The 2010 Fields Medal winners have been announced, and four individuals have been awarded the highest honor in mathematics. This year’s researchers hale from all over the world and have achieved tremendous breakthroughs in mathematics and physics, all in the first forty years of their lives. Although amazing, this is not unusual. Many mathematicians do their finest work while young, but dwindle off, as they get older. The award’s founder, John Charles Fields, wanted to stimulate high achieving mathematicians during their youth to allow them to continue performing at their highest potential well into old age. So, he set an age limit for nominees to ensure that those receiving recognition would have time to take advantage of the benefits of its honor.

This last August, the International Mathematical Union once again announced their selections for this most sought after honor at the International Congress of Mathematicians. The maximum of four individuals collected the golden medal adorned with the face of Archimedes and the US$15,000 monetary award this year in Hyderabad, the major Indian information technology hub located in the northwestern state of Andhra Pradesh. The location of the award changes every four years, but the prestige and honor it bestows upon the recipients do not.

Elon Lindenstrauss, following in his mathematical father’s footsteps, became the first Israeli presented with the Fields Medal. He made his start at the Hebrew University, completing his PhD titled, "Entropy properties of dynamical systems" in 1999. Elon barely snuck in under the age limit, having just turned forty on August 1st. His research has taken him to the prestigious Institute for Advanced Study at Princeton in New Jersey, where Einstein came to the United States to work on his unified field theory. In addition, he has taught at Stanford, Princeton, and most recently his alma mater, Hebrew University. As a number theoretician, Lindenstrauss spends his time considering how dynamic systems behave, especially when left to run for a long period of time. This is otherwise known as ergodic theory, and his work has led to breakthroughs in how to formulate and apply probabilities.

Another researcher from the Princeton Institute of Advanced Study born in Hanoi, Vietnam, Ngô Bo Châu, had one of the “Top 10 Scientific Discoveries of 2009” named by Time Magazine for proving the thirty-year-old “Fundamental Lemma” connecting number theory and group theory. Proving connections between branches of mathematics is sort of like finding the Holy Grail because it verifies decades of work by hundreds of mathematicians based on certain assumptions and is often rewarded with the Fields Medal. Robert Langland in the 1960’s created what has since been termed “Langlands Program” to outline where researchers should focus for making these connections. Ngô’s proof is a breakthrough for the program. Ngô also holds French citizenship, where he did his university studies, and has transitioned from the Institute of Advanced Study to the University of Chicago just this month.

Another winner about to turn forty, Stanislav Smirnov from Russia, won the award for his research on statistical physics, particularly for proofs exploiting the symmetry of finite, triangular lattice models used in theoretical physics to describe percolation processes such as the spreading of a disease. He has worked in the Mathematical Physics and Probability Group at the University of Geneva in Switzerland since 2003 and received his PhD titled, “Spectral Analysis of Julia Sets” from the California Institute of Technology in 1996. Smirnov was also the winner of the 2001 Clay Research Award and is one of the world’s foremost experts in the field of complex dynamics.

French mathematician, Cédric Villani, is the director of the Institut Henri Poincaré in Paris. He was awarded the Fields Medal for creating bridges between mathematics and physics with his research on statistical mechanics, kinetic theory and entropy, the overall amount of disorder existing in a closed system. His contributions on the Boltzmann equation, Landau damping, and optimal transport theory have helped significantly advance studies into partial differential equations and mathematical physics. He has been well recognized as of late, being awarded the European Mathematical Society Prize, the Fermat Prize, and the Henri Poincaré Prize all since 2008.

The detailed specializations of all these winners take years to accumulate. In modern mathematics, work is not always on the shoulders of giants in the field, but comes through intense collaboration across the globe. Having the Fields Medal as a carrot dangling for young and passionate mathematicians is just the ticket for building a new generation to take over where the last left off. Whether it is in number theory, statistical physics, or elsewhere, the contributions by previous Fields Medalalists have broadened and strengthened the foundation of all the applied sciences and helped shed light on solutions to problems that seemed insurmountable. Let us hope that this year’s excellent group uses this honor for even more leaps forward.

Sources:

http://www.mathunion.org/general/prizes/fields/details/

http://math.univ-lyon1.fr/homes-www/villani/

http://www.claymath.org/research_award/Smirnov/

http://www.claymath.org/research_award/Laumon-Ngo/

http://www.claymath.org/fas/research_fellows/Lindenstrauss/