The exclusive Interview of the Day: Lisa Sauermann

Lisa Sauermann is a research mathematician working in extremal and probabilistic combinatorics. Lisa currently has the third best performance in IMO history with 4 gold and 1 silver medals, and was the only contestant to have a perfect score in 2011. She did her PhD at Stanford and is currently at the Institute of Advanced Studies.

She participated in an online interactive session for IMO 2020, where she was interviewed by Parth Shimpi, a mathematics undergrad at the University of Cambridge.

Could you describe your IMO journey?

I went to the IMO five times and enjoyed every single one of them tremendously, as all the participants would agree. More than the maths I would say I loved meeting all the people from different countries, hanging out in the evening together and playing fun games. The IMO and the training camps leading up to it are opportunities to meet great people- I have met a lot of my friends at the German training camps ten years ago. It is very nice that the IMO is happening this year despite the pandemic.

What was your ‘formula’ for securing the IMO gold medals?

I don’t think there is a formula- the problems are hard every year and there is a bit of luck involved. I for one got very lucky because the area I struggled with the most- inequalities- appeared only once in the five years I participated in. Training and solving as many past problems as possible helps, of course. There are a lot of resources available where you can learn the tricks and techniques needed to solve problems.

What were your strengths when it came to olympiad problems, and did they influence your specializations later in your career?

Combinatorics and geometry were my favourite questions to solve when I did the olympiads. After highschool I did my undergraduate at the University of Bonn where I developed an interest in algebra, choosing to specialise in algebraic geometry. A few years later when I was in my PhD programme, the university had a new professor of combinatorics. Since I had never taken a combinatorics course as an undergrad, and because I liked combinatorics so much in the olympiads I decided to attend his course. I liked the course so much that I completely changed my mind and decided to specialise in combinatorics instead. It was not a direct route from olympiad combinatorics to research combinatorics, but there surely was some influence.

IMO-flavoured geometry on the other hand rarely comes up in research mathematics. It is a beautiful area of maths and is readily accessible at a highschool level, unlike research mathematics which often demands years and years of learning prerequisites. IMO in general is about creative application of elementary tools that aren’t necessarily relevant to current research. For me personally it was very fun, and the problem solving skills that you develop help later.

Do you look at recent IMO problems and try to solve them?

I haven’t looked at the recent problems, but I used to. I was a coordinator in 2015-16 and then it was necessary for me to be up to date, but now I am busier and have a child to look after. Hopefully when my daughter is a bit older I will find time to get back to these things.

How do you find your research problems?

As a PhD student, you have an advisor to help with that. That’s probably why PhD programs are so long, because selecting the right problem is a tough skill to acquire. It is hard to find research problems- it might be unsolvable, people might have tried it for years with no success in which case there is little chance you will solve it. Research problems are very different from IMO problems, and you can spend anywhere from a few weeks to a few years on the same problem.Typically I try to look at papers and address the conjectures made in those. Another great way to come across problems is to talk to people, since everyone has different ideas and perspectives. Collaboration brings these together and can provide insight into new problems.

In the rest of the interview Lisa discussed some of her mathematical work and her areas of specialisation.

(Interview transcribed by Parth Shimpi)