Hilbert's seventh problem [SEP] named after
Hilbert's seventh problem
Hilbert's seventh problem is one of David Hilbert's list of open mathematical problems posed in 1900. It concerns the irrationality and transcendence of certain numbers ("Irrationalität und Transzendenz bestimmter Zahlen").
Statement of the problem.
Two specific equivalent questions are asked:
1. In an isosceles triangle, if the ratio of the base angle to the angle at the vertex is algebraic but not rational, is then the ratio between base and side always transcendental?
2. Is formula_1
, B," and "N" if and only if "N" is a positive integer and A=B is definable in the arithmetic of rationals." 
Mathematical contributions Hilbert's Tenth Problem.
Hilbert's tenth problem asks for an algorithm to determine whether a Diophantine equation has any solutions in integers. Robinson began exploring methods for this problem in 1948 while at the RAND Corporation. Her work regarding Diophantine representation for exponentiation and her method of using Pell's equation led to the J.R. hypothesis (named after Robinson)