(06/24/21) Mathematician Asgar Jamneshan spent the past two years on a DFG grant at the Department of Mathematics at the University of California, Los Angeles (UCLA), where he conducted research as a member of Terence Tao's group on “Extending Structural Results in Ergodic Theory and Applications.” He spoke with the North American office of the DFG about subjects such as his current research interests, the atmosphere at UCLA (which is also inspiring for mathematicians), the dialectic of chance, and about mathematically induced
states of serenity.

Through its fellowship program and the Walter Benjamin Program, the DFG supports junior researchers in their academic careers by funding an independent research project abroad and, since 2019, in Germany too. A large proportion of these fellowships are awarded in the USA and to a lesser extent in Canada, reflecting the belief -- still prevalent in many disciplines -- that for a career in research it is helpful to have “been in America.” In this series of talks, we aim to give you an impression of the range of DFG funding recipients. This interview reveals who is behind funding number JA 2512.

DFG: Prof. Dr. Jamneshan, many thanks for taking the time to talk to us. You are talking to us via link from Turkey, but your name points in the direction of Iran. That sounds like an interesting story. Would you like to share it with us?

Asgar Jamneshan (AJ): Gladly! I appreciate the opportunity to tell you a little about my background and career, and to start I would like to thank the DFG most sincerely for supporting my research stay in the US.

You’re right in your assumption: I was born in Tehran. But when I was two, my parents had to flee Iran for political reasons – that was after the Iranian Revolution. We first went to neighboring Afghanistan and then, via Russia, we finally ended up in Berlin – Neukölln to be precise. When we got there, I’d just turned nine and had attended school quite irregularly up until that point, but I did speak Russian in addition to my mother tongue Farsi and the Afghan dialect Dari.

DFG: I would imagine that has not been of any lasting disadvantage?

AJ: To answer that question correctly you would need a control group! But you’re right: it may even have been useful in that I’ve been able to acquire a few more languages along the way since then and have learned to tackle new challenges swiftly. But what I’ve achieved also has a lot to do with the care and support I received from my family outside of school. My mother taught me reading, writing and basic arithmetic at home at an early age. As far as I can remember, I always liked to do sums in my head. In addition, I grew up in a home environment where education was highly valued. We always had lots of books at home and my mother read to me in the evenings. In Berlin, I regularly attended a chess club with other Iranian refugee children and my parents organized piano and painting lessons for me, to give me a channel to express my feelings through art. I still like to paint and draw to this day, sometimes quite intensely.

If something ever went wrong at school, the problem was immediately addressed in a very purposeful way. For example, German grammar probably isn’t easy for any nine-year-old to understand, especially if German isn’t their first language. We had many pupils at my primary school in Neukölln – the Sonnen-Grundschule – whose mother tongue was not German, but I was probably one of the very few whose family intervened early on by engaging a tutor, thereby enabling me to be recommended to attend Gymnasium (upper secondary school). When I think back, there were other gifted children all around me, but unfortunately their talent often fell by the wayside due to a chain of unfavorable circumstances. I’ll go out on a limb here and say that alumni of the Sonnen-Grundschule in Neukölln are significantly underrepresented at doctoral colloquia at Berlin universities. So I’m very grateful to my family for the fact that things worked out for me – and for making what was in itself a traumatic displacement experience intellectually enriching and strengthening for me, too. What’s more, I was fortunate to have had many very kind, wise, and supportive teachers (a trend that has continued to this day in the form of supportive and encouraging supervisors and mentors).

DFG: A little bit more about your family. Do your relatives have a marked affinity to mathematics? And what do your siblings do?

AJ: Yes, both my parents come from families with an above-average number of people in the fields of engineering and natural sciences. My grandmother was a math teacher at a village school, an aunt even studied math at university until the outbreak of the revolution, and my mother worked as a math teacher while pursuing her studies. My father was an engineering student at the renowned Sharif University in Tehran, ultimately receiving a scholarship to continue his studies at MIT in the USA, though he unfortunately never took advantage of this because of the outbreak of the revolution. My younger brother – there are only two of us – is a little different and is currently training to be a psychotherapist after completing his studies in psychology.

DFG: Is that really so far removed from mathematics? Couldn’t psychology also be described as a science of human thought – or of the structure of human thought?

AJ: Now you’re fishing for a philosophy. No, I firmly believe that we don't just make up mathematics but that we discover it. However, there are two sides to this coin – one of which is as hard as diamond, and that’s what unfortunately puts a lot of people off. The other side is that mathematics is not without a certain poetry or beauty, , in those very brief moments of insight when new connections open up. Günter Ziegler has explained wonderfully what these moments are all about. But he also made it clear that mathematics requires not just talent but also a fair amount of pain tolerance, because beauty only likes to reveal itself on very rare occasions.

DFG: In your doctoral thesis at the Berlin-Potsdam Graduate School “Stochastic Analysis with Applications in Biology, Finance and Physics” (RTG 1845) and at the Berlin Mathematical School, you worked on conditional set theory. When non-mathematicians describe beauty, it sounds different.

AJ: Yes, I admit that neither the language of mathematics nor the beauty of mathematical knowledge is readily apparent to everyone. When you look at a score, the beauty of the music expressed in it is only revealed to you if you understand the symbolic language and can “imagine” the music that is expressed in it. But not every form of mathematics is beautiful to everyone (just think of the different genres in music). I for one have not yet discovered the beauty of financial mathematics (despite having studied it for a long time), perhaps because I don’t really see it as the task of academic pursuit to help people or institutions who are already very wealthy to become even wealthier (often to the detriment of the common good). Anyone able to overlook this can certainly find beauty in this “genre” of mathematics. On the other hand, it’s interesting to note that conditional set theory – a method I developed with other collaborators during my doctoral work that was originally motivated by problems in financial mathematics – is now being applied to problems in areas that are more commonly associated with pure mathematics.

DFG: In your project proposal for the postdoctoral fellowship, you report on the state of research into the theory of a dichotomy of structure and chance. For a non-expert such as myself, this is noteworthy in that to me, chance and structure are a pair of opposites. I would perhaps even stick my neck out and say that there is no such thing as chance, at best situations in which we have not yet properly understood the determinants.

AJ: In that case, I hope you have a long neck! Chance really does exist and I suspect that chance is even a constitutive element of reality – not just our reality. Chance and structure are not pairs of opposites, but are connected in a dialectical unit, so chance and structure cannot be separated from each other. Chance contains structure and structure contains chance. I hope that a deeper mathematical understanding of this dichotomy or dialectic will lead to significant progress, for example with Riemann's conjecture, one of this century’s mathematical problems that remains unsolved.

DFG: Bearing this in mind, can you describe what you are working on in a way that is understandable to a non-expert?

AJ: I’ll give it a try: the focus of my research is the group of problems and areas associated with Szemerédi's theorem. This theorem establishes a connection between the size of a set of numbers, i.e. the number of its elements, and its arithmetic structure, in other words something like arithmetic progressions. An arithmetic progression is a sequence of numbers in which the difference between two consecutive numbers always remains the same, e.g. 4 9 14 19 is an arithmetic progression which has a length of 4. Surprisingly, understanding this simple-sounding connection between the size of a set of numbers and the arithmetic structure it contains requires deep and sophisticated techniques and connects several seemingly distant fields of mathematics (and theoretical computer science), such as combinatorics, dynamical systems, harmonic analysis and also mathematical logic. This sheer abundance and the resulting lively activity in this field which has been going on for about 80 years make it one of the central questions in mathematics today, since the ultimate hope is that it will lead to a deeper understanding of a mathematical expression of the dichotomy between structure and chance.

DFG: You spent your research fellowship at the University of California, Los Angeles as a member of Terence Tao’s group. Tao is one of the most famous mathematicians of our time. How did you get there?

AJ: It was more the result of a very gratifying coincidence. His curiosity was aroused by the method I mentioned earlier, which I had developed in my dissertation, and presumably my enjoyment of mathematics and desire to work. He is also an incredibly generous mentor and enriches his environment enormously – both mathematically and personally. He was interested in my work and we had a dialogue that was very fertile for both sides.

DFG: The prospect of productive dialogue was what probably also attracted Maryam Mirzakhani to California – an Iranian and the first woman ever to be awarded the Fields Medal.

AJ: She is a great role model for me because of her strong personality and deep mathematical mind. But first she went to Harvard on the East Coast and then to Stanford. Nevertheless, in both cases, as with the larger math departments in the USA in general, there is certainly a very fertile atmosphere overall, that is to say they offer very international, collaborative environments. The flatter hierarchies in the US as compared to Germany, Switzerland and now Turkey, and the generally more easy-going approach (perhaps even modesty) and open dialogue also facilitate the work.

At the top universities in the US, people really do come from all over the world. Diversity is not just a moral category, it’s also an invaluable source of creativity. The Berlin Mathematical School recruits 50% of its students from abroad, as do the Max Planck Institutes of Mathematics. Institutions such as the Hausdorff Center of Mathematics (HCM) in Bonn already have remarkable international appeal, too. But they’re still some way from achieving the level of internationalization at UCLA, Harvard, or Stanford.

In addition to this degree of internationalization, the size of the group may also be a factor in that you get more specializations together. This can be very productive. Nonetheless, excellent productivity is not something you can force by means of size and internationalization.

Allow me to make one more comment about Maryam Mirzakhani. She belongs to the first generation of significant female mathematicians in Iran. One consequence of the social upheaval caused by the Iranian revolution – something that is often little known in other countries – is an educational explosion that has brought many women to universities.

DFG: Mathematics is also an important part of the tradition of Iranian culture, isn't it?

AJ: Yes, and that is not without a certain irony in view of the theocratic revolution in Iran. Here I’m talking about Omar Chayyām, who not only made a name for himself as a poet in Iran in the second half of the 11th century but was also the first to systematically investigate solutions of cubic equations. He is the father of modern algebra – almost 500 years before these foundations were further developed in Renaissance Italy and later in France and Germany. Pascal’s triangle, i.e. the graphical representation of binomial coefficients, was addressed by Chayyām centuries before Blaise Pascal. Chayyām's mathematical legacy is still highly publicly valued in Iran today, unlike his poetry (that’s where the irony comes in). In his poems he praises wine in a very pleasure-oriented or even sensual style, and he is sceptical and sometimes mocking of organized religion.

DFG: A typical mathematician cliché is that of the cranky loner who devotes himself to solving a problem in seclusion over a period of years, only very rarely showing up at conferences and if so, then preferably in the rural solitude of Oberwolfach. Yet there are math departments like the one at UCLA with several dozen professors. Is mathematics now more of an individual pursuit or a team sport?

AJ: The answer to that is probably: both. Take for example the Polymath projects – an idea which originally goes back to British mathematician and Fields Medal winner Timothy Gowers. It attempts to solve mathematical problems through mass collaboration. In a video on YouTube, Tao explains what this is all about, taking the example of a paper in physics in which measurements taken at the Large Hadron Collider a few years ago were interpreted as proof of the existence of the Higgs boson. The paper had a list of 3,000 authors at the time, so it was a case of “mass collaboration.” The question first raised in this way by Gowers in 2009 was: in times of instant global connectivity, can’t mathematical problems be solved quickly and perhaps even elegantly by means of polymath – here meaning the mathematics of the many? In the meantime, experience has been gained from several projects and there are even results that have been published as papers under the pseudonym “Polymath.”

But mathematics is cumulative, too. This is shown by the classification of finite simple groups, for example, in which about 100 mathematicians were involved over a period of more than 50 years in the 20th century. You can also see it when you look at Andrew Wiles and his solution to a problem posed by Fermat: together with Grigori Perelman, he is perhaps the prime example of the lone wolf in mathematics, but both of course drew on the latest research in each case, which is the only way this kind of breakthrough is possible. But in effect you are raising the general state of knowledge to a much higher level in a very original or, if you like, “beautiful” way. Seclusion and interaction can be equally effective in producing such flashes of inspiration. After the event you can see which constellations were fruitful – beforehand it is much more difficult to tell.

DFG: This is in line with a statement by Yogi Berra, a philosopher who played baseball for the New York Yankees in the 1940s, who is fondly quoted as saying: “It's tough to make predictions, especially about the future.” The popularity of this quote reflects the widespread unease about not knowing what the future holds. You could be called a professional probabilist, someone who uses mathematical tools to keep the imponderables of the future in check. Does that make you feel more at ease overall?

AJ: At a rational level, I would probably be at ease even if I had not become a probabilist. But fear or unease with regard to the future tend more to be gut feelings: mathematics isn’t so reliable here.

DFG: Can you really respond to probabilistic experimental set-ups in a purely rational way? Let’s say I flip a coin in front of your eyes, and again and again the result is heads. At what point would you ask to be allowed to see if the coin was heads on both sides, i.e. whether or not the experiment was really fair?

AJ: Since you’re from the DFG, my gut instinct and my intellect would initially lull me into a sense of security that you were not trying to lead me down the garden path. My intellect wouldn’t rebel if the same result of the coin toss were to be observed ten times in a row – that can easily be made plausible mathematically. Somewhere between 30 and 50, my gut feeling might start to pipe up – but combined with the dilemma that I'd actually be very reluctant to accept that the DFG was attempting to lead me astray.

DFG: No worries – we wouldn't do any such thing. What are your plans for the future?

AJ: I’m currently at Koç University in Istanbul. This is a small, very recently established private university. My Turkish wife, who is also a mathematician and currently at Simon Fraser University in Vancouver, is due to start working at Boğaziçi University in Istanbul in September. Istanbul is currently the best place to solve the vexing two-body problem. For obvious reasons, I’m very interested in starting a family. My wife and I will go to any city or region in which we can start a family and continue our professional careers – preferably in Germany, of course. After all, my discipline thrives on challenge, on overcoming frustration and on the growing hope of solving something through experience. At least that’s something that helps eliminate any fear of the future.

DFG: If there was one thing you would like to see in the immediate future, what would it be?

AJ: To finally be able to knock chalk dust off my trousers again on a regular basis. It really makes a difference being able to stand in front of a blackboard with colleagues and engage in discussion. This was something that was clearly lacking during the pandemic – despite the fact that it has become very easy to get together virtually.

DFG: Thank you very much for this very entertaining and informative interview, also on behalf of my colleagues, and I wish you all the best for the future, both for your career and your private endeavours.

For the aforementioned video by Terence Tao, see:

• https://www.youtube.com/watch?v=elWIDVI6b18