Abel Prize awarded to John Willard Milnor

March 24, 2011 12:09 am | Updated November 17, 2021 05:50 am IST - New Delhi:

John Milnor

John Milnor

The Norwegian Academy of Science and Letters has chosen one of the living legends of mathematics, John Willard Milnor of the Institute for Mathematical Sciences in the University of Stony Brook, U.S.A, for the award of its prestigious Abel Prize for the year 2011.

This was announced on Wednesday in Oslo by Norwegian Academy president Øyvind Østerud. Professor Milnor will receive the Prize from His Majesty King Harald at an award ceremony in Oslo on May 24, 2011. The award carries 6 million Norwegian Kroner (approx. €750,000 or $1 m.)

The Prize is given in recognition of contributions of extraordinary depth and influence to mathematical sciences and has been awarded annually since 2003. The Prize is named after the great Norwegian mathematical genius, Niels Henrik Abel (1802-29), often compared with the Indian wizard Srinivasa Ramanujan, who died at a very young age of 26.

The past winners include such illustrious names as Jean-Pierre Serr (2003), Sir Michael Atiyah and Isadore M. Singer (2004), Peter D. Lax (2005), Lennart Carleson (2006), Srinivasa S. R. Varadhan (2007), John Griggs Thompson and Jacques Tits (2008), Mikhail Leonidovich Gromov (2009) and John Torrence Tate (2010).

The 2011 award is being given to Professor Milnor, as the citation notes, “for [his] pioneering discoveries in topology, geometry and algebra.” He has even made significant contributions in number theory.

“All of Milnor's works,” the citation adds, “display marks of great research, profound insights, vivid imagination, elements and supreme beauty.” His profound ideas and fundamental discoveries have shaped to a great extent the mathematical landscape since the mid-20th Century. Professor Milnor also has written tremendously influential books, loved in particular by graduate students, which are widely regarded as models of fine mathematical writing. In addition, given his affable personality, he has been called the ‘Gentle Giant of Mathematics'.

Professor Milnor was born on February 20, 1931, in New Jersey, and did his undergraduation at Princeton University. When he was barely 18 he proved what is known as Fary-Milnor theorem in knot theory. He did his doctoral work under Ralph Fox in knot groups and after completing his doctorate he continued to work at Princeton.

His most celebrated single result is his proof in 1956 of the existence of 7-dimensional spheres with non-standard differential structure. A one-sphere is a circle and a 2-sphere is the sphere that one is familiar with in 3-dimensions. An n-sphere is the mathematical abstraction of this idea in higher dimensions. Milnor termed spheres with non-standard differential structures ‘exotic spheres'.

Later with Michel Kervaire, a French mathematician, he showed that the 7-sphere has 28 differential structures.

Numerous mathematical concepts, results and conjectures are named after Professor Milnor — besides Milnor exotic spheres, Milnor fibration, Milnor number, Milnor map, and many more. More recently Milnor has turned his attention to the study of dynamical systems in low dimensions to which the Milnor-Thurston kneading theory is an important contribution.

Major awards

Professor Milnor has received all the major awards in Mathematics: He was awarded the Fields Medal in 1962, the Wolf Prize in 1989 and is the only person to have won all the three Steele Prizes of the American Mathematical Society (AMS) in 1982, 2004 and early this year for seminal contribution to research, for mathematical exposition and for lifetime achievement respectively. He also received the U.S. National Medal of Science in 1967.

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