[joe_the_user]

Yes, Ramanujan just floated around dealing with whatever number theories inspired him, sometimes in a nearly mystical way so he's not a good example.

Andrew Wiles is a better example, since he hit in plain sight working on Fermat's Last Theorem.

"He dedicated all of his research time to this problem for over six years in near-total secrecy, covering up his efforts by releasing prior work in small segments as separate papers and confiding only in his wife."

https://en.wikipedia.org/wiki/Andrew_Wiles

[Ma8ee]

Exactly. He proves the author's very well. Wiles was tenured, had published in the field already, and made sure that he could continue publishing while working on the Big Problem.

[nwjtkjn]

Tenured at Princeton, had already solved some fairly big problems in the field, and it helped that FLT had recently been "reduced" to proving a conjecture about elliptic curves which were already very much in Wiles's wheelhouse.

Not to take away from his achievement, but I think it is not stressed enough how much the proof depends on work from previous decades that a priori had nothing to do with Fermat.

[glaberficken]

Note that with Andrew Wiles all the secrecy and seclusion almost exploded on his face. When he first came public with the Fermat proof someone found a flaw in it within 2 months.

It took another 2 years (he was ready to give up by then) to finally come up with a "fix" for the flaw that had been found.

So in the end he was only successful after exposing it to the public for scrutiny and breaking down the problem into something smaller.

[joe_the_user]

Sure but if Wiles hadn't been secret, he'd be making progress reports all along and plausibly the person who made the fix would be the one who credited with the proof.

It's kind of shame that the quest for credit works this way, secrecy has all sorts of costs but in this instance it clearly had benefits too.