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Nowadays, getting reviewers is a challenging task for many pure mathematics journals. How would an editor be able to find a reviewer for a very new theory that nobody has worked on yet?

If the author is a big name in some field, an editor might consider doing the hard work in searching for referees and the referees will also agree to reviewing for them.

If it is from a not-so-popular author on the other hand, it might have a high chance of getting desk rejected. In such cases, how can we expect new theories to be developed with the current system?

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    If the people with a new theory can't explain it to others in their general area of research, what's the use in publishing it?
    – Bryan Krause ♦
    Mar 10 at 20:16
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    To be more explicit, if you "develop a new theory", then it's your job to convince the reader that it is an interesting and useful theory. People don't just "develop new theories" for the hell of it, they do it with a particular goal. For example, if you write hundreds of pages developing "inter-universal Teichmüller theory" because you think it's a neat generalization of Teichmüller theory (whatever that is), then it's perfectly reasonable that no-one would want to referee it. If you do it and promise that the payoff is a proof of the abc-conjecture, then it's a different story entirely.
    – Adam Přenosil
    Mar 10 at 20:20
  • @BryanKrause I am not telling that it can't be explained to others. But to verify it, one might require say for example experts from many fields then it would be a tough task to get those many experts to review it. So, one can simply put it in arxiv, I guess. Because the theory could be useful later on, who knows? Also to reply to Adam, if we have to convince readers at the initial stage itself, isn't it bad? Because nobody would try to develop new things and would work on current popular topics only
    – Hap
    Mar 10 at 20:24
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    "The theory could be useful later on, who knows" is not on its own a good reason to publish or read a paper. "If we have to convince readers at the initial stage itself, isn't it bad?" No, this entirely normal. No-one has any obligation to read your papers, or listen to your talks. "Nobody would try to develop new things and would work on current popular topics only." But people do in fact develop new theories and other researchers do invest the time in learning them, provided that they can expect some payoff from this (see also my example of inter-universal Teichmüller theory).
    – Adam Přenosil
    Mar 10 at 20:30
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    @AdamPřenosil: In fact, IUTT has very little to do with the original Teichmuller theory. It is not at all a generalization of the latter.
    – Moishe Kohan
    Mar 11 at 4:02

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In pure mathematics, few new ideas are so unconnected with the past that there aren't people available. The new ideas normally grow out of existing mathematical threads and theories and there are probably experts available that are "close enough" to get the job done.

Occasionally something really new pops up. Not-Standard Analysis (epsilons exist as values) was once (previous generation) thought very radical. It was despised by many for a while, but it turns out to be just a different axiomatic basis on which to build - so, not so different after all. The underlying logical process is the same.

But some new things get a lot of pushback initially and it takes a while for the ideas of the inner core of researchers to reach a broader audience. But it isn't lack of expertise that causes this pushback.

If a paper cites others, an editor can look to those authors, perhaps. If it cites none then it is a harder problem, but might be solved by just guessing based on their own experience. And a reviewer who doesn't feel competent might suggest another person who might be a better choice.

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    (+1) One can flip through the entire metaphorical rolodex of the most startling theoretical leaps in 20th century pure mathematics, and every last one of them, no matter how formidably high-tech, interfaces deeply with some body of already existing mathematics whose experts were competent to review the work and then digest it. Not even Grothendieck worked in a vacuum! [Non-standard analysis, for instance, had an initial audience from set theory and then from functional analysis.]
    – Branimir Ćaćić
    Mar 11 at 17:58
  • Sorry if this is a dumb question, but is this what you mean by "epsilons exist as values"?
    – jtb
    Mar 12 at 4:52
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    @JoshBone No, they mean infinitesimals.
    – Tassle
    Mar 12 at 8:18

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