Jürgen Moser, Who Proved Celestial Theory, Dies at 71

By SYLVIA NASAR

Jürgen Moser, one of the world's leading mathematicians who helped develop an influential theory for analyzing the orbits of planets, asteroids and other celestial bodies, died of prostate cancer on Friday in a hospital in Schwerzenbach, Switzerland. He was 71.

Like many other talented young Germans who came of age after Germany's glittering scientific establishment was gutted by the Nazis, Dr. Moser emigrated to the United States in the mid-1950's, soon after completing his doctorate. He spent most of his career at the New York University Courant Institute, where he served for three years as director.

After nearly 25 years in this country, Dr. Moser returned to Europe in 1980 to rebuild the once-stellar Mathematics Research Institute at the Federal Institute of Technology, Switzerland's equivalent of the Massachusetts Institute of Technology.

Much of Dr. Moser's research was inspired by problems that arose in physics. A lifelong astronomy enthusiast who as a boy built model gliders and as a father made boats for his children, Dr. Moser was fascinated by problems involving the stability of motion, or lack of it. He is best known for a fundamental contribution to celestial mechanics, the Kolmogorov-Arnold-Moser theory, that he published, in an article that appeared in a German journal in 1962.

The problem that Dr. Moser tackled, the stability of the solar system, was one that had tantalized scientists for centuries. Will the solar system remain as it is for all eternity, or will Jupiter one day collide with Mars and Venus drift into the Sun? Isaac Newton made his contribution to the invention of calculus while trying to prove that celestial bodies always travel in elliptical orbits.

But Newton's proof applied only to systems that consisted of two bodies, say Earth and the Sun. Nearly every leading 18th-century mathematician took up the problem of systems with more elements, a problem that involved both stable movements and unpredictable, chaotic ones, but by the end of the 19th century, the celebrated French mathematician Poincaré had concluded that the problem was essentially insoluble.

The KAM theory addresses the following question: What happens to well-behaved elliptical orbits if one tries to take into account the small perturbations resulting from the gravitational pull of smaller or more distant planets? In 1954, the Russian mathematician, Andrei N. Kolmogorov, announced that he had found the answer, arguing that if the disturbance was sufficiently small, many but not all of the orderly motions would survive, with orderly orbits coexisting alongside chaotic ones. But Kolmogorov outlined a general theory without supplying complete proof. His student, V. I. Arnold, proved one case; Dr. Moser proved another. ...

"The wonderful thing is that KAM theory also applies to airplane dynamics, submarine dynamics, automobile dynamics; in fact, practically any dynamical system described by Newton's laws." said Philip Holmes, an applied mathematician at Princeton University, who with Florin Diacu wrote the book Celestial Encounters, (Princeton University Press, 1996), a history of dynamical systems theory. ...