Salerno’s Eleven

The SQuaREs team, clockwise from the top: John Voight, Ursula Whitcher, Steven Sperber, and Tyler Kelly.

The SQuaREs team, clockwise from the top: John Voight, Ursula Whitcher, Steven Sperber, and Tyler Kelly.

Collaborating and coauthoring are quite common in math. Most often, however, mathematicians tend to work on their own or with only a few other collaborators. If you check the math arXiv you will notice that most papers have less than four coauthors. For the last year or so I have been working on a research project that, when finished, will have at least six coauthors, which in some ways is very rare. I have recently started calling this my “Ocean’s Eleven” project (and technically, eleven people have been part of the project at one point or another, I counted!), hence the title. Although, to be fair, the masterminds of this project are Ursula Whitcher and Chuck Doran, so it should probably be their eleven…

I have talked about how this project started when I wrote about our first group meeting back in 2013 at the Banff Centre in this blog post. Subsets (and additional members) of that group have met again throughout the last year or so, and I wrote about one other such meeting in the Clay Math Institute in another post. We again met in March in Edmonton, and just last week in Palo Alto for an AIM SQuaREs workshop. Like I said, the project started with an idea of Chuck and Ursula’s, and I was quickly inducted into the group (although I’m pretty sure that, as is common for me, I invited myself to join). But how did it get to be so many of us? I only recently came up with the best analogy for this collaboration, which is the other reason for the title. This is like a good heist movie: you need lots of people because each one brings unique and important skills to the plate. In a heist movie you have the mastermind, a getaway driver, a demolitions expert, a hacker, a safe cracker, an expert thief, some muscle, and so on. In our case, the elaborate heist we are trying to pull off is related to mirror symmetry, a project inspired by string theory that algebraic geometers have worked on, and that we want to study from a more number-theoretic point of view. It comes to reason then that you would need at least a few people from each camp. I especially like to think of myself as the demolitions expert. Because it sounds cool, true, but also because I am not the mastermind, my work is small and detailed (I am computing lots of things), but it is important for the project nonetheless. I don’t know about you, but this analogy really works for me, and highlights that you can have a huge group collaborating in which everyone is contributing something important.

Another place where you might have lots of authors is in science research. I asked my sister, Patricia, who is a biologist, and she says it is very rare to find single-authored papers in her field, and more likely that you would find articles in Nature, Science, and PNAS with anywhere between 12 to 20 authors (a quick look at any of these links will provide several examples). But for those papers you get coauthor credit even if you check someone’s math or help out with the lab work. Not that those are not important contributions, but in general there is a first author who does the bulk of the work, and many people get tacked on at the end that might not have done more than an hour’s worth of work on the project. For that reason, how many papers you publish as a first author (or at least near the beginning) is what “counts”, in terms of getting a job, tenure, or promotion. In math, we list authors alphabetically! Because for the most part, you all worked the same amount (of course, this is not entirely true, but the work is spread more evenly between coauthors). But sometimes it worries me that having lots of coauthors might make it suspicious, and that people may think that some of us are doing more work than others. Since there is no ordering by how much work you put in, there is no way to tell.

These type of papers, although rare, are becoming a lot more common with the rise of collaborative workshops. Things like Arizona Winter School (focused on graduate students), Women in Numbers (focused on, you guessed it, women number theorists), and the Mathematics Research Communities (focused on early career mathematicians), to name a few, have been sources for large collaborations which usually lead to publications. I have heard some people complain about this because of what I mentioned above, namely that there are a lot of young mathematicians with large collaborative publications and it is hard to see how much they contributed to them. Especially since, as young mathematicians, they have yet to prove their mathematical worth, so to speak. On the other hand, I think it is great for these to be some of your first publications (as one of mine was), provided you also publish some things on your own and find smaller and more focused collaborations.

At any rate, the people in my group are also very nice and very fun, so it’s been a blast to have a reason to spend time working with them on really cool math problems. And I guess that is the most important part of the collaborative process, find people that you can work with and that you get along with. So dear readers, any fun collaboration experiences you would like to share? Do you have a movie title that describes them? Any thoughts on the future of large collaborations in math? Please share your comments below.

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