In 2014, the prestigious Fields Medal — considered by some to be the equivalent of a Nobel Prize in mathematics — went to Artur Avila, Manjul Bhargava, Martin Hairer and Maryam Mirzakhani. The International Mathematical Union awards the prize every four years, naming up to four recipients under the age of 40. The selection is based on major early-career contributions, but also on the promise of future achievements — hence the age restriction.

Who will win in 2018?

One name on everyone’s shortlist is Peter Scholze. At 28, he’s been a full professor at the University of Bonn for four years. He’s the youngest-ever recipient of Germany’s distinguished Leibniz Prize. Now he’s rumored to be a top contender for the next round of Fields Medals.

As Erica Klarreich reports in her profile of Scholze for *Quanta Magazine*, other mathematicians regard him with “a mixture of awe and fear and exhilaration,” in the words of Bhargav Bhatt, a mathematician who has collaborated with Scholze. When Scholze was 22, he condensed a number theory proof from 288 to just 37 pages. His doctoral thesis on perfectoid spaces and the weight-monodromy conjecture has had far-reaching consequences for arithmetic geometry. And he has also made important contributions to the famously challenging Langlands program — the web of conjectures connecting number theory, geometry and analysis.

Mathematicians brace themselves when Scholze moves into their fields. “It means the subject is really going to move fast,” Bhatt said in the profile. This is yet another reason why Scholze is such a heavy favorite for the Fields.

Scholze himself tends to shy away from all the buzz surrounding his achievements. “At times it’s a bit overwhelming,” he told Klarreich. “I try to not let my daily life get influenced by it.”

Scholze has three more chances to win a Fields Medal before reaching the age limit. If, as many predict, he takes the prize at the 2018 International Congress of Mathematicians in Brazil, he will become one of the youngest winners in history.

*For more on this story, check out Erica Klarreich’s profile, “The Oracle of Arithmetic,” on **QuantaMagazine.org**.*

I hope he will win it in 2018. He is very inspiring to math students. Another nice thing is that there are more Germans with good chances to win a Fields Medal in 2018. It's maybe a signal that Germany is coming back to be one of the great powerhouses in mathematics. I may be wrong, but it seems that most math activity nowadays seems to come from USA, France, Germany, China… Maybe then Japan, Canada and Russia… Other countries look so much behind, and when they produce some great mathematicians they are generally quickly hired by USA, Canada, France, Germany… China, India, Russia and Brazil cannot compete with them in economic power. Or maybe China and India can, despite low per capita GDP, because they have huge populations, and they could be "patrons" of a few top places in their countries if they wanted (maybe this is already happening in China).

Anyway, it's always nice to try to predict the winners, even when we have no clue about what is happening in math, haha… Other than Peter Scholze, I hope that Ciprian Manolescu will get one too. He is a great mathematician, and his personal web-site is very useful to those who want to start studying topology, with many book recommendations and things like that. It would be nice to see another woman winning it, maybe Maryna Viazovska or Sophie Morel? I would like to see fellow Brazilian Fernando Codá Marques winning one too, specially because the ICM will be in Brazil, but if another differential geometer gets it I will like it very much too. 😀

By the way, I think that the age limit should be changed to 50. People live more years nowadays, and at 50 they should still be considered young mathematicians… I remember that Vladimir Arnold did not get a Fields Medal, and even when he was "old" he was producing new amazing mathematics… For example, Arnold's discoveries on the topology of plane curves in the 1990s where done when he was already past the age of 50.

Anyway… As of now, it seems there are like more than 80 people (?) with good chances, and only Scholze's medal is almost guaranteed (?). 🙂

I do not understand how the title of this article relates to the content. What handicap? Am I missing something?

I hope the Brazilian Fernando Codá Marques win!

This is one of the definition of handicap in Merriam-Webster's Dictionary:

to assess the relative winning chances of (contestants) or the likely winner of (a contest)

Dear J Plasmeier,

To elaborate on Yu-Chi Huang's response, in golf, a "handicap" is a way to make a contest with more even odds when one competitor is seen to be better than another; if I were golfing against Tiger Woods, he will certainly win; but if you wanted to make a more interesting bet, you should bet on whether he will beat me by, say, 20 strokes (or maybe 40, or 200–I'm not much of a golfer); 20 strokes would be my handicap. Deciding on the relative strengths of players is therefore "handicapping".