Caffarelli, Kohn, Nirenberg, Griffiths, Goldsto, Pintz, Yildir, 张益堂。。。 - eNewsTree.com

Luis Caffarelli, Robert Kohn, and Louis Nirenberg (pictured above, left to right) are receiving the 2014 AMS Leroy P. Steele Prize for Seminal Contribution to Research. Caffarelli is professor of mathematics at the University of Texas at Austin. Kohn and Nirenberg are professors of mathematics at the Courant Institute of Mathematical Sciences at New York University. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics. The prize will be awarded on Thursday, January 16, 2014, at the Joint Mathematics Meetings in Baltimore. (Photo of Luis Caffarelli © Becky Rische.)

Caffarelli, Kohn, and Nirenberg are honored for their paper, "Partial regularity of suitable weak solutions of the Navier-Stokes equations" (Communications Pure and Applied Mathematics, 1982). "This paper was and remains a landmark in the understanding of the behavior of solutions to the Navier-Stokes equations and has been a source of inspiration for a generation of mathematicians," the prize citation says.

The Navier-Stokes equations are fundamental to the mathematical understanding of fluid dynamics and are at the center of one of the million-dollar Millennium Prize Problems of the Clay Mathematics Institute. The work of Caffarelli-Kohn-Nirenberg was a major advance in understanding these equations. Their paper has functioned as a kind of textbook for a whole generation of researchers who worked on the Navier-Stokes equations and motivated many later developments and simplifications.

Phillip A. Griffiths is receiving the 2014 AMS Leroy P. Steele Prize for Lifetime Achievement. Griffiths is professor emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton. Presented annually by the American Mathematical Society, the Steele Prize is one of the highest distinctions in mathematics. The prize will be awarded on Thursday, January 16, 2014, at the Joint Mathematics Meetings in Baltimore. (Photo of Phillip A. Griffiths by Cliff Moore.)

His work in algebraic geometry has inspired at least two generations of leading mathematicians working in this area and will undoubtedly continue to inspire new generations long into the future. He also made fundamental contributions to differential geometry and differential equations, developing a style and research program that was all his own and that has proved extraordinarily fertile.

His teaching career and research leadership, as measured by the numbers of individuals he mentored who have gone on to stellar careers in mathematics and other disciplines, is "simply astounding," the prize citation says. Many of his expository papers and books have become classics, and many have remained in print and continue to inspire students.

Griffiths has supported the field of mathematics by serving on and chairing numerous committees and boards, both nationally and internationally. He has carried on a remarkable research career while serving eight years as the provost of Duke University and twelve years as the director of the Institute for Advanced Study. He currently chairs the Science Initiative Group, which aims to assist the development of mathematical training centers in the developing world. The prize citation states: "His example of service and leadership has inspired so many in the mathematics community to emulate him in some degree, and our mathematical world is much the richer for it."

Simon Brendle (pictured at left), professor of mathematics at Stanford University, is receiving the 2014 AMS Maxime Bôcher Memorial Prize. Presented every three years by the American Mathematical Society, the Bôcher Prize recognizes an outstanding research paper in the field of mathematical analysis that has appeared in the preceding six years. The prize will be awarded on Thursday January 16, 2014, at the Joint Mathematics Meetings in Baltimore. (Photo: Margarete Eisele.)

Brendle is honored for "his outstanding solutions of long-standing problems in geometric analysis," the prize citation says. The work being recognized includes Brendle's proof, carried out jointly with R. Schoen, of the differentiable sphere theorem ("Manifolds with 1/4-pinched curvature are space forms," Journal of the AMS, no. 1, 287-307 (22) 2009) and the solution of the Lawson conjecture ("Embedded minimal tori in S3 and the Lawson conjecture", to appear in Acta Mathematica). Also recognized by this prize are Brendle's deep contributions to the study of the Yamabe equation.

Daniel Goldston, János Pintz, and Cem Y. Yildirim (pictured left to right) are receiving the 2014 AMS Frank Nelson Cole Prize in Number Theory. Goldston is professor of mathematics at San Jose State University, Pintz is a research professor at the Alfréd Rényi Institute of Mathematics of the Hungarian Academy of Sciences in Budapest, and Yildirim is on the faculty of Boğaziçi University in Istanbul. Presented every three years by the American Mathematical Society, the Cole Prize recognizes an outstanding research paper in number theory that has appeared in the preceding six years. The prize will be awarded on Thursday, January 16, 2014, at the Joint Mathematics Meetings in Baltimore. (Photo of Daniel Goldston by Ryoko Goldston; photo of János Pintz by László Szelényí.)

Goldston, Pintz, and Yildirim are honored for their work on "small gaps" between prime numbers, which is presented in their paper "Primes in tuples. I" (Annals of Mathematics (2) 170 (2009), no. 2, 819-862, subscription required).

One of the oldest problems in number theory is the Twin Prime Conjecture, which says that there are infinitely many pairs p and q of primes with p - q = 2. While the Twin Prime Conjecture has motivated a great deal of research in number theory, an actual proof of the conjecture has remained out of reach. In 2005, Goldston, Pintz, and Yildirim achieved a surprising breakthrough when they proved that the there are infinitely many pairs of consecutive prime numbers p and q such that the gap between p and q is far smaller than the average gap between consecutive primes. Their ingenious methods paved the way for another major advance, made by Zhang in 2013, which established that there are infinitely many pairs p and q of primes such that the difference p - q is less than 70,000,000. In recognizing the achievements of Goldston, Pintz, Yildirim, and Zhang, the 2014 Cole Prize honors landmark work in the history of number theory.

News about the Goldston-Pintz-Yildirim work appeared in Science magazine on May 27, 2005: "Third Time Proves Charm for Prime-Gap Theorem," by Barry Cipra (subscription required). See also "Together and Alone, Closing the Prime Gap," by Erica Klarreich in the November 2013 issue of Quanta (no subscription required).

Yitang Zhang (pictured at left), lecturer in mathematics at the University of New Hampshire, is receiving the 2014 AMS Frank Nelson Cole Prize in Number Theory. Presented every three years by the American Mathematical Society, the Cole Prize recognizes an outstanding research paper in number theory that has appeared in the preceding six years. The prize will be awarded on Thursday, January 16, 2014, at the Joint Mathematics Meetings in Baltimore. (Photo: Lisa Nugent, University of New Hampshire Photographic Services.)

In May 2013, the online magazine Quanta published an article about the work of Zhang: "Unheralded Mathematician Bridges the Prime Gap," by Erica Klarreich; see also the story by Klarreich posted in November 2013, "Together and Alone, Closing the Prime Gap" (no subscription required).