Translation: Lenore Messick

He’s a number theoretician by profession. And he’s held that title for about twenty years. But explaining what that means is still not exactly easy.  

“At family celebrations, I usually say that I’m looking for new numbers between 0 and 1. But I work on the real numbers and their properties,” explain the associate professor from the Department of Mathematics at AU. 

He continues:

“If you take the square root of two and look at the decimal expansion, you get this long, long string of decimals that’s actually infinite. And so in light of this, it’s reasonable to ask whether there are infinitely many fives. This is a major open question in number theory – or more precisely, it’s a special case of a major problem. And it’s something we don’t know about numbers.”

When I ask Simon Kristensen why he does research in this field, the answer is clear:

“I take a strong personal interest in it.” 

But the big foundations don’t share that interest. And that's a problem.

Number theoreticians shouldn’t count on money 

Although the mathematics professor has no doubts about the value of his research, he has to admit that it’s difficult to find funding for it. And he points out that there are actually very few foundations that fund research on pure mathematics.

“And those that do prefer to fund very large groups, I mean huge initiatives where they make basic research centres. And we have one of those on the floor just below us (at the Department of Mathematics, ed.) 

In relation to foundations that support pure mathematics research, Kristensen points primarily to Independent Research Fund Denmark (DFF). 

“The Lundbeck Foundation used to give too, but they’ve narrowed the field in relation to what they fund. And those are the conditions with the private foundations – they decide what areas to prioritize themselves. And if your metier is making pills, you’re probably more inclined to support the health sciences. The Villum Foundation also gives once in awhile, and I’ve gotten money from the Carlsberg Foundation.”

Even though previous applications have been successful, Kristensen is by no means swimming in money: 

“I seem to have hit a drought. I have one application out right now, with the Research Council.

Why do you only have one application out if it’s so hard to get funding?

“Because there are so few places to apply. I might be able to send it out more places if only there were more places to send it to. But no one wants it!”

What’s more, he spends time helping other people with their applications, and there’s not much of a point in sending two applications in the same field to the same foundation.

“I have a protegé who has tried to come here on a Marie Curie research fellowship, and I was involved in that. And I was also involved when my PhD student, who’s since finished, applied for Carlsberg. Unfortunately for both of them, without luck.” 

Lightbulbs or just better candles?

In other words, it’s difficult for him to find money to fund his research, which isn’t oriented towards a concrete application. And according to Kristensen, this is not exclusively a problem for his field, but for the research landscape in general.

“We don’t discover anything new if everything has to have an application. In that case we keep discovering the same thing again and again. If no basic research had been done before us, we wouldn’t have had the lightbulb. Just better and better candles!”

Illustration: Morten Voigt.

In other words, Simon Kristensen believes that it’s impossible to predict the potential applications of basic research –which also applies to his own research on number theory.

“I usually say that my metier is not figuring out applications, because my metier is doing basic research. But once in awhile there’s someone who can use what I do for something in their own field.” 

Engineers found a use for Kristensen’s math
Most recently, some engineers working on how to optimize 3G and 4G networks have used Kristensen’s math in their analyses.

“And I’m sure 5G too, when that’s a reality. But that was not at all what I and my colleagues around the world were after with our research. We actually didn’t care about at all,” Kristensen explains. 

He realized that engineers were interested in his math when he started getting cited in engineering journals.

“At first I though it was an indexing error. But no, it was true – they were using my mathematics in their analyses. And I certainly don’t have anything against that. But that’s not why I do it, and well, I do prefer that they don’t use it to make bombs!”

Kristensen is well aware that in our day and age, some people might find a researcher who insists on research for research’s sake provocative. But as he puts it: 

“I think it’s important to make a stand for basic research. And after all, it’s not certain that the problems the engineers were stuck on had been solved if some idiot hadn’t thought it was fun to look for new numbers between 0 and 1.”

G. H. Hardy, Alan Turing and the art of code-breaking in wartime

 In support of his position, Kristensen refers to the example of the famous British number theoretician G.H. Hardy.  Hardy, a prominent Oxbridge mathematician, was actually directly opposed to the idea that his research should be ‘useful’. 

But according to Kristensen,  if it hadn’t been for Hardy’s contribution to number theory, Alan Turing – another famous British mathematician – would not have been able to break the Nazis’ Enigma code during WW II.  A breakthrough which was a decisive contribution to the Allied victory.  

“Turing drew on all kinds of number theory, and Hardy was a central contributor to that,” Kristensen explains. And adds:

“He didn’t ask for permission. He probably wouldn’t have gotten it.”

G. H. Hardy’s opposition to the use of his research as a springboard to new inventions arose from a conviction that it was often the wrong people who profited from the work of mathematicians like himself.  

“I force all of my students to read Hardy’s A Mathematician’s Apology, where he explains why he devoted his life to mathematics. And he had a lot of reasons, and one of them has to do with the utility aspect. For Hardy, mathematics was more of an art than an applied science, and he communicates that incredibly clearly in the book,” Kristensen explains.

“I’d like to pass that perspective on to my students. Even though it’s not that I have anything against my research being used as such. That’s just not why I do research.”

More researchers fighting over the same piece of cake

The theory of Numbers has always been regarded as one of the most obviously useless branches of Pure Mathematics. The accusation is one against which there is no valid defence; and it is never more than just when directed against the parts of the theory which are more particularly concerned with primes. A science is said to be useful if its development tends to accentuate the existing inequalities in the distribution of wealth, or more directly promotes the destruction of human life. The theory of prime numbers satisfies no such criteria. Those who pursue it will, if they are wise, make no attempt to justify their interest in a subject so trivial and so remote, and will console themselves with the thought that the greatest mathematicians of all ages have found it in it a mysterious attraction impossible to resist.

G. H. Hardy, professor of number theory at Oxford and Cambridge 

The narrowness of his research interests don’t completely explain Kristensen’s funding problems. He is also an example of a phenomenon known as the hourglass effect.

Most research grants go to well-established researchers at the height of their careers and junior researchers – PhD students and postdocs – in the early stages of theirs. This is because research funding is increasingly taking the form of grants to large research centres, or is awarded as large temporary grants. And this means that professors can hire a large number of PhD students and postdocs in temporary positions. 

While associate professors are in the middle, where there is least money – in other words, where the hourglass is narrowest.  

“The foundations often have an interest in the young up-and-coming researchers, and they’re enthusiastic about giving to the really big guns who can pull off a basic research centre. If you can do that, there’s a certain probability that you’ll get one. But for a number of reasons, I wouldn’t be able to cope with getting such a big bag of money. So there aren’t really programs dedicated to people like me who’re in the middle of their careers. It can be difficult to attract funding then.” 

In addition, the competition for research funding has become more intense over the course of Kristensen’s close to two decades as a researcher.

“We’re all pushed to apply a lot more, so all of the universities have bigger and bigger appetites. But there’s less and less cake. So if you’re not aggressive with your fork, you get nothing.”

The death of research fields in Denmark?

Kristensen also views the favorization of large centres by current government research funding policy as a structural problem. Because he doesn’t believe that these initiatives will create the intended critical mass in particular fields. 

On the contrary, he believes that there’s a risk that some fields will die out.

“The mathematics research community in Denmark is quite small, and when you make a basic research centre here and one in Copenhagen, as they did almost ten years ago, then these huge initiatives in some particular areas of mathematics end up determining the entire direction of Danish mathematics, standardizing it completely. So I also see a risk that in the future, we’ll have a hard time making our mark in very many areas in the larger world.”

So what has characterized us up until now in the larger world?

“We’ve been at the forefront internationally in a relatively large number of fields within mathematics – and have had international superstars. And as far as that goes, we still do, but it’s something that can change as a consequence of the standardization of mathematics.” 

So you fear that this position will be undermined over time?

“I fear that when funding is concentrated in large grants to large projects that we’ll be known for doing a particular kind of mathematics here in Denmark, or physics or whatever else for that matter, because this applies to all of the sciences. Instead of like now, where Denmark is known for being a good country for mathematics. And then there’s also the aspect that the money that’s now being centralized could support a lot of researchers quite well.”

New Public Management control

On the whole, Kristensen thinks that the politicians’ decision to make such a large proportion of research funding competitive in recent years is a fundamental problem. One of his arguments is that this policy forces researchers to spend a lot of time on competition, and that this is a misuse of researchers’ time.

“It takes time to write an application. And there are also students to take care of. And supervise. And then it’s also really nice to be able to find the time to sit down and think about those new numbers between 0 and 1 instead of spending your energy writing about what you would be doing if you weren’t sitting here writing an application!”

As you see things, what should the politicians do?

“They should remove this massive New Public Management control over the universities. And make them into what they were meant to be – institutions of free and independent knowledge. And instead of us competing for research funding, it should be given to the universities again so that we can allocate it according to our own criteria. The universities should be autonomous entities, like they used to be.”

But some people also think that the universities mutated from the inside back then – and didn’t understand the importance of opening themselves up to the rest of the world. What do you think about that?

“I didn’t experience it, because I’m not thatold, after all. But yes, it’s possible that there’s some truth in that. But on the other hand, one might also ask whether there was any reason to throw the baby out with the bathwater. In any case, I think that the approach has been very drastic in relation to removing the universities’ autonomy. And much more than was justified by the problem you outline, and which they were attempting to solve.”