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A monthly survey of math news
This month's topics:
Paris-Match ran a photo essay on Alexander Solzhenitsyn (died August 3, 2008) in its August 7-13 issue. It included this picture of the author tutoring his children in mathematics.
Solzhenitsyn teaching his children the derivation of the quadratic formula. ©1981 Harry Benson. Click for full-size image.
Paris-Match's caption reads: "1982: pour ses trois fils il retrouve le tableau noir du professeur de maths qu'il a été." For more details we can turn to his 1970 Nobel Prize Autobiography.
An article published online September 7, 2008 by Nature bears the title "Individual differences in non-verbal number acuity correlate with maths achievement." The authors, a Johns Hopkins team led by Justin Halberda, elaborate in the Abstract: "Our results show that individual differences in achievement in school mathematics are related to individual differences in the acuity of an evolutionarily ancient, unlearned approximate number sense." What is this ancient unlearned number sense? There turns out to be an "approximate number system," or ANS, which is "shared by adults, infants and non-human animals." These groups "can all represent the approximate number of items in visual or auditory arrays without verbally counting, and use this capacity to guide everyday behaviour such as foraging." The authors set out to investigate whether this ancestral ability is uniform among humans, and if not whether it correlates with other, more symbolic, mathematical talent.
They studied a group of 64 14-year-olds and measured their "ANS acuity" by trials in which "subjects saw spatially intermixed blue and yellow dots presented on a computer screen too rapidly (200 ms) to serially count. Subjects indicated which colour was more numerous by key press and verbal response."
Images like this one were flashed on a screen too rapidly for the dots to be counted. Subjects were asked to estimate which color was more numerous. Here there are 8 yellow dots and 6 blue; ratios varied randomly from 1:2 to 7:8.
The authors discovered a "surprisingly large variation in the ANS acuity." Some subjects could detect excesses as relatively small as 10 over 9 with 75% accuracy; others "had difficulty with ratios finer that 2:3." When it came to comparing ANS acuity with success in symbolic mathematical achievement, the authors found a significant correlation. These children's symbolic ability had been tested every year starting in kindergarten; the authors found that the correlation strong enough so that "ANS acuity in ninth grade retrospectively predicted the symbolic maths performance of individual students from as early as kindergarten, a 9-yr time span." The authors mention that these results "are consistent with at least two interpretations." One is that the ANS, since it is already present in infants, "may have a causal role in determining individual maths achievement." Another is that "individual differences in the quantity or quality of engagement in formal mathematics might increase ANS acuity."
This research was picked up by Natalie Angier in the September 16 2008 New York Times under the headline "Gut Instinct's Surprising Role in Math."
stands for the National Institute for Mathematical and Biological Synthesis, which will be hosted at the University of Tennessee in Knoxville. The NSF / DHS (Department of Homeland Security) award was described in a News piece by John Whitfield in Nature for September 4, 2008. "The institute's creation reflects the growing strength of mathematical biology, and growing concerns about the potential impact of animal diseases on agriculture and human health ..." Whitfield tells us. "Besides ecology and evolution, which already have strong mathematical components, NIMBioS aims to bring mathematics to parts of biology that it has so far had little impact on, such as development and immunology." "The eight or nine groups planned in the first year include investigations of the links between the mathematics of invasive species and cancer metastasis; the dynamics of social networks in animals; and modeling the spread of pseudorabies among feral pigs in the southern United States."