Hilbert's eighth problem
Encyclopedia
Hilbert's eighth problem is one of David Hilbert
's list of open mathematical problems posed in 1900. It concerns number theory
, and in particular the Riemann hypothesis
, although it is also concerned with the Goldbach Conjecture. The problem as stated asked for more work on the distribution of primes and generalizations of Riemann hypothesis to other rings where prime ideal
s take the place of primes. This problem has yet to be resolved.
David Hilbert
David Hilbert was a German mathematician. He is recognized as one of the most influential and universal mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many areas, including invariant theory and the axiomatization of...
's list of open mathematical problems posed in 1900. It concerns number theory
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, and in particular the Riemann hypothesis
Riemann hypothesis
In mathematics, the Riemann hypothesis, proposed by , is a conjecture about the location of the zeros of the Riemann zeta function which states that all non-trivial zeros have real part 1/2...
, although it is also concerned with the Goldbach Conjecture. The problem as stated asked for more work on the distribution of primes and generalizations of Riemann hypothesis to other rings where prime ideal
Prime ideal
In algebra , a prime ideal is a subset of a ring which shares many important properties of a prime number in the ring of integers...
s take the place of primes. This problem has yet to be resolved.