Alex Amenta, participant #hlf14: Before arriving in Heidelberg for the 2014 Heidelberg Laureate Forum, I spent some time thinking about the purpose of the forum, a kind of overthinking which has become characteristic of myself. There’s an obvious benefit to putting hundreds of enthusiastic students in one place, but is the presence of the laureates necessary? As usual, I did not answer my own question, but instead I went off on some tangents and thought about other things. This post is the result.

(Note to the reader: I have no experience in computer science, so I have only written about mathematics and mathematicians. I don’t know if computer scientists share the same views. Feel free to let me know your opinions!)

In mathematics, we emphasise the achievements of great mathematicians. Fields medalists, Abel prize winners, and so on. We do this for many reasons. Of course, we do it to celebrate individual achievements, but also for the benefit of mathematicians as a broader group. We celebrate and emphasise beautiful and revolutionary work, in order to inspire others to strive for greatness in their own work. By celebrating the best, we hope to improve our craft as a whole.

We also single out great work for people outside of mathematics, to show the broader community examples of what mathematicians think and what top-quality mathematics is about. Particularly to break misconceptions about math: to show people that it’s not just high school algebra, not just manipulating numbers. That there is real beauty in it. Just as we celebrate great artists by exhibiting their work, we celebrate great mathematicians by, for example, giving them prestigious awards. This works for the most part. People see top mathematicians, they hear about how great their work is, maybe they even learn a bit of the maths. And they think, ‘wow, this is quite cool, I had no idea math could be so exciting’ (maybe not in those words). Even more, we hope that some people will be inspired to follow in this path.

However, there can be a downside to this, which takes a bit of explanation.

Like many mathematicians, I think of maths as a science of self-expression, somewhat like a form of art (one of my PhD advisors has pointed out similarities with skateboarding culture, and I was going to write about that originally, but this really is another story). With art, for example with music, it’s well known that one can pick up an instrument, learn some basics, and start to play. Most importantly, one can derive great enjoyment from music without having to be an expert! But people generally don’t know that this is also the case with maths. One can pick up a math book, read, and experiment. With just a small amount of exposure to mathematical ideas, one can start to legitimately ‘do maths’ and have fun with it, even at a basic level. Because of this lack of public awareness, we must be careful about the image that we propagate of mathematical success. This may be the only image that people see.

The most famous mathematicians are undoubtedly the Fields medalists. Non-mathematicians generally see these people as prime examples of what mathematicians are. They see somebody who is energetic, motivated, brilliant, young, and passionate. Often they see child prodigies with a great deal of luck. They may think, ‘these are the qualities that I need if I want to do maths’. And then they may think further, ‘I don’t satisfy these criteria: I’m not a math genius, in fact I have no mathematical experience at all. There’s no hope that I could ever get to this level’. Finally, they may extrapolate from these misconceptions and conclude that they are incapable of doing mathematics. (There is much irony in the derivation of this conclusion.)

I recently attended the International Congress of Mathematicians (ICM) in Seoul, where (among other things) the Fields medals were awarded. There were quite a few undergraduate participants. Some of them were not even studying mathematics; they were just there because they were interested in math and wanted to learn more. I talked to quite a few of these students, and they loved the experience of the ICM. Those who were already studying mathematics had their postgraduate ambitions cemented by the experience.

On the other hand, I met a few students in particular who were not math students, and despite their enthusiasm, the things they had seen at the ICM indicated that they were not capable of joining the mathematical world. They had the impression that, to do mathematics, one must be as good as a Fields medalist, or at least a plenary speaker. They thought that all mathematics was like this. Most sadly, they thought that they were incapable of enjoying math for its own sake, because they were simply not smart enough. It was very difficult to convince them that they were wrong.

We need to emphasise the openness that mathematics has: the fact that absolutely anybody can do maths, and that one doesn’t have to be the best to have a lot of fun. Just as anybody can paint or play music without technical ability and nevertheless have a good time. So I believe that celebrating greatness in the way that we do, although it has its benefits, can be misleadingly dangerous. We may be inspiring some people to reach their full potential, but at the same time we may be preventing others from doing the same.

When I was at the ICM, there was a high school activity of some sort going on. All the participants, us as well as the high school students, were wearing lanyards for security purposes. Our lanyards were standard name tags, but these students had special lanyards. These said ‘Dream the Fields medal!’. This worried me a bit. Is this the sort of image we wish to create for mathematics? One where the goal is a prize?

Alex Amenta lives the math life. Upon finishing high school he discovered mathematics on Wikipedia by accident. Today he a PhD student at the Australian National University and Université Paris-Sud. His research involves harmonic analysis of differential operators.