
January
12, 2004
UC San Diego Computer Theorist
And Mathematician
Ronald Graham Elected To AAAS Council
By Doug Ramsey
Leading
American mathematicians have elected Ronald Graham of the University
of California, San Diego (UCSD) to represent them on the Council
of the American Association for the Advancement of Science (AAAS).
Graham will serve a threeyear term beginning in February 2004.
“Mathematics is the language of science, and as all disciplines
become more advanced, scientists rely increasingly on math to
frame new discoveries,” said Graham. “Part of my
job will be to see that the Association and its members are
fully aware of the exciting developments occurring in the mathematics
world.”
Graham holds the Irwin
and Joan Jacobs Endowed Chair in Computer and Information Science
in UCSD’s Jacobs School of Engineering, and is Chief Scientist
of the California Institute for Telecommunications and Information
Technology [Cal(IT)2]. He joined the UCSD faculty in 1999,
after a 37year career with AT&T, ultimately as chief scientist
at AT&T Labs. Graham received his Ph.D. in mathematics from
U.C. Berkeley in 1962. Currently he is the Treasurer of the
National Academy of Sciences, and President of the Mathematical
Association of America. He has won numerous awards in the field
of mathematics, including the Polya Prize in Combinatorics and
the Steele Prize for Lifetime Achievement from the American
Mathematical Society in 2003.
Mathematics is one
of eight AAAS sections electing Council Delegates to take office
in 2004. The other sections electing new delegates to the AAAS
Council included Anthropology, Astronomy, Biological Sciences,
Chemistry, Geology and Geography, Neuroscience, and Physics.
Graham was the only UCSD nominee on the 2003 ballot.
Graham has previously
been the Secretary and Chair of the Mathematics Section of the
AAAS, and also served on its Program Committee for four years.
“Even in the social sciences, math is a powerful way of
expressing concepts and finding solutions, especially in disciplines
where patterns are involved, because math is basically the science
of patterns,” said Graham. “As a result, if we can
find a new mathematical tool to solve one problem, it can often
be used to tackle seemingly very different problems which however
share the same mathematical structure. And as these new mathematical
tools are created, scientists can use them to revisit existing
problems in areas that until now seemed unanswerable.”
In looking at breakthroughs
in mathematics on the horizon that should be of interest to
all AAAS members, Graham notes that a Russian mathematician
appears to have solved the first of the seven fundamental questions
known as the Millenium Prize Problems. The Clay Mathematics
Institute issued the challenge in 2000, focusing on classic
problems that have resisted solution over the years, and offering
a $1 million prize for each one that is solved. In this case,
the Poincare Conjecture – named after the Frenchman who
proposed it in 1904 – posits that the threedimensional
sphere is the only bounded threedimensional space with no holes.
The problem is central to the field of topology, which looks
at the properties of surfaces that don't change no matter how
much you stretch or bend them. Russia’s Grigori Perelman
recently posted a proof that is based on a method called Ricci
flow, which breaks a surface into parts and smoothes these parts
out. This particular approach was initially pioneered by former
UCSD mathematician Richard Hamilton, now at Columbia University.
Perelman’s proof joins topology and geometry, by stating
that all spacelike structures can be divided into parts, each
of which can be described by one of three kinds of simple geometric
models. His work sent shock waves through the math community
at conferences in December. “Perelman’s proof could
change our perspective in many branches of mathematics and physics,”
said Graham.
Graham and his wife,
fellow UCSD mathematician Fan Chung Graham, were recently involved
in corroborating new insights into an ancient problem posed
by Greek mathematician Archimedes over 2,200 years ago. The
socalled Stomachion involved 14 irregular polygonal
shapes. As a simple puzzle, the pieces could be configured into
many different shapes. Historians have wondered why Archimedes
was taken with the problem. A longlost copy (circa 975 A.D.)
of Archimedes’ document dealing with the puzzle surfaced
in 1998, and sold at auction for $2 million. Since then, scientists
have been able to rescue much of the original writing, and Stanford
historian Reviel Netz has championed a new understanding of
the Stomachion treatise: that Archimedes was interested not
in how many shapes could be created, but rather in how many
ways the pieces could be combined to form a square. In calculations
that took weeks, the Grahams confirmed that there are exactly
17,152 different ways of making a square from the assembled
pieces. For Graham, this new insight has special meaning. “My
specialty is combinatorial mathematics, which often involves
enumerating the number of different ways to solve a problem,”
he observed. “For most of us, combinatorics didn’t
come into its own until the advent of computer science, and
there was certainly no evidence of scientists looking at math
problems in this way in ancient texts. Now it seems clear that
Archimedes, already the father of integral calculus among many
other things, is also the father of combinatorics.” The
research was featured in December in the New York Times.
Note to Editors: A
highres photo of Prof. Ronald Graham can be downloaded from
the “Faculty & Students” section of the Image
Gallery at http://www.jacobsschool.ucsd.edu/news_events/gallery/.
Media Contact: Doug
Ramsey (858) 8225825
