This month's topics:
"Complex Math, Simple Sum: 3 Awards in 5 Years" was the headline for Lisa Foderaro's article in the May 31 2009 New York Times. The occasion was Mikhael Gromov's Abel Prize (the Times ran a photograph of him with Queen Sonja and King Harald of Norway) which turned out to be the third won by a Courant Institute professor. The prize has only been awarded since 2003, so the Courant has won three, vs. four for the rest of the universe (their others were Peter Lax in 2005 and Srinivasa Varadhan in 2007). Foderaro sketches the mathematical biographies of all three, along with a recounting of the whynoNobelinmath story: "Some speculate that Alfred Nobel, a Swedish industrialist who invented dynamite and who established the prizes, simply wasn't a math guy. Others cite a bit of lore that he harbored a grudge against math because a love interest rejected him in favor of a wellknown mathematician." She ends with a quote from Varadhan: "We had a very good math teacher in high school who instilled in us the idea that math didn't have to be work. You could do it for fun." Those evil mathematicians, again This time it's from Time magazine (July 9, 2009, in a story by David von Drehle and Jay NewtonSmall about the present and future of Sarah Palin.) "If ever there has been a time to gamble on a flimsy résumé ... this might be it." The reason: "Résumés ain't what they used to be; they count only with people who trust credentialsa dwindling breed. The mathematics Ph.D.s who dreamed up economykilling derivatives have pretty impressive résumés." Etc. Cortical circuits for mental arithmetic "Throughout the history of mathematics, concepts of number and space have been tightly intertwined." This is the beginning of the abstract of a report in Science for June 19, 2009. The authors (André Knops, Bertrand Thirion, Edward M. Hubbard, Vincent Michel, Stanislas Dehaene, based at various institutions in and near Paris) "tested the hypothesis that cortical circuits for spatial attention contribute to mental arithmetic in humans." The underlying neurobiological context is that "cultural inventions such as writing and mathematics" are "too recent for natural selection to have dedicated specific brain mechanisms to them. It has therefore been suggested that they coopt or 'recycle' evolutionarily older circuits with a related function ... ." It is known that people think of numbers as positioned on a "mental number line" with (for lefttoright readers) smaller numbers to the left and larger ones to the right. This and other pieces of evidence suggest searching in the parts of the brain related to vision for activity related to mental computation. The authors concentrated on regions associated with saccades (the quick simultaneous movements with which the eyes track moving objects; they also occur in reading), and "predicted that mental addition, which increases number size, would be associated with a rightward shift of attention and subtraction with a leftward shift." They tested this hypothesis by first training a computer to distinguish the fMRI records of subjects moving their eyes to the right, from those moving their eyes to the left; and then asking the computer to predict, from fMRI records, whether subjects were performing mental addition or mental subtraction. "Equating addition with rightward saccades and subtraction with leftward saccades, the mean accuracy for inferring whether an addition or subtraction was performed, averaged over all participants, was 55.0 ± 1.8%, which is significantly greater than chance."
Tony Phillips 
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