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 Tony Phillips' Take on Math in the Media A monthly survey of math news

# This month's topics:

## Sophie Kowalevski in the New York Times

This elegant portrait of the great Russian mathematician was printed in the Times for November 12, 2013. The occasion was their review of an exhibition ("Extraordinary Women in Science and Medicine"), then up at the Grolier Club in New York. Denise Grady, who wrote the review, gives us a thumbnail biography: Kowalevski, "born in Russia in 1850, became a noted mathematician in spite of a father who 'had a horror of learned women,' according to the catalog. As a young woman, she could study math and physics only in secret. She married a man she did not love just to get away from her father and obtain a formal education. The marriage turned out to be a disaster. And when the couple moved to Berlin, she had trouble finding a university that would allow a woman to earn a degree. But a renowned mathematician agreed to provide tutorials, and she eventually received a doctorate and went on to fame in her field." Other extraordinary women featured in the show include the geneticist Barbara McClintock, the astrophysicist Cecilia Payne-Gaposhkin and the crystallographer Dorothy Hodgkin. Photograph: Institut Mittag-Leffler, reproduced with permission.

## How much math do we really need?

The Daily Dish (October 23, 2013) links to "The Death of math," posted October 19 by Gary Rubinstein on his blog at teachforus.org (where we learn that "Teach For Us is the organization that connects Teach For America teachers with each other for support and shares their stories with the broader public."). Rubinstein, a Teach for America veteran, is on the math faculty at Stuyvesant High School in New York. As the Dish reports, Rubenstein would "gleefully chop at least 40 percent of the [math] topics that are currently taught from K to 12," and recommends making all math instruction optional after 8th grade.

Here are Rubinstein's two proposals:

• "Greatly reduce the number of required topics, and ... expand the topics that [remain] so they can be covered more deeply with thought provoking lessons and activities."
• "Make Mathematics, beyond eighth grade, into electives." The rationale for this point depends on the first. "I really think we would have more people interested in Math with the better K-8 courses, so many people would choose those electives" and the electives in turn would be much more successful in producing strong graduates since they would not be "slowed down by students who had no interest in those courses."

This posting generated much comment, some of it enlightened, both on the Dish and in the responses on Rubinstein's blog. Rubinstein surveys recent treatments of this problem in the media; two of them were picked up here (in 09/12 and 03/13).

## Mathematicians in Science: Bourguignon and Gauss

On November 1, 2013, Science reported that Jean-Pierre Bourguignon has been named the new president of the European Research Council, "Europe's funding agency for basic research." Martin Eskerink, who wrote the report, refers to A Beautiful Formula, the 8-minute video Bourguignon made last year about $e^{i\pi}+1=0$, and where he gives an example of a "change in point of view [that] turns out to be an extremely powerful tool in mathematics." Eskerink remarks that Bourguignon's own point of view "is about to shift dramatically, giving him greater control over the course of European science." Eskerink emphasizes the diplomatic problems that Bourguignon will confront in his new position; he mentions the pressure from "countries in southern and eastern Europe that want a bigger part of ERC's pie" (€7.5 billion for 2007-2013, and scheduled to almost double for the next six years); and the difficulty in keeping the ERC independent of politics and European Commission. A fuller account of Bourguignon's mathematical career was given (by David Larousserie in Le Monde on Sept. 2, 2013) after his retirement, this year, from the directorship of the IHÉS and from his position as professor at the École Polytechnique.

On November 8, 2013, Science, in a "Random Sample," reported that the jar labeled "C. F. Gauss" in the University of Göttingen's elite brain collection did not in fact contain the brain of the "Prince of Mathematics," and had not for many, many years. The brain in that jar had a rare anatomical feature, a surface "bridge" between the parietal and frontal lobes, which had been first identified by the anatomist Rudolph Wagner in the brain of C. H. Fuchs, a famous physician who died the same year as Gauss, and who also made it into the "elite" collection. Somehow the two brains got swapped back in the 19th century; the substitution was noticed just this year by Renate Schweizer of the Max-Planck Institute in Göttingen: Wagner's original, precise drawings of both brains were still available and allowed the switch to be rectified.

Rudolph Wagner's lithographs of the brains of C. H. Fuchs (left) and C. F. Gauss (right), made shortly after their deaths. The surroundings of the central fissure, separating the parietal and frontal lobes, have been highlighted in yellow. Note that in Fuchs' brain a bridge crosses the fissure. According to Science, Schweizer noticed that the brain in Gauss' jar had this unusual configuration, remembered having seen a picture of such a brain before, and realized this was in fact Fuchs' brain. Sure enough, in Fuchs' jar, was a brain that matched Wagner's lithograph for Gauss. Images © Jens Frahm and Sabine Hofer / Biomedizinische NMR Forschungs GmbH 2013.

Tony Phillips
Stony Brook University
tony at math.sunysb.edu

Math Digest
Summaries of media coverage of math

If you thought you'd heard the last from the twin primes conjecture, boy were you wrong. Since Tom Zhang stunned the mathematical world with his May proof that there are infinitely many pairs of primes separated by no more than 70 million, a flurry of activity has been centered on that arbitrary, finite but enormous number. On May 30, Scott Morrison of Australian University in Canberra dropped that distance to 56 million and change. The comments on his blog post chronicle the bound's precipitous drop over the next few days, engineered by Morrison, Terence Tao, and others. By the end of May 31st, Morrison had brought the bound down to 42 million and change; by June 2nd, Tao had introduced improvements bringing the bound down to 13 million and change. By June 4th, Tao had created the Polymath Project, an open, online collaboration to improve the bound, and by June 27th, the maximum infinitely recurring separation between primes was 4,680. "At times, the bound was going down every thirty minutes," says Tao. But it seems the prime gap conjecture was an idea whose time had come: on November 19th, University of Montreal postdoc James Maynard posted an independent proof showing that there are infinitely many pairs of primes no further than 600 apart.

This fascinating article takes a close look at some of the working parts of Zhang's and Maynard's proofs, the techniques being used to improve them, and the interplay between open collaboration and independent research that has driven the advances. Zhang's proof involves three pieces, each of which has been refined by the Polymath Project. First, Zhang used a collection of results by Pierre Deligne to draw conclusions about the distribution of primes, and in turn derived specifications for a new class of sieves--which Klarreich describes as "a comb with some of its teeth snapped off." Second, he used results from the calculus of variations to determine how many teeth one of his sieves would need to "catch" infinitely many pairs of primes. Finally, he calculated how large a comb he would need to start with to end up with a sieve with enough teeth. Progress has been made on all three fronts, even eliminating Deligne's difficult machinery from the proof. But Maynard has taken a different approach, by looking at the sieves themselves and obtaining more precise information about them, to show that certain sieves are much more powerful than originally thought. The Polymath Project is already working on Maynard's result, hoping that his insights can be combined with theirs. Meanwhile, Zhang has a "secret weapon" in reserve, a technique he developed before publishing his proof, which may bring the bound down even further--so stay tuned.

--- Ben Polletta

 Reviews Books, plays and films about mathematics

Citations for reviews of books, plays, movies and television shows that are related to mathematics (but are not aimed solely at the professional mathematician). The alphabetical list includes links to the sources of reviews posted online, and covers reviews published in magazines, science journals and newspapers since 1996.