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This month's topics:
Electronic topology of annulenes
Stephen Strogatz's column has been appearing every Monday since January 31 in The New York Times online. He planned to revisit mathematics from an adult perspective starting with Kindergarten, and has now gone from 1 + 1 = 2 to differential geometry; "The Joy of x" on February 28 was about solving equations in high school. The columns are living up to their promise: "to give you a better feeling for what math is all about and why it's so enthralling to those who get it." Issey Miyake meets William Thurston Models at the rollout of the Issey Miyake FallWinter 2010 readytowear collection (Paris, March 5). "The collection, in an eyepopping rainbow of mostly hightech fabrics, riffed on the idea of oblong shapes and loops, circles and spiralsThurston's model metaphors for the universe." Image courtesy Issey Miyake USA. "Fashion and advanced mathematics collide at Japanese label Issey Miyake" said the press release, datelined Paris and picked up by abc News/Entertainment on March 5, 2010. "On hand at the display was Cornell University Professor William Thurston, whose Geometrization Conjecture inspired Miyake designer Dai Fujiwara. Thurston's theory was described in the collection notes as 'a comprehensive vision of eight geometries that are sufficient to form an ideal shape for all possible threedimensional topologies.'" "Professor Thurston, sporting a Miyake blazer for the occasion, said his discussions with designer Fujiwara had uncovered real areas of overlap between their seemingly disparate professions." Hear them both on this YouTube clip. The Harvard Crimson's article about "Summer's Theory of Inequality" published January 25, 2010 (referring to Lawrence Summer's "infamous speech in which he implied that the reason few women seem to excel in mathematics is genetic") brought up another example of the confluence of fashion and higher mathematics. "Austrian artist Peren Linn has designed jeans with Fermat's Last Theorem imprinted on them, to merge elliptic curves with feminine ones." Article by Jonathan D. Farley and Autumn Stone. See "Math meets Fashion" on Peren's website.
When Byron Cook, a computer scientist and researcher at Microsoft's Cambridge UK research laboratory, needed new symbols to present his work on the halting problem, he "enlisted the help of a friend, New York Citybased artist Tauba Auerbach, a former professional sign writer whose artwork has played with language and technology." This from a NewsFocus item by Angela Saini in the July 24 2009 Science. His research involves relations. As we are taught, a relation R on a set S is no more and no less than a subset of SXS. But you can do some pretty fancy things with relations, and some of them are tedious to spell out every time they are used. One of Prof. Cook's concepts is the restriction of a relation R on a set S to the Cartesian product [with itself] of the image of the reflexive, transitive closure of R. For Auerbach's symbol
Prof. Cook has graciously supplied us the standard notation: it is the restriction of R to
where
and
R^{m} is defined inductively by and .
Tony Phillips 
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