Was a PhD necessary to solve outstanding math problems?

Greater Wrong:

This is my second post investigating whether a terminal degree is practically ~necessary for groundbreaking scientific work of the 20th century.

Mathematics seems like a great field for outsiders to accomplish groundbreaking work. In contrast to other fields, many of its open problems can be precisely articulated well in advance. It requires no expensive equipment beyond computing power, and a proof is a proof is a proof.

Unlike awards like the Nobel Prize or Fields Medal, and unlike grants, a simple list of open problems established in advance seems immune to credentialism. It’s a form of pre-registration of what problems are considered important. Wikipedia has a list of 81 open problems solved since 1995. ~146 mathematicians were involved in solving them (note: I didn’t check for different people with the same last name). I’m going to randomly choose 30 mathematicians, and determine whether they got a PhD on or prior to the year of their discovery.

The categories will be No PhD, Partial PhD, PhD, evaluated in the year they solved the problem. In my Boyle’s desiderata post, 215 (13%) of the inventors had no PhD. I’d expect mathematics to exceed that percentage.