- MODERN NUMBER THEORY 195
other zeros have real part equal to 5. This Riemann hypothesis forms one of the
still-outstanding unsolved problems of modern mathematics, standing alongside the
Goldbach conjecture and a famous conjecture in topology due to Henri Poincare
(1854 -1912). 7 The first two were mentioned by Hubert in his address at the 1900
International Congress of Mathematicians in Paris. Hubert gave the Riemann hy-
pothesis as the eighth of his list of 23 unsolved problems and suggested that solving
it would also solve the Goldbach conjecture. Despite a great many partial results,
the complete problem remains open a century later. A summary of the work on
this problem through the mid-twentieth century can be found in the book by Ed-
wards (1974)- The zeros of æ(æ) are now being computed at a furious rate by the
ZetaGrid project, an Internet-based distributed program linking tens of thousands
of computers, similar to the GIMPS mentioned above (see http://www.zetagrid.net).
Poster of Riemann at the Mathematisches Institut and street
named after him in Gottingen.
1.8. Fermat's last theorem. Work on Fermat's most famous conjecture contin-
ued in the nineteenth century. In 1847 Gabriel Lame (1795-1870), published a
paper in which he claimed to have proved the result. Unfortunately, he assumed
7 This conjecture may now have been solved (see Section 4 of Chapter 12).