Why do pure mathematicians tend to start publishing good papers a bit late?

Question

Why is it so common for pure mathematicians to start publishing "good" quality paper a bit late? Maybe towards the end of PhD or start of Post-doc. Whereas in some fields people start publishing research papers as early as in their masters.

I know there are some undergrad research programs, for e.g.- REU, but only in some cases do they get published; but not in some good quality journals. Most of the times they maybe just arxived or in some cases not even that.

I know some people, from different fields, who had 2 or 3 publications in their masters itself, while some of them are in their 2nd/3rd year of PhD and already have around 10 publications.

Maybe such a thing is also possible in mathematics, but there must be some good reason why mathematicians or graduate student, along with their supervisor, agree to publish good results in good journals, a bit late.

Answer 1

One fundamental distinction between mathematics and more-obviously experimental scientific and engineering disciplines is that, in math, there is no analogue of "reporting on several months of experiments". There's no analogue of "keeping experiments running, and whatever turns out, is a paper".

That is, while there is in fact a large experimental aspect to mathematics, it is not the same sense of "experiment" as in other sciences, and the conventions are such that this does not generate papers.

Yes, the ambient pressures do push PhD students in math to try to arrange at least one or two publications prior to PhD completion. Not entirely a bad thing, but definitely not a convivial atmosphere.

Edit: and it may be worthwhile to observe that most of prior mathematics does not become obsolete or wrong due to new discoveries, unlike sometimes happens, and is always possible, apparently, in more experimental sciences/etc. Thus, mathematicians cannot too much disregard prior work... of which there is a great deal. Many excellent (and not-so-excellent) results known prior to 1900 are rediscovered on a regular basis, and do indeed show evidence of insight!, but are not "publishable".

This "problem" is the reason I tell myself, and my research students, to not even think in terms of "verifiable novelty", because it is just a mess, for mathematics. Better to follow a good, natural line of inquiry, and leave the appraisal of "novelty" till later. (It is admittedly hard to ignore academic-administrative pressures... and, yes, this is corrupting academic mathematics, among other disciplines...)

Answer 2

A key difference between pure math and many other areas is that there are typically only 2, maybe 3 authors. The papers you cite with Masters students are often in larger collaborations wherein the Masters students do some of the menial tasks: data collection, data analysis, but not necessarily theory development that require more years of training. In pure math, these sorts of papers are quite rare: You have to understand the theory if you're writing with just one or two co-authors, because otherwise there is nothing for you to contribute. As a consequence, there is just no opportunity for students in pure math to be part of authors earlier in their career.

Answer 3

The other answers do a great job explaining why math is quite different from experimental sciences. But I don't think this is the full answer, as computer science, statistics, and theoretical physics are "mathematical sciences" and it's less clear why they should be any different than math. In fields where there's substantial overlap (e.g. there are people working on tensor categories in math and in condensed matter physics) I think there's also different publishing conventions in terms of what level of originality is expected of publications. For example, working out an example that any expert could do and writing it up is much more acceptable in physics than it is in math. There's advantages and disadvantages to both approaches (in particular, math ends up with far too much "folklore" that is hard to learn without social connections to experts), and I think a lot of this difference is cultural. For example, the culture in math departments is that the main goal of a PhD is to have a substantial result, while in CS the expectation is that you will have multiple less substantial papers. There's similar cultural differences within mathematics, e.g. combinatorics is more amenable to short papers and homotopy theory or Langlands number theory are more amenable to people who publish more rarely in larger papers. I think these cultural differences (like many inter-departmental cultural differences) are going away as there is increased pressure for mathematicians to publish more and publish earlier even if that means not doing as substantial work.

Finally, I should point out that most of the humanities is even more extreme than math in terms of focusing on a large substantial work, and the expectation is that your PhD should be a publishable book which you will still be editing several years after graduation. Again, I'm not saying this means math is "better" than other mathematical sciences, or that history is "better" than math, there's advantages and disadvantages to both approaches.