Scientists from 80 countries flocked to Berlin this week to attend the European Congress of Mathematics. One main takeaway: some of the continent's leading mathematicians are surprisingly young - and very down-to-earth.
Time is a precious resource for Peter Scholze (pictured above). Despite his constant lack of it, he's agreed to a short interview on the steps near the main auditorium at Berlin's Technical University. Scholze is polite, but you can tell he's more comfortable speaking to an audience of mathematicians than an audio recorder.
Since the 28-year-old became Germany's youngest professor at the age of 24 and the youngest ever Leibniz laureate at 27, both the academic and the media world have taken notice of him.
Now, five years on, the European Mathematical Society (EMS) has honored Scholze for his groundbreaking research in the field of arithmetic algebraic geometry. With two key lectures, he's one of the heavy weights at this year's European Congress of Mathematics, which saw 1,300 mathematicians from all around the world attend.
1,300 participants from all around the world attended the seventh European Congress of Mathematics in Berlin
'I don't believe you always have to understand everything in mathematics'
"I can't even make mathematicians understand what I'm currently working on," Scholze laughs. After finishing his lecture on the opening day, he tells me, quite a few colleagues told him that they had given up trying to follow his trail of thought halfway through the lecture. Does this bother him? Scholze shrugs. "I don't believe you always have to understand everything in mathematics," he says.
"Gerd Faltings, the only German to have been awarded the Fields Medal, regularly holds a lecture on arithmetic geometry at Bonn University. I used to go there as a student and I would never understand anything. But in hindsight I feel like I learned so much during that time. There's this misconception that certain parts of lectures are pointless if you don't get it straight away."
The 'lone genius' - an outdated concept?
This is something James Maynard finds equally frustrating. The 29-year-old number theorist has been a research fellow at the University of Oxford since 2013 and is one of this year's 10 EMS laureates. Despite being a celebrated young academic, Maynard doesn't believe that mathematics should be reserved only for the highly intelligent few: "It's unfortunate that maths has this air of being inaccessible. Professional mathematicians quite often have the same experiences as normal people, that there's an abstract concept and they don't get it straight away. In some ways it can be quite damaging for mathematics that there's this idea of the lone genius."
Three dregrees, three international prizes, but still down-to-earth: British mathematician James Maynard
James Maynard's research focus is one of mathematics' old mysteries: prime numbers. "Some of the most basic questions you might ask about them have been open for thousands of years. I find that really fascinating," he says with contagious enthusiasm. Maynard's reply when asked what he enjoys most about math has the potential to convince even the most committed skeptic that curve sketching and stochastics are beautiful things.
"In some sense I'm still just a kid who enjoys playing logical puzzles, but, for some reason I've convinced people to pay me to do this as a job," he laughs. "I guess at the same time there's this idea that mathematics underlies a huge amount of how the world works. It really excites me as a challenge that you can understand something fundamental about the universe just by sitting at your desk with a piece of paper."
A refugee's story: 'Math was a language I understood'
Sara Zahedi is this year's only female EMS laureate. The Iranian born 34-year-old has been an assistant professor at the Royal Institute of Technology in Stockholm since 2014. Her research focuses around computational methods to calculate and emulate dynamic geometry, for instance fluid interfaces. Her findings could benefit the production of biochips that are expected to replace tedious and expensive lab work when analyzing blood tests.
Today, these kinds of applications are what Zahedi enjoys most about mathematics, but the subject has always been an important part of her life. Her father was killed by the regime when she was a child and the family had to leave Iran. Zahedi came to Sweden on her own at the age of 10, her mother followed her a few years later. "I didn't have any friends and I didn't know any Swedish. But math was a language I understood. In math class, I was able to communicate with my peers and I was able to make friends by solving problems with them. I didn't do well in everything, but I do have nice memories of the math classes."
Just like her colleagues Peter Scholze and James Maynard, Sara Zahedi believes that in principle anyone can understand a lot of math. She is critical of her own scientific community for not communicating enough with the general public. "We should be reaching out to much younger age groups and educating them about how math can be applied in real life. I also think we should teach programming in schools."
A bleak future of post-Brexit science?
Peter Scholze, James Maynard, Sara Zahedi: three young mathematicians at the beginning of a highly promising career. How worried are they about the political instability in Europe and its potential effects on science? "I've heard from colleagues that professor positions in Britain were not taken because people were worried that after Brexit you may not be able to apply for EU grants," Zahedi says. "As a scientist, I believe the world is global, but I also understand that these things happen if you don't listen to people's worries. For me personally, there aren't any immediate consequences, but I think it's bad for the research community."
Being British himself, James Maynard is also worried to some extent. "Mathematics is a very tight-knit community, there's well established links between people and I can't imagine them breaking down quickly. But I can certainly imagine short term instability to do with funding issues and precisely how resources are allocated. I can imagine it being a concerning next few years, particularly for British and European science."
'There are just some things I would like to understand'
It's Monday, the first day of the congress. Peter Scholze strides across the stage of the packed main auditorium, clutching a laser pointer, his dark curls tied back like a professional soccer player. He explains the connection between his recent findings and the 1968 Fontaine-Winterberger theorem.
At the end of the lecture, the audience has no questions. An old gentleman gets up from his seat and addresses the young mathematician: "It will take 20 years to prove what you just outlined on the last few slides. How do you expect to manage that?"
Peter Scholze smiles a crooked smile, scratches his head, and replies: "I have already thought of some arguments. I don't think it will take that long." Maybe he is more of a genius than he is willing to admit. So what is next? "There are just a few things I would like to understand and that I'm thinking about," he says with the grin of a 28-year-old.