One of the most famous of all unsolved problems in Diophantine theory, the so-called Hilbert's tenth problem, was brilliantly solved in 1970 by Yu. V. Matijasevic, a 22-year-old graduate student at the University of Leningrad. In 1900 the great German mathematician David Hilbert compiled a list of 23 outstanding unsolved problems that he hoped would be solved during the twentieth century. Problem 10 was to find a general algorithm that would decide whether any given polynomial Diophantine equation, with integer coefficients, has a solution in integers.

Matijasevic proved that there is no such algorithm. In other words, he "solved" Hilbert's tenth problem by proving it had no solution. The Fibonacci number sequence plays a key role in his proof.

For details see "Hilbert's Tenth Problem," by Martin Davis and Reuben Hersh in Scientific American, November 1973, pages 84-91, and "Hilbert's Tenth Problem is Unsolvable," by Martin Davis in The American Mathematical Monthly, Volume 80, March 1973, pages 233-269.

0 0

Post a comment