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With hindsight, some of my past rejections have become amusing. With a coauthor, I once almost solved a conjecture, establishing the result with an "epsilon loss" in a key parameter. We submitted to a highly reputable journal, but it was rejected on the grounds that it did not resolve the full conjecture. So we submitted elsewhere, and the paper was accepted.

The following year, we managed to finally prove the full conjecture without the epsilon loss, and decided to try submitting to the highly reputable journal again. This time, the paper was rejected for only being an epsilon improvement over the previous literature!

(This paper was also submitted elsewhere, and accepted; and I have subsequently published in that highly selective journal since. Being an editor myself, and having had to decline some decent submissions for a variety of reasons, I find it best not to take these sorts of rejections personally, and move on to other journals, of course after revising the paper to address any issues brought up by the rejection.) (2/2)

@tao @gregeganSF OK, even I am mathematically literate enough to emit a sensible chuckle at this outcome.

@wa No; and given the quite slow timecycle of the journal submission process (with months between referee reports, and weeks between editorial board discussions, and most of the workflow being done via email and editorial platforms, when the editors have some free time to devote to the task) I doubt that the process is influenced that much by heated emotion.

However, it is not uncommon for an editor or referee to recuse from a submission in which they have a personal or professional relationship with the authors that could compromise their objectivity. (For similar reasons, it is generally not a good idea for an author to submit to an editor that is a close personal friend or professional colleague, precisely because that friend may have to recuse and hand the paper off to a different editor.)

@TonyVladusich Yes, this has happened several times. In particular, there are several times when I was asked to chair a committee to produce a report on a topic which was important, and relevant to my interests, but which I had no experience speaking with authority on. But the other committee members collectively had much greater experience than I, and I eventually realized that the role of a chair is not to produce the majority of the content, but rather to create an environment and structure in which the other members are eager to contribute their own thoughts and ideas.

@tao

Did you ever feel similarly in your mathematical studies?

For example, when entering a new subfield did you remain confident that, while you may not have expert domain knowledge, you had the requisite skills and processes in place to tackle the new domain?

@TonyVladusich Yes, this has happened also, particularly when venturing in fields that heavily involve either algebra or topology, which have always been my weakest fields of mathematics. In many cases, it is my coauthors that supply the needed expertise in these areas (and such collaborations end up being a very valuable learning experience for me); in other cases I have leaned on consulting with some old friends (going all the way back to grad school in some cases) to get me up to speed on the basics. Online resources such as Wikipedia, MathOverflow, and more recently large language models are also quite good at getting key background information (such as what the correct notation is for a concept, why it is studied, and what are the standard references), though of course in all cases one should view these resources as a starting point for one's knowledge, rather than as the definitive answer, and one should try to independently verify the information from those sources as much as possible.

@TomL @tao
An easy example: Suppose in the year 3000, nobody has friends, except Santa Claus. So everybody except Santa has 1 friend, and he has millions. So the average number of friends of your friends is hugely larger than than your own number of friends.

@rustoleumlove @tao This is a great article! We have so much of this ”scientists as gods”, that somehow their popular status is what gives their work relevance, way of thinking around these days.

This inherently hierarchic worldview is poisoning thinking about the sciences, because so many alternative health and ”bro scientists” never understood the scientific method to begin with, and with their popular success it has been also spreading their attitudes.