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A monthly survey of math news
More backstage math. The February 1 2002 Science ran ``Beautiful Mind's Math Guru Makes Truth = Beauty,'' a piece by David Mackenzie about Dave Beyer, the Barnard College professor who advised the director on mathematical matters. The focus is on the problem that the Nash in the movie proposes to his MIT class:
For the purposes of the script, Beyer needed a problem that could be stated in terms appropriate for the course (which seems to be the old M351 Advanced Calculus for Engineers), was subtle enough to be out of reach for most undergraduates, but ``accessible enough so that Connelly's character, a bright physics student, might concoct a plausible, though incorrect, solution.'' He also wanted a problem that mathematicians would recognize as worthwhile if they thought about it. But he hoped they wouldn't. Mackenzie quotes him as saying: ``If you put enough effort into making the math credible, at a certain point you win the war. They're caught up in the movie and barely have time to recognize it's a problem in de Rham cohomology.''
``Highly enjoyable and interesting people" Nous? David Auburn, the playwright autor of Proof says in fact: ``The more time I spent with mathematicians, the more I found they were highly enjoyable and interesting people to be around.'' This quotation is highlighted in a January 27 2002 Boston Sunday Globe article by their staff writer Maureen Dezell, entitled ``Setting dramas of love and loss in the world of mathematics.'' Dezell spends most of her time on Proof and its author, who says he began writing ``a story about sisters fighting over something they found after their parents die,'' and chose a mathematical proof as the disputed object ``because its fathership could be called into question the way a painting or a manuscript couldn't.'' Auburn was particularly pleased that the mathematical community took the play seriously enough to organize a symposium (at NYU in October, 2000) on the topic. ``All these prominent mathematicians flew in and saw the show and spoke on panels.'' He reports that Ben Shenkman, the young actor who played Hal, and who never got beyond calculus in college, turned to him at one point and said: ``I feel like George Clooney at a medical convention.''
Math on 42nd street. ``Solve this problem and win a Snickers bar.'' The challenge is thrown by Prof. George Nobl, who holds forth on 42nd Street between 5th and 6th Avenues every Wednesday at noon. He stands by an easel with a whiteboard and a sheaf of problems. This activity is reported in the New York Times for February 7, 2002: ``Problems on the Street, Solvable with a Pencil'' by Yilu Zhao. The problem of the hour, when the accompanying photograph was taken, is ``Pete sells a six inch pizza for $6.00. How much should he charge for a twelve inch pizza?'' Professor Nobl's goal is ``to promote the fun of math,'' and to further his own pedagogical agenda. ``It's so easy to teach math right. Why teach it wrong?'' Wrong means using rote learning and memorization. Right is instilling understanding. He says, according to Zhao, that once a student truly grasps a rule, getting the correct answer is easy. And he is now seeking grants to start a nonprofit group to hire a few teachers who would put up similar stands around the city.
Fourier transform of the fossil record. This research, reported in a January 3 2002 Letter to Nature by James Kirchner of UC Berkeley, uses spectral analysis methods ``to measure how fossil extinction and origination rates fluctuate across different timescales.'' His data were compilations of fossil marine animal families and genera over the last 500 million years (Myr); his conclusion: ``Compared with extinction rates, origination rates have equal or greater spectral power at long wavelengths (>100 Myr), but much lower spectral power at short wavelengths (<25 Myr).'' Implication of this analysis: ``either the processes regulating originations have more inertia than those driving extinctions, or that origination events tend to be diverse and local, whereas extinctions (particularly mass extinctions) tend to be coherent and global.'' What this means for us: ``If the continuing anthropogenic extinction episode turns out to be comparable to those in the fossil record (which is not yet clear), my analysis shows that diversification rates are unlikely to accelerate enough to keep pace with it. Thus, widespread depletion of biodiversity would probably be permanent on multimillion-year timescales.''
Large-scale sign error. Sign errors are the plague of calculation. But they are usually not as interesting as the one that ensnared two groups in 1995. In one of the Feynman integrals for the computation of the ``predicted value of the muon's magnetism,'' using the Standard Model, they were ``misled by an extra minus sign.'' When last year a group at Brookhaven National Laboratory obtained an experimental value that was significantly different, the discrepancy was interpreted by many physicists as possible evidence of supersymmetry. But no; when Marc Knecht and Andreas Nyffeler (Center for Theoretical Physics, Marseille) refined the calculation, they found a different sign for that term. The 1995 groups rechecked their work and found where they had gone wrong; the predicted and observed values are now only slightly farther apart than expected errors would allow. The story is told in ``Sign of Supersymmetry Fades Away'' by Adrian Cho, Science (News of the Week), December 21, 2001.
``The Shape of the Universe: Ten Possibilities'' is the title of a long and lavishly illustrated article in the American Scientist for September-October 2001. The autors are Colin Adams and Joey Shapiro, respectively professor and undergraduate at Williams College. The article starts from scratch with an explanation of the topology of surfaces, and then leaps into three dimensional manifolds. Given that the universe is Euclidean (average curvature zero), as recent observations of the cosmic microwave background radiation (CMB) seem to imply, and orientable, there are only ten possible topologies. Six are compact (finite volume); four are not; all are illustrated. Adams and Shapiro end by explaining how more accurate CMB measurements in the near future may give us a better idea of the shape we're in.