(As said Russian guy proves, sometimes this heuristic fails; but your prior should be that it's likely correct.)
He had a PhD in math with enough success to be offered faculty positions at Princeton and Stanford.
The fact that he recluded from academic life after that doesn't matter.
There also is the nice example of https://en.wikipedia.org/wiki/Marjorie_Rice
Assuming you mean Ramanujan. Although he was self taught in mathematics and did much of his work outside the university setting, the vast majority of his significant discoveries and publications where made within the academic framework.
Is that a safe assumption, though? Won't it limit the field to people who are happy making a low salary and don't mind teaching?
The field simply has far less low hanging fruit than it did a century, or even a half-century ago. It's not reasonable to expect that a lone genius with little to no academic background in mathematics could resolve a famous open problem through sheer creativity. For literally generations the field's most intelligent researchers have spent their careers chipping away at this problem.