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Faculty of Mathematics

 

Gabriel Paternain has just finished a nearly five year stint as the Head of the Department of Pure Mathematics and Mathematical Statistics (DPMMS). As he hands over the reins to James Norris, he tells us about his experience of being HoD, his personal highlights of the period, and what he thinks makes a good maths department.

The department needs to be supportive of young people, it has to be a place where there is harmony, a place that thrives on the diversity of staff and being open-minded. Gabriel Paternain

"The most important thing [in a mathematics department] is that there is the right atmosphere and the right conditions so that people feel happy and can carry out their research dreams to the best of their ability," says Paternain. "In particular, [the department] needs to be supportive of young people, it has to be a place where there is harmony, a place that thrives on the diversity of staff and being open-minded. With these conditions, good research and good teaching will naturally follow because the people we have here are very talented."

"Another very important thing is a strong admin team," he adds. "And I have to say, at the moment DPMMS has a dream admin team. I have had a huge amount of support and the rest of the staff feel the same."

Guardian of time

Paternain doesn't see himself as a leader who's there to keep people in line and implement a particular strategic vision. "If anything, I am a facilitator of the leadership of the collective," he explains. "[DPMMS] works from the bottom up: decisions are being taken collectively. This is a cultural tradition, and it's one of the things that I liked most when I first arrived here seventeen years ago."

His main task as HoD, Paternain says, is to manage and protect people's time. "Time is one of the most precious commodities, so if I had to define [my role as HoD] in a brief way, it's as the guardian of my colleagues' time. A mathematician needs uninterrupted time, without distractions, to do research. Sometimes you engage with a topic very intensively, and other times are sort of idle: it looks like you are not doing research but your brain is actually processing. You need time to talk to people, to go to conferences, and you need time to read. If you don't have this your research will not move forward."

The kind of things that can distract researchers include, routine and ad hoc meetings, box-ticking exercises, surveys, etc. These tasks need to be done, of course, so the secret lies in distributing them wisely. "I have to think very carefully if I ask someone to do something. I don't want to interfere with their time and I also want to ask them to do things they enjoy doing."

Supporting young people

Uninterrupted research time is particularly important for the younger members of the department, who may still be finding their research feet and feel the ever-present pressure to publish more intensely than established researchers. "They have to feel that this is a place that loves them and welcomes them, and gives them the time to explore," Paternain says. "They need to feel that they can take a gamble with what they think about. There's no pressure to publish immediately, but they can take their own time to explore their curiosity."

Young researchers clearly value this freedom to take risks with their research. Dr Oscar Randall-Williams, whose work on pure mathematics has recently won him a prestigious Leverhulme Prize, thinks it's been a major factor in his success. "My work is not obviously applicable, it's not even mainstream in pure maths yet. But the department understands the value and recognises the importance of novel work," he said in a recent interview about his prize.

Equally important in making younger researchers feel welcome, Paternain thinks, is to involve them early on in important decisions, such as whom to hire for vacant posts. "Hiring is done collectively, everyone gets involved. We incorporate the views of everyone, in particular young people because hiring determines the future."

Mixing it up

Paternain is adamant he didn't come to the job with a strategic vision in mind, but he does have to admit to a bit of an agenda: to keep the department diverse in every sense. "People's backgrounds have to be diverse, gender has to be diverse, intellectual views have to be diverse," he says. "A lot of the very exciting stuff in mathematics happens at the interface of areas, things that involve people from many different fields."

Part of this strive for diversity is Paternain's desire for close cooperation with the Department of Applied Mathematics and Theoretical Physics (DAMTP). "If you want to do good mathematics you have to have a broad view of mathematics," he says. Divisions between areas such as pure and applied maths, Paternain thinks, can also have a negative impact on teaching of undergraduates: if they focus on one area too soon it might limit their education.

"It has always been my view that this place would be better off if the two departments were collaborating at a deeper level," Paternain says. "I have worked hard in that direction and got a wonderful reception from the colleagues in DAMTP."

The Cantab Capital Institute

DAMTP and DPMMS have long collaborated at the level of teaching, but during Paternain's time other collaborations have come into being. One that he is particularly happy about is the Cantab Capital Institute for the Mathematics of Information. "The institute is a great example of a joint initiative, not just at the level of teaching, but at an intellectual level" he says. "It involves a great diversity of mathematics. On the DAMTP side it involves applied and numerical analysis, quantum information, optimisation and fluid mechanics to name a few, and here on the DPMMS side it involves the very important Statslab and lots of people who were previously classified as pure mathematicians, like Tim Gowers, Jake Rasmussen and myself."

"It's a dream project because the people at Cantab understand very well the importance of basic research in mathematics and they know what we need. The donation had essentially no strings attached. We were able to use the money in the way we thought best to make research progress, and this is exactly what it has been used for. Also, the institute has a phenomenal director in the form of Carola-Bibiane Schönlieb." You can find out more about the work of the institute in this feature article.

The Corfield Lectureship

Another highlight of Paternain's time as HoD pertains again to diversity: it's the establishment two years ago of the Corfield Lectureship in collaboration with Murray Edwards College and funded by Nick Corfield. The lectureship, which is endowed all the way to the position of Chair, is intended for a person with a high research profile who will also engage in activities that raise the profile of women in mathematics. The current Corfield Lecturer, Holly Krieger, does this through all sorts of activities, including giving public lectures, going to conferences, appearing at University open days, and taking part in initiatives like the Women in Mathematics Photo Exhibition.

"It was clear that for this to work you needed to offer the lecturer some kind of time protection, so the position comes with a reduced teaching load, both on the department side and the college side," explains Paternain. "This was quite adventurous because, frankly, when we got into this we didn't know if it was going to work. But the creation of this post turned out to have completely unexpected consequences (another reason why I am sceptical about strategic planning): it created some momentum into this direction that wasn't there before, prompting other places to create similar posts."

What next?

Paternain has enjoyed his time as HoD on a professional level, but also on a personal one. He particularly enjoyed the chance to get to know all the forty-odd members of DPMMS more than he might otherwise have, and is proud and to have finally become an expert at taking brief power naps during seminars and to be able to answer emails efficiently during boring meetings. He is now starting a well-deserved sabbatical year, trying, as he tells us, to give a final push to his football career and have more time to drink mate in the mornings.

Failing that there is always mathematics. Paternain is also planning to go to the University of Washington at Seattle, where he will work with collaborators on geometric inverse problems. "I have been very lucky as Head of Department because I have been able to keep my research going, thanks to my wonderful co-authors and collaborators," he says. "I don't have so much time left on my mathematical clock, so I may try a couple of more risky things. I still feel I need to prove one or two things to myself, so this is a good opportunity."