On a rare sunny afternoon in London, Jens Marklof welcomed us at De Morgan House, in the south-eastern corner of Russell Square, in the heart of London. It is the home of the London Mathematical Society (LMS), of which Jens has been president since last November. We sat down with Jens to chat all things quantum, life as a mathematician and diversity within academia.
A somewhat rocky start
Jens grew up in Munich before moving to Hanover at 11 years old. Although he is now an accomplished mathematician, his first interaction with the subject was not as enjoyable as one might expect. He told us: “My very first maths lesson in primary school was set theory, where we had to group triangles into one family, squares into another and circles into the third.” Instead of drawing lines around each family of shapes, Jens had a different approach: “I was putting everything in one set and then just marking the boundary lines between the different families. My teacher was quite angry that I could do such a bad job. I had to stay behind at break time and redo the whole booklet, which I was pretty upset about. So that wasn’t a good start for my mathematical career.” He raises a faint smile. “I think I actually got it right… just my solution was a bit unconventional maybe.”
Despite this unfortunate start, Jens persevered in his studies and later applied to study physics at the University of Hamburg. He was drawn to Hamburg due to the major research facilities there: “When I did my A-levels, my school organised a tour through the various physics research institutes around Hamburg, and something particularly impressive was the electron synchrotron.” Jens is referring to DESY (Deutsches Elektronen-Synchotron), a particle accelerator located just outside Hamburg. DESY is somewhat similar to the larger and more famous Large Hadron Collider in CERN, beneath the Swiss–French border. The research facilities weren’t the only thing that inspired Jens to study in Hamburg. Like all prospective undergraduates deciding on which university to attend, he was interested in more than just the course itself: “I was playing in bands and perhaps more interested in music back then than in science or maths. A big factor in picking Hamburg was also that the city had one of the best music scenes in Germany.”
Although he was studying for a physics degree, Jens soon started leaning more towards the mathematical side: “My studies were very, very mathematical: about half of my lectures were in the mathematics department.” This interest in maths was cemented during his PhD at the University of Ulm, and specifically during a stay in the US. “I was very fortunate to win a fellowship to go to Princeton for one year during my graduate studies, which really defined the future of my career. I worked with Peter Sarnak who made me realise that some of the very best pure mathematicians actually think very geometrically, and use the same intuition that I had learned in physics. Then, in addition, they have these extremely powerful tools that turn intuition into rigorous proofs. I found this incredibly fascinating and rewarding. That, I guess, turned me into a pure mathematician, although most of the questions I am now interested in are still motivated by fundamental problems in physics.”
Around the world
After obtaining his PhD in 1997 in Germany, Jens held different postdoc positions in the UK and France. He returned to the UK in 1999, joining the University of Bristol as a lecturer. By that time, Jens had gained a unique experience in different academic environments.
Asked about the variations in academia between countries, he noted that a key difference lies within the contents of maths degrees themselves: “In Germany, there were overall fewer students who studied maths as a single honours subject. If you have broader interests, you will more likely go to study physics, perhaps with a focus on theoretical physics if you are into mathematics. Because that’s often an avenue to get into industry or even do something non-science related, such as management consulting.” He contrasted this to the UK: “Maths is the most popular A-level subject, and many more students start a maths degree in the UK than in Germany, say, because here mathematics is understood in a much broader sense. It includes training in theoretical and mathematical physics, statistics, as well as engineering mathematics, all of which in other countries would be part of different degree programmes.”
“Congratulations Jens, you’re hired.” Image: The Royal Society
Bristol’s new mathematics building. Image: Wikimedia Commons users Pamaths, CC BY-SA 4.0
A further point Jens had noticed during his postdocs is the difference in support and opportunities for early career researchers. “Especially in mathematics, may of the great advances happen if you create an environment where early career researchers can flourish and really build their careers, and that’s where I see the biggest differences. In Germany for example,” Jens told us, “you typically spend many years in quite an insecure position until you become a chair professor. That’s often the first permanent appointment you get in Germany.” This differs with Jens’s personal experience in the UK after his PhD, where was appointed to his first permanent lectureship a few years after his PhD. Jens emphasised how being able to secure such a position at an early stage was beneficial to his research, saying “I cherished the security of a permanent position, to be able to plan ahead, both personally and with my own academic research and development. I think this still is something very unique and attractive in the UK’s academic system.”
Chaotic researcher
Jens describes his research as very multifaceted, straddling several areas of pure and applied mathematics, as well as mathematical physics. One focus of his research is in statistical mechanics where one “asks whether it is at all possible to derive the evolution of a macroscopic system (such as a drop of milk diffusing in a cup of tea) from the dynamics of atoms and molecules governed by quantum theory,” as he explains on his website.
The ideas of randomness and chaos are key in Jens’s research. But what does this exactly mean? “In classical mechanics, we have a very precise notion of chaos. Chaotic dynamics is defined by exponential sensitivity to changes in initial conditions,” he explained. In layperson’s terms, this is sometimes called the butterfly effect, where a small change—a butterfly beating its wings—can lead to drastically different evolutions of our system—such as the formation of a hurricane—in the future. He continued: “A chaotic system has other important features like the so-called mixing property,” meaning that a particle cloud evolves in time and becomes uniform, for instance sugar mixing in coffee. “It’s chaotic when that happens very, very fast, often as a consequence of the exponential instabilities in the system.”
In quantum mechanics, things are a bit more complicated, Jens explained: “Here, you can’t measure the position and momentum of a particle simultaneously,” as it’s forbidden by the Heisenberg uncertainty principle. For Chalkdust readers unfamiliar with this law, it tells us that there is a minimum amount of uncertainty associated with the particle position and momentum: one can know a particle’s position with great accuracy, at the expense of not knowing its momentum, or vice versa, but it is impossible to determine both at the same time. “So this notion of understanding individual trajectories, and how sensitively they depend on initial data, doesn’t really make sense in quantum mechanics. You have to look for other fingerprints of ‘what does it mean to be chaotic’ in the quantum realm.”
And how do we do that? Jens described that one way to approach this is by studying “semi-classical limits of quantum systems, that have an underlying chaotic or non-chaotic limit”. While there are a lot of open questions in this field, Jens told us that “one of the amazing observations is that quantum spectra of these systems, in the chaotic case, are described by random matrix theory, whereas in the regular case, they seem to be described by Poisson processes, so have maximal independence. It’s a bit counterintuitive because you get maximal randomness for the regular systems; whereas you see random matrix correlations in the chaotic case.”
A hurricane generator
Quantum chaos is a relatively new field, as Jens explained: “Quite a few high-energy and nuclear physicists moved to an up-and-coming area in the early and mid 80s called quantum chaos. That was a fascinating time because it also started attracting pure mathematicians and theoretical physicists and a lot of new phenomena were discovered that begged for an explanation.” Jens’s research involves bringing tools from different areas and fields to tackle problems that are too difficult to solve using traditional approaches. He told us: “I still feel today that most of the great breakthroughs happen when you bring areas together and when you can transfer your techniques from one area to the other. That’s why it was always critical for me to remain up to date with developments outside my subject and to always learn new things. And indeed, the discoveries that I’m probably most known for are of this type, where I was able to apply a technique from ergodic theory or the theory of modular forms, say, to a completely different area, for instance number theory, kinetic theory, or quantum mechanics.”
Fellow of the Royal Society
Jens’s contributions to the subject have earned him numerous awards and honours, including the LMS Whitehead prize, the European Commission’s Marie Curie excellence award and, perhaps most notably, the election as a fellow of the Royal Society (FRS) in 2015. We asked Jens to share how this works.
“To become an FRS, you must, first of all, be nominated by two current fellows of the society. Then your case is judged by a committee, the famous sectional committee 1 which is responsible for mathematics,” Jens explained, while we looked at each other, wondering if we should have indeed heard of this sectional committee. He proceeded: “The committee evaluates your research, the impact it has had on the subject, and finally makes a recommendation to the council of the Royal Society.” The council then proposes new fellows, and an election is held, where all current FRS and foreign members of the society can vote. If elected, you become an FRS. Previous fellows include the likes of Issac Newton (elected in 1672) and Stephen Hawking (elected in 1974), so Jens is certainly in good company.
“Being elected was a tremendous honour for me,” he explains, “especially since I had made the UK my home and so very much appreciate this recognition by the community.”
The entrance to the Royal Society in St James’s, London. Image: The Royal Society, CC BY-SA 3.0.
We spoke about the importance of awards for celebrating achievements. Jens said: “It might sound strange, but I often feel uncertain how the work that I’m doing is impacting others, how it is valued and appreciated. Recognition in the form of awards, grants, promotion, getting your paper accepted in a good journal, or even the occasional pat on the back by a senior colleague is really important.” He remarked that this was especially key for him at the early stages of his career, saying “the awards early on were quite important to me to give me breathing space and keep me going. I probably appear as very self-confident, but on the inside, it often looks different, and I think that’s the same for many people. Certainly, the early awards and recognition by my peers made a big difference at the start of my career, and I am extremely grateful for that.”
Jens in front of De Morgan House in Bloomsbury, home of the LMS
But Jens was keen to emphasise that the system for awards is far from perfect, saying “I also feel that I’ve been very lucky—there are people who would be deserving of prizes and awards and just miss out.” Speaking specifically about the FRS, he said “a lot of people don’t get through, not because they don’t deserve it, but because there are only a finite number of slots in each subject area. One always has to keep that in mind.”
The LMS
In November 2023, Jens started his two-year term as president of the London Mathematics Society (LMS)—one of the five learned societies for mathematics in the UK, founded in 1865. “The London Mathematical Society views itself very much, despite the historic ‘London’ in the name, as a UK-wide (and indeed global) mathematics society, representing pure and applied mathematics, as well as adjacent areas like mathematical and theoretical physics, mathematical biology, statistical sciences, computer science, and so on,” he explained.
The LMS is organised as a charity and has over 3,200 members, mathematicians and maths students, with undergraduates and postgraduates making up 10% of the LMS membership community. The LMS generates most of its income through publications and invests the funds back into the mathematics community “to support grants, to support early career researchers, PhD student conferences and workshops,” Jens explained. “That’s what the LMS does—it’s supporting mathematics and mathematicians at all career stages with everything from fundamental research to applications.”
In 2023, the LMS awarded almost £750,000 in grants, across all its programmes, to support the mathematics community. This ranges from grants to run student conferences, travel grants to attend conferences or undertake short research visits, and two annual Cecil King travel scholarships to undertake three months of study and research abroad, among others.
There are some great magazines in the De Morgan House common room (in a magazine rack just to the right of where this photo was taken).
The LMS also awards around 12 main prizes for achievements and contributions to mathematics, including the prestigious De Morgan medal, Pólya prize and Whitehead prizes. In fact, in 2010 Jens was awarded the latter himself for his research. Now, Jens has the opportunity to sit on the committees awarding these prizes. “One of the responsibilities of the LMS president is to chair various working groups and committees, including the prize committee, which is so important, particularly for giving recognition to the many outstanding early career researchers we are lucky to have in the UK.”
Despite being a UK-based society, “20% of our members are living and working overseas,” Jens explained proudly. This inspired one of his biggest goals for his presidency: “In particular, what I’m very keen on as president is to have much more global engagement. I think the London Mathematical Society has an exciting opportunity here to reinvent itself as a more global rather than national society.” He aims to establish stronger connections with mathematical societies from around the world, especially in Asia and Africa.
When we asked what he liked most about his role as president, he replied: “I think one of the most exciting things is that you meet lots of new interesting people—in academia, business and industry, policy makers and philanthropists, in the UK and abroad—and to explore with them how we can better support the mathematical sciences in the UK and internationally; how we can better support students and colleagues at all levels. That’s what I love about the job.”
Diversity and literacy
Part of the support Jens is referring to is how to help make mathematics more inclusive and diverse, a key goal of the LMS, as outlined in their diversity and strategy plan. We asked Jens for his thoughts on this. “Diversity is really one of the key pillars. We want to improve diversity in the subject through more engagement with the community, including going out to schools, and to really increase the so-called pipeline into mathematics,” he explained. Jens’s pipeline is a metaphorical view of the (mathematical) education path, from primary school to higher education and a professional career; and this pipeline is still leaking too much. The focus is on understanding how we can attract and retain more people from diverse backgrounds in the subject, from primary school all the way to undergraduate and postgraduate studies.
Jens elaborated further: “What I think we recognise is that there are a lot of talented kids out there who would be great mathematicians, but because they don’t have the right role models, or they don’t have an inspiring teacher, or indeed an encouraging background, that they just don’t think mathematics is for them.” He continued: “The issue for mathematics is that often it’s not so clear to people that mathematics is quite a diverse and broad subject that is both fun and can lead to great jobs in a wide range of sectors. Maths is now everywhere: in the digital economy, finance, health, and the global environmental challenges around climate change and natural disasters. I think we have to promote that more,” he concludes.
While the issue of the lack of diversity within mathematics, particularly within higher education, is complex and multifaceted, Jens believes that one way to help is to change the way we present and teach maths. “You can’t just say, ‘OK, we all have to study maths.’ To have a more diverse pool of people, you have to actually make it attractive to them. Why is maths exciting? What should the ideal mathematical science degree of the future look like?”
By changing the way we promote and teach mathematics, Jens thinks it will increase the number and diversity of students going into the subject. “There really is a place for many more different types of thinkers and personalities than the current stereotypical image of a mathematician. And that will help with increasing diversity.”
And this is what Jens hopes we move towards in the future: “We need to do a much better job in explaining what is fun about mathematics and what you can do with it later on—which professions you can get into. And that’s certainly one of the things we want to do at the LMS, to put those mechanisms in place, working with our partners in academia, business and government.”
Despite the great amount of work and challenges that lie ahead in these matters, Jens is determined to keep pushing to make mathematics more diverse and inclusive. Our final question to Jens was what advice he would give to his younger self and to all our readers: “Persevere even if things are not going well. If you struggle, perhaps in your first days at university or in your research project, keep believing in yourself, but also give yourself permission to fail. What helped me throughout my life is to set ambitious aims, look for role models, but at the same time not to cling to just one goal. It is liberating to have a plan B in your back pocket in case things don’t work out. But never let the self-doubts take over, and never give up too early.”
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