Edward Witten (born August 26, 1951) is an American mathematical physicist, Fields Medalist, and professor at the Institute for Advanced Study. He is one of the world’s leading researchers in string theory (as the founder of M-theory) and quantum field theory. Witten is widely admired among his peers. This includes the renown 20th century geometer, Sir Michael Atiyah, who said of Witten, “Although he is definitely a physicist, his command of mathematics is rivaled by few mathematicians… Time and time again he has surprised the mathematical community by his brilliant application of physical insight leading to new and deep mathematical theorems… he has made a profound impact on contemporary mathematics. In his hands physics is once again providing a rich source of inspiration and insight in mathematics.” He also appeared in the list of TIME magazine’s 100 most influential people of 2004. He was mentioned in a 1999 episode of the cartoon Futurama. Witten has the highest h-index of any living physicist. he h-index is an index suggested in 2005 by Jorge E. Hirsch of the University of California, San Diego to quantify the scientific productivity of physicists and other scientists based on their publication record. The index is calculated based on the distribution of citations received by a given researcher’s publications. Hirsch writes: A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np – h) papers have at most h citations each. In other words, a scholar with an index of h has published h papers with at least h citations each.The index is designed to improve upon simple measures such as the total number of citations or publications, to distinguish truly influential physicists from those who simply publish many papers; the index is also less sensitive to single papers that have many citations. The index works best for comparing scientists working in the same field; citation conventions differ among different fields. The h-index is calculable using free Internet databases and serves as an alternative to more traditional impact factor metrics which are available for a fee. Because only the most highly cited articles contribute to the h-index, its determination is a speedy process. Hirsch has demonstrated that h has high predictive value for whether or not a scientist has won honors like National Academy membership or the Nobel Prize. In physics, a moderately productive scientist should have an h equal to the number of years of service while biomedical scientists tend to have higher values. Criticism
It is not difficult to come up with situations in which h may provide misleading information about a scientist’s output. Most importantly the fact that h is bounded by the total number of publications means that scientists with a short career are at an inherent disadvantage, regardless of the importance of their discoveries. For example, Evariste Galois’ h-index is 2, and will remain so forever. Had Albert Einstein died in early 1906, his h index would be stuck at 4 or 5, despite him being widely acknowledged as one the greatest physicists ever to have lived. Proposals to modify the h-index in order to emphasize different features have been made. Based on the SPIRES HEP Database (Particle and High energy Physics, As of August 2005,):

Grigory Perelman, the Russian who seems to have solved one of the hardest problems in mathematics, the Poincaré conjecture, has declined one of the discipline’s top awards. Dr Perelman was to have been presented with the prestigious Fields Medal by King Juan Carlos of Spain, at a ceremony in Madrid on Tuesday. There had been considerable speculation that Grigory “Grisha” Perelman would decline the award. The Russian has been described as an “unconventional” and “reclusive” genius who spurns self-promotion. The Fields Medals are commonly regarded as mathematics’ closest analog to the Nobel Prize (which does not exist in mathematics), and are awarded every four years by the International Mathematical Union to one or more outstanding researchers. “Fields Medals” are more properly known by their official name, “International medals for outstanding discoveries in mathematics.”
He is possibly the cleverest person on the planet: an enigmatic and reclusive genius who shocked the academic world with his claim to have solved one of the hardest problems in maths. He is tipped to win a “maths Nobel” for his work on possible shapes of the universe. But rumours are rife that the brilliant Russian mathematician will spurn the greatest accolade his peers can bestow. Since Grigory “Grisha” Perelman revealed his solution in 2002 to a century-old maths problem, it has been subjected to unparalleled scrutiny by the best academic minds. But no one has been able to find a mistake and there is a growing consensus that he has cracked the problem. Little is known about Dr Perelman, who refuses to talk to the media. He was born on June 13 1966 and his prodigious talent led to his early enrolment at a St Petersburg school specialising in advanced mathematics and physics. At the age of 16, he won a gold medal with a perfect score at the 1982 International Mathematical Olympiad, a competition for gifted schoolchildren. After receiving his PhD from the St Petersburg State University, he worked at the Steklov Institute of Mathematics before moving to the US in the late 80s to take posts at various universities. He returned to the Steklov about 10 years ago to work on his proof of the universe’s shape. The maths world was set humming in 2002 by the first instalment of his ground-breaking work on the problem which was set out by the French mathematician, physicist and philosopher Jules Henri Poincaré in 1904. The conjecture, which is difficult for most non-mathematicians even to understand, exercised some of the greatest minds of the 20th century.

It concerns the geometry of multidimensional spaces and is key to the field of topology. Dr Perelman claims to have solved a more general version of the problem called Thurston’s geometrisation conjecture, of which the Poincaré conjecture is a special case. “It’s a central problem both in maths and physics because it seeks to understand what the shape of the universe can be,” said Marcus Du Sautoy at Oxford University, who will be giving this year’s Royal Institution Christmas Lectures. “It is very tricky to pin down. A lot of people have announced false proofs of this thing.” The obsession with the problem, shared by several great mathematicians, has been dubbed Poincaritis. But Dr Perelman seems to have succeeded where so many failed. “I think for many months or even years now people have been saying they were convinced by the argument,” said Nigel Hitchin, professor of mathematics at Oxford University. “I think it’s a done deal.”

In mathematics, the Poincaré conjecture is a conjecture about the characterization of the three-dimensional sphere amongst three-dimensional manifolds. Loosely speaking, the conjecture surmises that if a closed three-dimensional manifold is sufficiently like a sphere in that each loop in the manifold can be tightened to a point, then it is really just a three-dimensional sphere. The analogous result has been known to be true in higher dimensions for some time. The Poincaré conjecture is widely considered one of the most important questions in topology. It is one of the seven Millennium Prize Problems for which the Clay Mathematics Institute is offering a $1,000,000 prize for a correct solution. After nearly a century of effort by mathematicians all over the world, a series of papers made available in 2002 and 2003 by Grigori Perelman, following the program of Richard Hamilton, produced an outline for a solution. Following Perelman’s work, several groups of mathematicians have produced works filling in the details for the full proof, though review by the mathematics community is ongoing.

Grigori Perelman proved the Poincare conjecture and then refused a million dollar prize (the Millennium Prize). He is the only mathematician who has declined the Fields medal.

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