In 1801, Gauss proposed three conjectures about the class numbers of quadratic fields. Two of these conjectures have been proven. However, the conjecture that there are infinitely many real quadratic fields of class number 1, still remains open today. In this talk, we will explore some progress that has been made toward the understanding of this conjecture, including a series of more recent conjectures, brought about by the Cohen-Lenstra heuristics.
Classy!