# A Happy Mathematical Birthday

# BLOG: Heidelberg Laureate Forum

During yesterday’s boat ride on the Neckar River, I had the chance to interview one of the youngest participants in this year’s Heidelberg Laureate Forum: Lisa Sauermann, an undergraduate at the University of Bonn, who was celebrating her 21^{st} birthday. Even at such a young age, she has already accomplished some amazing things. She is one of only five people ever to win four gold medals at the International Mathematics Olympiad (IMO), and in her last year (2011) she won with a perfect score.

I found Lisa to be a friendly and amazingly confident person for her age, clearly comfortable with speaking English and comfortable speaking to a journalist. She has already done many interviews, with reporters who were invariably shocked to discover that the world’s top high-school math competitor was a girl. However, she says, no one at the Olympiads ever treated her differently because she was female. “Only journalists ask about it,” she says.

Lisa says that her first math competition came when she was 10 years old, and in fourth grade. She was too young to qualify for Germany’s national competition, so she had to settle for a bronze medal at the regional level. “That motivated me to train more,” she says.

The IMO originated in Eastern Europe, and the old German Democratic Republic (East Germany) had a very strong record in the competition. Even today, she believes that math competitions are more popular in eastern Germany, and the training programs there were a big part of her success. “In Saxony, where I live, we have a one-week training camp, and the University of Dresden had weekly meetings” for math competitors, she says. The university sessions were especially valuable for broadening and deepening her experience of mathematics. “In high-school courses you only calculate,” she says.

At the International Olympiads, she says that her most cherished memories were “meeting other young people and trading ideas.

When I ask her what her favorite problem was from her five years at the IMO, she instantly tells me two of them. One was the “grasshopper problem,” the sixth problem in the 2009 Olympiad. Imagine that a grasshopper stands at the origin of the number line. The grasshopper is to make N jumps of various integer lengths, which he can make them in any order. However, on the number line there are placed (N-1) traps that he has to avoid. Can he always find a way to escape the traps? Clearly, if one trap is at the endpoint (the sum of the lengths of the N jumps) he can’t avoid that one. But otherwise, it turns out, he always can. The IMO asked the competitors to prove that fact.

It’s a beautiful, first-rate problem, because it looks as if it must be easy and yet it’s ferociously hard. Only three competitors in the world’s most elite mathematics competition got a complete solution, and one of them was Sauermann. (I asked her not to tell me the solution. Like any mathematician, I want to think about the problem first!)

Both Lisa and Jens are now studying at the University of Bonn. It’s a natural choice for an Olympiad medalist, with a math faculty that includes Gerd Faltings (Germany’s only Fields Medalist, and one of the laureates at this year’s Heidelberg Laureate Forum) as well as Peter Scholze (a teammate of Sauermann at the 2007 Olympiad, who is now a math professor at the age of just 25). Now that she is studying math in the university, she says, “It’s absolutely different. It is a new world. I feel as if I’m done with Olympiad math—that was a hobby and now I’m getting serious.”

Within a few years, I’m sure that Lisa Sauermann will be teaching us all new mathematics. For now, happy birthday, Lisa, and enjoy the rest of the Heidelberg Laureate Forum!