Noam Elkies

Noam David Elkies ( born August 25, 1966 in New York City ) is an American mathematician who deals with number theory and combinatorics.

Life

Elkies won more than undergraduate student ( undergraduate ) three times the Putnam Fellowship, first in 1982 with only 16 years. He received his PhD in 1987 at Harvard University with Barry Mazur and Benedict Gross with Super singular primes of a givenName elliptic curve over a number field. In 1990 he became an assistant professor at Harvard, where in 1993 he received a full professorship ( at age 26, which he set the previous record of the lawyer Alan Dershowitz ).

Mathematics

In his thesis he proved that there is any elliptic curve E over the rationals infinitely many supersingular primes ( " supersingular " means in this case that the number of points of E modulo p considered, ie over the finite field, congruent to 1 mod p ).

In 1988 he gave a counterexample to a conjecture of Euler about power sums of integers. This claimed that if

Needs to be. Lander and Parkin had in 1966 given a counterexample for k = 5, Elkies gave a for k = 4 ( In 1988, Roger Frye with computer methods based on Elkies work, a smaller solution ).

About the same time, he developed Shioda Tetsuji 1990, the theory of Mordell -Weil grating that handles the Mordell -Weil group (group of rational points on an elliptic curve or abelian variety over a global body ) in a grid.

Elkies also worked on numerical / algorithmic problems in number theory of elliptic curves, especially important for cryptographic applications. With AOL Atkin he improved the algorithm by René Schoof for determining the number of rational points on elliptic curves.

Elkies is a puzzle game fan, and also worked in the field of combinatorial games. He is also known for the discovery of many new interesting configurations in John Conway's game of Life. In the field of combinatorics, he worked among others on grid, sphere packings and codes.

In 1994 he was invited speaker at the International Congress of Mathematicians in Zurich ( Linearized algebra ). In 2004 he was awarded the Levi L. Conant Prize -.

Chess

Elkies is an active composer study and Grand Master in solving chess compositions. He has more than 40 chess studies composed. In 1996 he was World Champion in Tel Aviv in solving chess problems and studies.

The chess tournament he finished his early twenties when he had received about 2260 ELO points, something necessary about the 2200 points for a U.S. champion.

Solution: In order to answer the question below the chart is to educate with a retro analysis, the history of the position shown.

White is in check and apparently it's checkmate. In this case, Black would have won. Since the black pawn in check, while the white king can not escape, this chess can only be countered by hitting the farmer. This farmer, however, could only be captured en passant by the white pawn f5. In this case, Black would be dull and White would have won.

A necessary condition for the en passant - hitting is the double step to beating maker in the immediately preceding train. Because of giving check the g- pawn must have last drawn. The game outcome depends on whether the farmer has moved from g7 to g5 or g6.

This question can be clearly decided by the last train of white is determined.

Music

Elkies composes music and plays the piano since he was three years old. He has focussed on applications of mathematics in music. Some of his pieces were broadcast on radio stations in Israel and the United States.