Hilbert's eighth problem [SEP] named after
Hilbert's eighth problem
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 ideals take the place of primes. This problem has yet to be resolved.
Subtopics.
Subtopics Riemann hypothesis and generalizations.
Hilbert calls for a solution to
set of whole numbers but smaller than the set of all decimals". Cohen found that there existed two equally consistent mathematical worlds. In one world the Hypothesis was true and there did not exist such a set. Yet there existed a mutually exclusive but equally consistent mathematical proof that Hypothesis was false and there was such a set. Cohen would subsequently work on Hilbert's eighth problem, the Riemann hypothesis, although without the success of his earlier work.
"To Infinity and Beyond" Hilbert's tenth problem.
Hilbert's tenth problem