Interview with mathematician Arjeh Cohen

### "I never thought of myself as a mathematician”

“I do not really know how to give shape to my retirement”, Arjeh Cohen admits. “I still have so many things to do.” That is the story of his life: a portrait of a busy man.

Text Anouck Vrouwe, May 2014

“I am quite picky about the mathematical problems I work on. But every now and then I decide that this one is mine. And then I will not let go. I guess that is my strength.” Arjeh Cohen shows an article that is about to be published. “This story, for example, started 25 years ago, in 1989. All those years, the problem stayed on my mind. I worked on it every now and then, together with a colleague. And finally, we solved it. The result was not as great as we had hoped for, but I am really happy we brought it to its conclusion.”

He chose to study math because of its beauty, not because he was planning to become a mathematician. But a mathematician he became. And a good one too. Arjeh Cohen, now Professor Emeritus Discrete Mathematics, gave his farewell speech in a packed auditorium at Eindhoven University of Technology. “I never thought of myself as a mathematician. At university, there were guys in my year who were a lot brighter than I am. But slowly, they disappeared, they followed other interests. And I turned out to be the go-getter with a career in science”, Cohen explains.

He once tried to do something else, after finishing his dissertation at Utrecht University. Finite complex reflection groups was the subject of Cohen’s dissertation. His supervisor was Tonny Springer – a respected mathematician, one of the world’s greatest experts on the theory on algebraic groups. “My dissertation was a tough job. Things were different then. My supervisor threw me in at the deep end. You make it or break it anyway, was his vision. I did not discuss my research topic with him more than three times. There was no room for failure. I saw good people drop out. I struggled a lot, but I made it. After this period of very abstract math, I decided it was time to do something useful.”

Cohen applied to a job at the environmental department of Openbaar Lichaam Rijnmond – a former authority between the city council of Rotterdam and the Province of South Holland. He refers to it as his traineeship. “I modeled the impact of the industrial environment on citizens. I learned a lot about applied mathematics, like statistics and numerical mathematics. But it was not my world. I disliked the way politicians took decisions without proper knowledge of the problem, and I disliked how officials made their way up by acting important.”

So when a job opened up at Discrete Mathematics in Enschede, Cohen was more than happy to apply. “So far for the excursion. I really liked my new job, the concreteness of it. It was the start of my career, I found my favorite kind of math.” Soon after, Cohen changed jobs again. CWI, the Dutch research institute for mathematics and computer science, started a new research group in Discrete Mathematics.

“That was when I started doing useful things with computers”, Cohen understates. His first love is the geometry of the classification of mathematical groups, like Lie groups. “That work will last – some of the things I have proven may still be used in next centuries.” The computer was the second important theme in Cohen’s career. “Doing computer algebra is a challenge, and I liked it. You cannot fool a computer; you have to fully understand a mathematical problem to be able to program it. If you take 1,2,3,4,5 for example: that is a list of numbers, but it is a way of ordering them too. A human is aware of these two meanings at the same time, but a computer is not: if that ascending order is important to you, you will have to tell the computer that this is more than numbers. You have to be very explicit and precise, and that made working with computers good practice for me.”

During his time at CWI, Cohen helped lay the foundation for CAN, the foundation Computer Algebra Nederland. The goal was to stimulate and coordinate the use of computer algebra systems in education and research. “We became the central distributor of computer algebra systems, like Mathematica and Maple. But we also promoted their use, by teaching people how to use them.” At Eindhoven University of Technology, Cohen shaped the university's vision on the use of computers in education. “To give all the freshmen a laptop was one of my ideas, for example. That was quite extraordinary in those days.” And after his retirement Cohen will develop an interactive book on calculus for Sowiso, an e-learning platform for mathematics. “I am convinced that adaptive learning will become more and more important; it makes it possible to educate people at their own speed and level.”

In his own work, Cohen used the computing power of computers for his proofs a lot. “One of my best results was a search for a special small subgroup in the biggest exceptional group in group theory, E8. I had a Macintosh at home, and I managed to break the problem down to a solvable set of linear equations. I remember how I looked at the result of the calculations – I saw the numbers and immediately realized that the solution of my problem presented itself. It is unforgettable if your logic turns out to do the trick.”

So the Eureka-moment really does exist? Cohen: “Sure. I remember one time at Utrecht Central Station – the moment I left the train, just before my foot touched the platform. I immediately knew I found the solution to the problem I had been working on for quite some time.”

Another thing Cohen is really proud of is his book Diagram Geometry, which he finished last year with co-author Francis Buekenhout. “It took quite some time to mature. It describes the most important things I worked on for all these years.” Group-related incidence geometry is a wonderful subject. Cohen tells how he loves the wonderful objects that arise from just a simple set of points, lines and some rules. “It is fascinating.”

Since 1992, Cohen has been a full professor of Discrete Mathematics in Eindhoven. In his inaugural speech What is the point of algebra? he pointed out that algebra is a world in itself, where ‘finite groups like the Monster live’. He stated that his world holds enough challenges and rewards to forget about the real world. But Cohen was not a mathematician who simply closed his door and did his math. Though he did not like the political games at the Openbaar Lichaam Rijnmond, he became very active in management duties in Eindhoven. He was dean at the Department of Mathematics and Computer Science from 2009 till 2013. Thoughtfully: “It was not my ambition to become dean, not at all. For your math, it is better to stay out of governance as much as possible. You will publish more if you do, and get more praise. But to be able to do so, you need a healthy and well organized department. It never felt like I had a choice; it was important work that needed to be done and there were not many people who could do it.” Though becoming dean might not have been his first choice, Cohen's colleagues say he did a good job: he was an attentive and straight manager. He left a healthy department behind. One of the things he professionalized is the fundraising of the department. “Mathematicians always think they only have to do great math to get grants. But that is not enough anymore. The competition has hardened: you have to sell your ideas – also to people who are not experts in math. We hired professional trainers to polish our presentations. That may sound expensive, but it pays for itself in the long run.”

Cohen was also involved in national initiatives to improve the position of mathematics in The Netherlands, like Platform Wiskunde Nederland (PWN) en AMI, the collaboration of the three technical universities. “I believe in cooperation. Take Mastermath; the universities bundled their forces to organize the best courses for master students. That is good for all of us.”

One of his other priorities as dean was to increase the number of women in the department. His farewell reception showed how men still dominate the field: his wife, professor in Medical Psychology, was the only female professor at his farewell reception. “A lot of people noticed. We do have two female professors at our department”, Cohen says, “and we are working hard to increase their numbers. That will not happen on its own, you have to actively search for women. In general, women do not put themselves at the forefront as much as men.” All his 21 PhD-students were male too. “But luckily, I still supervise two PhDs – and one of them is female.”

Cohen has been phasing out activities in preparation of retirement, but he is as busy as before. He works on an interactive book on calculus, has some papers in preparation and supervises his last PhDs. “I don’t really know how I will shape my retirement. It is weird. But I do like the idea of spending more time with my grandchildren.” A short laugh: he realizes very well that he will have to plan such precious time in his overloaded schedule. Retired or not – Cohen is still that energetic man he has always been.

CV - Arjeh Cohen (1949, Haifa)

1971 – Master degree, Utrecht University

1975 – Dissertation ‘Finite Complex Reflection Groups’, Utrecht University

1975 – Researcher at Openbaar Lichaam Rijnmond

1976 – Researcher at University of Twente

1979 – Researcher at CWI, Amsterdam and Professor of Discrete Mathematics, Utrecht University

1992 – Full professor of Discrete Mathematics at Eindhoven University of Technology

2009 – Dean of the Department of Mathematics and Computer Science

** Note: thanks to Onno Boxma for his help**

*Date: 14 May 2014*