Magazine article Science News

Math Prizes: Fields for Further Study

Magazine article Science News

Math Prizes: Fields for Further Study

Article excerpt

Math prizes: Fields for further study

The surprising discovery of deep, hitherto hidden links among vastly different mathematical fields is one of the strongest threads that tie together the research of three young mathematicians who this week were each awarded a Fields Medal. To mathematicians, this award, named for Canadian mathematician John C. Fields, carries the prestige, if not the monetary value, of a Nobel Prize.

Michael H. Freedman, 35, of the University of California at San Diego, was honored for his work on classifying four-dimensional shapes or manifolds, part of the study of topology (SN:7/17/82, p.42). Freedman's methods for constructing the startling variety of forms possible in four-dimensional space was a key element in the solution to this problem. His research brought together powerful ideas in both geometry and algebra.

Simon K. Donaldson, 29, of Oxford University in England, although also studying four-dimensional manifolds, took a very different approach. To provide a new geometric tool, he borrowed methods from theoretical physics--a set of nonlinear differential equations widely used for describing electromagnetic effects and other phenomena. Together with Freedman's work, his results revealed that four-dimensional space has more than one possible structure.

"When Donaldson produced his first few results on four [-dimensional] manifolds,' says Oxford's Michael Atiyah, a previous Fields Medal winner, "the ideas were so new and foreign to geometers and topologists that they merely gazed in bewildered admiration. …

Search by... Author
Show... All Results Primary Sources Peer-reviewed

Oops!

An unknown error has occurred. Please click the button below to reload the page. If the problem persists, please try again in a little while.