Producing solo work

Question

For context I am in pure mathematics and I just started my first postdoc.

I am worried that I cannot produce solo work. I have a fair number of papers so far which are all collaborations with peers and/or some more senior people in my field, and I think all these are decent papers, and that I contributed substantially to each of these. I would like to produce some work on my own however, but I feel that all the problems that I can pin-point are either too easy to be considered a good result or too hard for me to address.

Has anyone here struggled with similar problems in the past? Any advice for such a situation, or how to build the skill of working solo? Not having single authored work makes me feel uncomfortable and less confident about my skills.

Answer 1

I would like to produce some work on my own however, but I feel that all the problems that I can pin-point are either too easy to be considered a good result or too hard for me to address.

Have you actually tried to do solo work? I can think of three scenarios depending on your answer to this.

1. If you haven't tried to do solo work, then the answer is simple: try it! What I mean is, don't just spend time agonizing over your lack of solo publications and ruling out candidate problems you can think of as being either too easy to be interesting, or too hard to be solvable. Pick an actual, concrete problem, and spend actual, concrete (and significant) time trying to solve it, and writing up the solution or any ideas you come up with. What sometimes happens is you don't solve the original problem, but you come up with something else that's interesting and possibly publishable. That's why working on very difficult problems, or even on very easy problems, isn't always the waste of time that some people imagine it to be.

2. If you did try to do solo work, look back on what happened and consider the possibility that you only think you tried, and you didn't really Try with a capital T. Was your attempt half-hearted? Did you give up too easily because you found the problem too hard or headache-inducing? Or did you get bored quickly because you found the problem too trivial, ruling it out as something that wouldn't interest anyone or that you would be embarrassed to publish? (Note: I'm not saying that your judgment in either of these cases would necessarily be wrong; some problems are too hard, and other problems are too boring. I'm merely asking you to critique your thought process, looking for places where your judgment may be worth revisiting.)

3. If you did Try (with a capital T) to do solo work, and you still didn't succeed, then... you should know that that's actually pretty normal! This is actually what happens around 90% of the time when I try to do solo work. (Those 10% of the times when I did succeed led to my solo publications, which represent about half of my entire research output.) So the thing to remember is that doing successful research in mathematics is just really hard. You need to try many times to get one success. And each individual attempt should typically require a real, serious, concerted effort.

A final thought: in my experience, some people are technically brilliant and can do very good collaborative work, but lack the sort of creative spark that can lead them to identify the sort of "tasty" problems to work on that lead to good solo work. So as others said, it may be useful to keep in mind that doing good solo work isn't entirely necessary to be a successful researcher or to have a good academic career.

Answer 2

It is hard to judge the difficulty of a math problem before you attack it. Some things that seem easy are hard and the opposite is also true.

But there is no reason to work on a single problem at a time. Having a few problems "in progress" is a good thing and switching between them is a good approach based on how the brain works.

Perhaps you could write up drafts of the "easy" problems and show them to a few colleagues for comment on impact. Perhaps they will find them non-trivial, in which case they might be worth submitting while you work on the harder things. The feedback you get will, in any case, help you firm your judgement on the quality of those problems and solutions.

But, collaboration is a good thing in math. Ask Erdős or any of his collaborators.

Answer 3

Well, currently, multi-author papers in math seem to be the norm, unlike some decades ago. In part, this is surely due to the ease of long-distance communication "in modern times". :)

And, yes, it is generally easier and happier to not necessarily work in a vacuum, but, rather, have someone else to bounce ideas off.

Nevertheless, when you'd come up for tenure, having no solo papers provides a target for anyone wanting to argue against you.

Answer 4

This is a stage that one can pass through. I had relatively few solo papers early in my career, and the ones I did have were served up to me on a silver platter by my mentors. (I did the work myself, but they gave me the project ideas in a very well-defined form.) Like you, I worried about my ability to work in a self-directed way. What I found eventually was that this skill kind of develops on its own with time.

Keep doing research, and keep talking to senior people around you about research problems. Keep thinking up your own project ideas, and gradually they will get better. i.e. they'll be worth doing and also approachable with your toolkit. (It helps that your toolkit will also grow.)

Another thing that helped me was being forced to write grant proposals. I couldn't just ask my mentors what I should put in the proposal, so I had to come up with future research questions myself. My first couple of proposals were very bad. But I got better at it, and occasionally my proposals even get funded.

These days, producing solo papers isn't strictly necessary to have a successful research career. However, the ability to identify important but doable research problems IS important, whether you end up working on these problems by yourself or with others. And this ability comes with time. One day you'll realize you have too many ideas for projects, and not enough time to work on them all.