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 Tony Phillips' Take on Math in the MediaA monthly survey of math news |
Why math books are hot:
a piece by
Jane Boursaw and Tameka L. Hicks
in the USA Weekend Magazine for September 21, 2003. In their
investigation of why "... math books meant for pleasure
reading are adding up to a trend," they spoke with Angela von der Lippe,
a senior editor at Norton: "We're feeling comfortable with a subject
that used to be disconnected from reality" and at the same time
"There's an incredible appeal
to math because it explains the mysterious." They spoke with Paul Nahin,
a mathematician with a "popular" book underway:
"Even people who aren't into math can appreciate how it makes the
world go around." They spoke with Vicki Kearn at Princeton University
Press, who blames it all on Andrew Wiles and Fermat's Last Theorem:
"That seemed to be the beginning of math in the news.
It was like beating Babe Ruth's record." Kearn goes on to comment
on the recent flurry of public interest in the Riemann Hypothesis:
"Probably, no one is going to solve it by reading one of these new
math books, but it's very intriguing." Their article is available
online.
The view in dodecahedral space (if the framework of the docecahedron is visible). Adjacent cells are just the cell you're in, seen from different points. A spherical wavefront will intersect with itself in "circles in the sky." If detected, these would give an experimental confirmation of the theory. Three dodecahedra fit together evenly around an edge only if the space is positively curved. In physical terms, this means a value strictly greater than 1 for the mass-energy density parameter Ω0, another point subject to experimental test. Click to enlarge the image. Image courtesy Jeff Weeks, used with permission |
At home in dodecahedral space. The cover story in the October 9 2003 Nature
is "Dodecahedral space topology as an
explanation for weak wide-angle temperature correlations in the cosmic
microwave background." Dodecahedral space was invented a hundred years ago
by Henri Poincaré -he used it as a counterexample to
an early
version of his famous conjecture.
You make a 3-dimensional space with no boundary by taking
a solid dodecahedron and identifying opposite sides
(after a rotation by π/5). If you are living in this space you
don't feel any boundaries: as you cross one of the original
faces you re-enter, slightly rotated, from the opposite side.
This should feel perfectly natural, because the authors of
the article (Jean-Pierre Luminet,
Jeffrey Weeks,
Alain Riazuelo, Roland Lehoucq and Jean-Philippe Uzan) give evidence to
show that dodecahedral space may in fact be
the shape of the universe we live in. The evidence comes from the spectrum of the temperature fluctuations on the microwave sky ("the waves from the Big Bang"). The data from the Wilkinson Microwave Anisotropy Probe reveal that the lowest-mode observable vibration (the quadrupole) is "only about one-seventh as strong as would be expected in an infinite flat space". The team calculated the spectrum of dodecahedral space, which "depends strongly on the assumed mass-energy density parameter Ω0". They observe that for 1.012 < Ω0 < 1.014 the values for both the quadrupole and the next-lowest mode (the octopole) give good matches to the experimental numbers from WMAP, while their range for Ω0 falls "comfortably within WMAP's best-fit range of Ω0 = 1.02 +/- 0.02". Numbers from upcoming experiments including the Planck Surveyor should determine Ω0 within 1%. "Finding Ω0 < 1.01 would refute the Poincaré space as a cosmological model, while Ω0 > 1.01 would provide strong evidence in its favour." |
Math on the golf course.
"Math Institute wants MH move" is the headline on a story by
Carol Holzgrafe in the October 17 2003 Morgan Hill Times,
from San Benito County in California. The story gives the local
take on ex-math-student millionaire John Fry's plans to install
the American Institute of Mathematics
on a golf course in Morgan
Hill. The old Flying Lady Restaurant is being remodeled into a
conference center. But there's more. Holzgrafe describes the
Institute's unusual style of fostering progress in mathematical
research: group work. As implemented by Fry and co-founder
Steve Sorenson, you "bring a hand-picked group together
in one room for a week or so and work on the problem together,
in a kind of focus workshop." An alternative scenario works
with larger groups: "30 or so men and women from the United States and around the world hear the problem outlined. They discuss, break up into smaller groups, then return and bat ideas around some more in an informal setting."
AIM's specialty is "bringing together people from different disciplines ... Varied participants add new dimensions, perspectives and resources from which to find solutions." This according to Brian Corey, the Institute's Executive
Director, who is quoted as saying: "They can connect the dots better working together." Holzgrafe goes on to enquire about the hallmarks of a good
problem ("It must be important." "It must be beautiful.") and to recount
the
efforts of Associate Director Helen Moore to win more young women over
to careers in mathematics by telling them about "the joys of math."
-Tony Phillips
Stony Brook
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