In 2013, Annals received nine hundred and fifteen papers and accepted thirty-seven. The wait between acceptance and publication is typically around a year. When a paper arrives, “it is read quickly, for worthiness,” Nicholas Katz, the Princeton professor who is the journal’s editor, told me, and then there is a deep reading that can take months. “The paper I can’t evaluate off the top of my head, my role is to know whom to ask,” Katz said. “In this case, the person wrote back pretty quickly to say, ‘If this is correct, it’s really fantastic. But you should be careful. This guy posted a paper once, and it was wrong. He never published it, but he didn’t take it down, either.’" From "The Pursuit of Beauty: Yitang Zhang solves a pure-math mystery." By Alec Wilkinson-New Yorker. [Emphasis added--ES]
After my friend, M. Ali Khan, the mathematical-economist, called my attention to this piece during his trip to Tokyo, I saw it posted and discussed all over the internet among fellow academics. Evidently, narratives about a lone, non-bragging (male?) genius that while working in obscurity, even at times outside academia, gets a big, non-applicable question right resonates with our desires for purity, beauty, and truth. Wilkinson's piece is full of comments by fellow mathematicians who comment on the fact that Dr. Zhang's public disposition does not conform to academic self-promotion that is the norm.
As the quoted passage at the top of the post reveals, the odds of getting a paper published in the top mathematics journal are very low. (This is also the case in philosophy.) Not unlike the once too common norm among philosophy journals, the referees apparently knew the identity of the author of the paper. Moreover, this identity was not sterling, but rather damaged goods. It is to the credit of the journal's editors and referees that they were willing to look past their partially informed bias here. Perhaps, it's their sense of fairness, or, perhaps, the expected pay-off ("really fantastic") and initial plausibility made it worth everybody's effort to dig deeper into a paper by a lowly regarded peer.
It must be a well established fact that first impressions matter a lot in most psychological judgments. Among professional philosophers it used to be the case, and presumably still is the case, that making mistakes (or, worse, blunders) can mark one as untalented/unskilled and unfit for professional philosophy. Among the highest virtues, if not the highest (after clarity?), prized by analytical philosopy is carefulness. This virtue -- and it has a lot in its favor -- has a status quo bias built into it because it discourages experimentation and boldness. For to be bold means to work on topics where the side-constraints that can prevent obvious-to-others' mistakes are less evidently available (because not as well explored). Of course, once one is senior/established in the field people are more forgiving of one's mistakes. (Life really is unfair that way.) But one rarely gets established in fields with advanced intellectual division of labor by being very bold in the first place.
Evidently "he left it [the posted paper--ES] up because he hopes to correct it." If we take this at face value, it seems the paper was left as a kind of externalized pre-commitment to keep working on a project that had run into barriers. To have something incomplete, or something falling short of professional standards, visible to the world can be a way to motivate oneself to complete or purify it; it can also be a way of quietly asking for help on the project from one's peers. But...in a zero-sum, almost unforgiving, competitive environment it is also a way of risking not getting an audience at all.