Master," by Alison Abbott. Nature, 9 February 2006, pages 648-650.

 Doug Arnold (left) and Dan Rockmore. Richard Taylor, a physics professor at the University of Oregon, was asked to examine six recently discovered paintings to determine if the artist was Jackson Pollock. Taylor has discovered fractal patterns in works known to be Pollock's (in fact, he found that the fractal dimension of the paintings increased through the years), so his input was sought to help settle a controversy about the disputed paintings. There are 32 paintings in the group, and art historians are at odds over who painted them. Fractal analysis can not replace that of an art historian, but it can add evidence to the inquiry. Taylor found that none of the six paintings he examined had the fractal geometry that he had found in known Pollock works. The Nature article includes photos of a real Pollock and a student attempt to copy his technique. The Star Tribune article discusses some of the above and mentions a timely seminar on math and art that took place at the University of Minnesota's Institute for Mathematics and Its Applications. Dan Rockmore (pictured at right with Institute Director Doug Arnold), who has done mathematical analyses of other artists, was a featured speaker at the seminar. (Photo taken by Kumsup Lee, IMA.) --- Mike Breen

"Mathematician defines beauty in new exhibition," by James Renderson. The Guardian, 1 February 2006;
"Truth plus beauty," by Justin Mullins. New Scientist, 28 January 2006, page 18.

An exhibition of "mathematical photography" by Justin Mullins opened in London on February 1, 2006, and ran for two weeks. The correspondent asks Mullins for an example of a beautiful equation: "His supreme example of mathematical beauty is Euler's identity. Discovered by the 18th century Swiss mathematician Leonhard Euler, it links the five most important numbers in mathematics. It is the special case of a broader equation that links the fields of geometry, the study of space, and algebra, the study of structure and quantity." Mullins, who early on gave framed equations as gifts, started a website at www.justinmullins.com three months ago which has reportedly already received 2 million hits.

--- Annette Emerson

"Space race inspires math booster effort: Backers want federal dollars," by Sharon Theimer, Associated Press (AP). The Boston Globe, 31 January 2006 (also titled "Using Sputnik to Recruit Math Teachers," CNN.com, 31 January 2006);
"President Proposes Billions for Basic Research and Teaching of Math and Science," by Kelly Field. Chronicle of Higher Education, 1 February 2006;
"Parents, students don't see a crisis over science and math," by Ben Feller, AP. USA Today online, 14 February 2006;
"Math back in forefront, but debate lingers on how to teach it," by Keith Devlin. San Jose Mercury News, 19 February 2006;
"Giving students a thirst for math," editorial. San Jose Mercury News, 19 February 2006.

The Associated Press (AP) article by Theimer begins this way: "Business and science groups are reviving images of the Cold War space race in an effort to persuade lawmakers to spend millions to recruit and train high-caliber math teachers". The article was picked up in various newspapers around the country just as President Bush's State of the Union address proposed the "American Competitiveness Initiative." Business lobbies, looking for a future workforce of scientifically-trained U.S. citizens, are pushing for better math education. Raytheon, General Electric, IBM, and other companies are developing programs to get children interested in math. Math for America was mentioned as a program that offers fellowships to young mathematicians to work as high school math teachers. The more recent AP story by Feller reports "If improving science and math education is suddenly a national priority, someone apparently forgot to tell the parents and the students." The apathy is based on a poll by Public Agenda, a public opinion research group that tracks education trends. Keith Devlin briefly presents the solutions desired by the mathematics community ("ensure student mastery of numerical, algebraic and computational skills") and by the mathematics education community ("produce conceptual understanding"), and explains how the answer likely falls somewhere in the middle.

--- Annette Emerson