Dear Early Career

If I give a talk on work that I haven’t yet finished, should I worry that someone might use my ideas to prove my result before I do?

—Concerned

Dear Concerned,

It’s good to hear you have some research progress you are excited about! If this work is joint with anyone else, then certainly ask them for their opinion—this is a slightly touchy subject. It is also likely that attitudes toward giving talks before a preprint is available differ from subfield to subfield, and so consulting your mentors is advisable.

With those caveats out of the way, presenting results before the preprint is available is done pretty routinely in mathematics. It can be very positive to create some buzz for a result or let people know it is coming, and as an early career researcher every opportunity to present is valuable.

It seems a little unlikely to us that someone in the audience would merely copy your proof (and if they did, then your public talk on the topic would likely establish priority from the perspective of the community), but it is plausible that someone could find an extension of it, or find a simpler proof, in which case your forthcoming paper might gain an author. If that possibility does not appeal to you at all, then maybe it is best to wait for the preprint to appear. (A more unlikely outcome that cannot be ruled out is someone finding a simpler proof and submitting it immediately by themselves. While we think that one could still publish the original proof in these circumstances, we have to admit that if this had ever happened to us then this answer would be very different.)

We may be a particularly cautious editorial team, but in the absence of a preprint, our main question to ourselves in this circumstance is this: Have we really proved the result, or are there substantial issues that remain? It can be a bit problematic if one presents a forthcoming result and no preprint ever appears, as interested researchers in your field would be left in limbo. Therefore, we would recommend that before presenting you have a detailed account of the proofs that could be circulated (this is a long way from a finished preprint, but could also help establish priority if has been circulated to a few trusted people prior to your talk). Furthermore, if your work solves a problem with some reputation, then having some discussions with mentors and experts would also be a great idea before going full steam into a talk.

In our experience, the opportunity that comes from presenting your ideas outweighs the risks of people acting in an unprofessional manner.

—Early Career editors

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