126 // Mathematical Prizes

What is the area of the lattice polygon in the second diagram?

Find the area.

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Answer on page 279

Mathematical Prizes There is no Nobel Prize in mathematics, but there are several equally prestigious prizes and a vast range of smaller ones, among them:

Fields Medal The Fields Medal was instituted by the Canadian mathematician John Charles Fields and was first awarded in 1936. Every four years the International Mathematical Union selects for the award up to four of the world's leading research mathematicians, who must be under 40 years old. The prize consists of a gold medal and a small sum of money ­ currently around $13,500 ­ but is considered equivalent to a Nobel Prize in prestige.

Abel Prize In 2001 the Norwegian government commemorated the 200th anniversary of the birth of Niels Henrik Abel ­ one of the all-time greats of mathematics ­ with a new prize. Each year, one or more mathematicians share a prize in the region of $1,000,000, which is comparable to the sum that Nobel Prize winners receive. The King of Norway presents the award at a special ceremony. Mathematical Prizes // 127

Shaw Prize Sir Run Run Shaw, a prominent figure in Hong Kong's media and a long-standing philanthropist, established an annual prize for three areas of science: astronomy, life sciences and medicine, and mathematics. The total value awarded each year is $1,000,000, and there is also a medal. The first Shaw Prize was awarded in 2002.

Clay Millennium Prizes The Clay Mathematics Institute in Cambridge, Massachusetts, founded by Boston businessman Landon T. Clay and Lavinia D. Clay, offers seven prizes, each of $1,000,000, for the definitive solution of seven major open problems. These `Millennium Prize Problems' were selected to represent some of the biggest challenges facing mathematicians. For the record, they are:

. The Birch and Swinnerton-Dyer Conjecture in algebraic

number theory. . The Hodge Conjecture in algebraic geometry. . The existence of solutions, valid for all time, to the Navier­

Stokes equations of fluid dynamics. . The P = NP? problem in computer science. . The Poincare Conjecture in topology.

´ . The Riemann Hypothesis in complex analysis and the theory

of prime numbers. . The mass gap hypothesis and associated issues for the Yang­

Mills equations in quantum field theory.

None of the prizes has yet been awarded, but the Poincare´ Conjecture has now been proved. The main breakthrough was made by Grigori Perelman, and many details were clarified by other mathematicians. For details of the seven problems, see www.claymath.org/millennium/

King Faisal International Prize Between 1977 and 1982 the King Faisal Foundation instituted prizes for service to Islam, Islamic studies, Arabic literature, medicine and science. The science prize is open to, and has been

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