Some weeks ago, as I was attending SageDays70, I had an interesting conversation with a friend Sylvain about impact and my work. Both of us are researchers, advocating for open source science, he works in a private company and I am in academia. Here is the question he asked me:
Isn’t it frustrating to work on mathematical questions without any concrete applications when you have the skills to have a direct impact?
Since I made the choice of orienting my research towards fundamental mathematics, I have been asked this question many times in different forms. At first, I did not really know what to answer but with time, I have put more thoughts into it. With the creation of this blog, I thought now was a good time to share my answer!
Maybe, I should first say that my decision to become a researcher was not impact driven. I actually made quite a selfish choice: I decided to do what I really enjoyed since I was lucky enough to be paid to do it. At this stage, I really did not ask what it was useful for. What I really liked was the mental challenge that research was offering: I have always liked combinatorics and the kind of twisted problems it offers. I have a taste for complicated algorithms and mind scratching questions. That said, I cannot say that impact has no importance for me, maybe it is just not an engineering point of view: I do not attach myself to practical applications. This is what I want to explain today.
Impact of fundamental research
I could go on and on about how fundamental research has long term applications that we cannot see, or even guess, right now, look at prime numbers blah blah blah. It is all true but if you don’t think fundamental research is important for the future, it is probably because you don’t want to listen so I won’t waste my time trying to convince you. And actually, this is not what motivates me. I consider mathematics as a field of knowledge, as being part of the world as it is. It is not a tool, it can be used as a tool, but it is something that exists for itself and is worth exploring for the sake of it. Under certain assumptions, there are properties that are true and other that are false and we want to know which ones. Why? Well for the same reason astronomers look at the sky and and try to understand the universe or historians read ancient books to understand how people lived two thousand years ago. As humans, we want to understand the world and as mathematicians, that is exactly what we do in our little universe.
Yes but what not focus on the real world? Well, for me, this IS the real world, that is what I’m trying to say. Plus, I might not be that good at the other stuff. If I were forced to work on different questions, I might just lose interest and the skills Sylvain was mentioning would be of no use. By choosing combinatorics, I chose not only the field I preferred but also the field I am best at. I believe I am good enough at solving questions from algebraic combinatorics (most of them without any direct application what so ever), much better than if I had to find those applications. So let’s stay where I’m good at: as long as I have an impact there, I will be happy.
But the question is now: do I have an impact there? This is quite a difficult question and I have to be honest, and modest: my impact is probably limited. There are some, rare, great mathematicians who just change the way we understand the whole thing. Even though I am only at the beginning of my career, I have no hope of being among those great names. But despite what people think, mathematics are a collective artwork and not a masterpiece. We build a mountain by manually piling up grains of sand, each one them having a unique form. And I do believe that I bring my own set of unique grains: proving my own theorems and having my own unique ideas. I don’t need to be a genius. I have been working with mathematicians I consider to be way ahead of me and still was able to usefully contribute, to bring ideas they would not have had without me. Not because I am a genius (I am not) but because I come with my own perspective, my own background, my own understanding of things. The question remains: is something going to be piled up on top of my little grains or will they just fall off, being forgotten? This I cannot know and I have to keep going without knowing.
Now, enough with the metaphors. Maybe you were not convinced by this whole mountain and sand story. But pure research is only part of my work and I believe my impact goes beyond that.
Programming, open source, community
As a researcher, whenever I have a new result, I write a paper and publish it. Long before it is accepted by an official journal, I make it public on an online repository and promote it among my scientific community. Because I am paid by public fund, I do believe everything I produce should be public and free to be used by other scientists or who-ever. But my research is not only made of abstract proofs of neat theorems: I am also a programmer. If you want to know why one needs to program to do pure mathematics, you can watch my Pycon 2015 video Experimental pure mathematics. And the same way I want my mathematical results to be freely available, I want the code that goes with it to be free. This is why open source development has taken a big part in my day to day job.
I have been a contributor to the mathematical software Sage since I started my thesis in 2010. Basically, if I create some kind mathematical content that can be translated into code, I make the effort of putting the code into Sage so that it can be used by other mathematicians. I would not say I am a big contributor, but I do my best because this is also a way to share my research, to make sure my contributions to mathematical knowledge as a whole can be used by others. And my impact in Sage is not limited to my git commits: I am part of the community. I attend and organize Sage Days, I promote Sage within mathematicians and also in the outside world. I am trying to find ways to make the software more accessible and doing so, I believe I help the mathematical community. Sometimes, I also develop tools not only for my own research but because I believe they are useful for research like the FindStat project.
Another aspect to consider, one I had not considered that much before being part of the OpenDreamKit project, is that by coding our little mathematical things in our little world, we actually encounter quite interesting technical challenges. And even though it is a bit outside of our direct research interests we have an impact there. This is why we put resources and energy in the same kind of tools Sylvain’s company has been investing in. This is why both Sylvain and I advocate for open source, because we know it is the best way for the two worlds to benefit each other. This is I why I am part of Python community, attend PyCon, follow Data scientist on twitter, give talks so that people know what we are doing and so that I know what they are doing. And this is where we have our little direct impact on technology as a side effect of our passion for research.
This leads me to talk about another of my “side” activities: my teaching. Teaching is part of my job as a university researcher and, there, I definitely have an impact. I teach mostly basic computer science: programming, algorithmic. Sometimes I am lucky enough to teach combinatorics but not that often: you do not get that many combinatorics students while there are 300 first year students in need of programming 1.0. But that’s ok because I do love programming. I enjoy teaching and I put lots of efforts and energy into it. I am still quite new at it, but I am doing my best, and learning, and improving I hope. I believe the fact that I am a researcher gives me a good perspective and also a motivation. Probably, if I had not gotten my job at university, I would not have been a teacher at all. I would have taken a job in the industry and I am not sure I would have had the energy to go for extra teaching time…
This is the last point I want to discuss, the main one actually, the real reason I love my job. As a researcher in a public institution, I am free, I can decide where to have an impact. Of course I have some obligations, the teaching for example, and some administrative hassles like everybody. But I am free. No one tells me where to go with my research (or even where to go physically), no one checks what I am doing. Sometimes I have to report, I am expected to publish, but I decide what I publish on. If I want to learn about machine learning, I can. If I want to lose hours on a very annoying conjecture, I can. If there is a seminar somewhere near by and I want to go, I just go. I don’t ask anybody’s permission. If I want to spend an entire afternoon talking with grad students about their future in research, because I believe it is part of my mission, I don’t have to take the day off, I just do it. If I ever feel that combinatorics is a dead end and I want to take a different direction, no one will stop me… How I can I be sure I am going in the right direction, doing the right thing, having the right impact? Well I do not know but at least no one is forcing me to go where I don’t want to.
Something that often bugs me is that people assume that if you work in industry then you automatically have an impact. And somehow, this is not the case if you are in research. I don’t see why. What impact do you have? For who? I mean, you probably have an impact for your company or clients, does it mean you have a great impact on the world? (I am not saying I have, but at least, I am free to try.) I must say, I am not sure I would be satisfied if my only impact was to make sure some people are making money selling some stuff. Of course, I know it is not like this. I know many people in industry who have great impact. But it is not automatic. Whatever you feel like doing, you have to convince your company that it is the right direction to go. If they are taking bad decisions, somehow so are you. I might lose time proving some useless theorems but there are the theorems I chose, not some pointless clients requirements (and I lost plenty of time as a web developer doing some pointless required features). Now I only have myself to blame for my pointless theorems.
I think freedom is the number one thing I like in my job. If I felt like it was not there any more: if public funding was pressuring me into taking this or that direction (it is already the case, but not at a point where it restricts me), if administrative hassles did not leave me the time to do what I love, if somehow I had to constantly justify my own research decisions and my own schedule, this is when I would consider leaving research. Because if I don’t have the freedom to to do what I feel is good, I can just as much go and work for who ever has interesting problems to offer.