As I learned years ago as a graduate student, if you don’t publish in some form, you won’t get far as an academic. My own graduate students typically know very little about how academic publishing works when they begin their studies. The purpose of this post is to give some pointers to those just starting out on their journey of publishing in academic journals.

Mathematicians publish their work predominantly in peer-reviewed journals, with some papers appearing in refereed conference proceedings. There are thousands of such outlets, and many focus on some specific topic or field. Journals like *Transactions of the American Mathematical Society* or *Annals of Mathematics* are generalist publications, publishing from any area of mathematics. Active mathematicians often publish in specialist journals within their own field.

The number of publications in mathematics is staggering. Mathematical Reviews (MR) adds over 70,000 items to their database each year. MR lists 1.6 million authored items by about 337,000 different authors.

My work is graph theory and combinatorics. As such, I publish in journals in that area. A few journals are harder to publish in than others, and there is pecking order that is not scientific. For instance, a top journal like *Journal of Combinatorial Theory, Series B* accepts only a handful of submissions. Impact factor can play a role in the pecking order, depending on your discipline.

The process of submitting a paper to a journal is relatively straightforward. You submit your original work to one journal. After submission, the editor assigns anonymous referees to write reviews. The review time varies drastically. Journals may have strict guidelines for reviewers that see reviews turned around in two months. Most mathematics journals allow for longer review times, largely owing to the technical nature of the work submitted.

If you plan on submitting to a journal, be prepared to be rejected. It is just a fact of life. Rejections can be curt or lengthy. Reviewers might think the results or not deep enough, not right for the journal, or the paper is too poorly written to be published. Read the reviews carefully, and adjust the paper as needed. If the paper is salvageable, then resubmit to another journal.

My journal horror story was waiting three years for a review on a ten page paper. The result was out so long, a well-known mathematician proved the same result independently! Fortunately for us, he was amiable, and we added him as a co-author. The paper was ultimately published, but the four-year process just felt too long. Other academics have told me stories of waiting years and, after inquiring with the editor, their submission was never received. With on-line submission systems generating automatic replies, this happens less often but it still can happen.

I do recommend to my post-docs and students to publish their best work and to publish frequently. However, you must review your own work many, many times before submission. In mathematics, one error can fry the whole paper. Colleagues I know are happy to publish one paper a year. Others shoot for 10+ papers. I say just do what you find comfortable.

In the end, quality matters more than quantity.

Anthony Bonato