In 2010, a 22-year-old graduate student named Peter Scholze won widespread acclaim after condensing a 288-page proof into a svelte 37 pages. Two years later, he was hired by his alma mater as a full professor, and earlier today, his contributions to the study of arithmetic geometry earned him a spot amongst the most influential mathematicians in the field.
At 30 years old, Scholze—now a professor at the University of Bonn in Germany—is one of the youngest recipients of the Fields Medal, an award often described as the Nobel Prize of mathematics. The four newest winners, honored this morning at the International Congress of Mathematicians in Rio de Janeiro, form an eclectic group: In addition to Scholze, there’s 40-year-old Caucher Birkar, a University of Cambridge professor who arrived in Great Britain as a refugee fleeing Iran; 34-year-old Alessio Figalli, an expert at the Swiss Federal Institute of Technology who specializes in optimal transport, or the most efficient method of moving materials from one location to another; and 36-year-old Akshay Venkatesh, a math whiz based out of Princeton’s Institute for Advanced Study who is being recognized for his “profound contributions to an exceptionally broad range of subjects in mathematics.”
According to the International Mathematical Union’s website, the Fields Medal is awarded every four years in recognition of “outstanding mathematical achievement for existing work and for the promise of future achievement.” In addition to garnering universal acclaim within the field, recipients receive a cash prize of 15,000 Canadian dollars, or roughly $11,540. All honorees must be 40 years old or younger.
Quanta Magazine’s Kevin Hartnett writes that Cambridge’s Birkar was raised in the Kurdistan province of Iran amidst ongoing conflict with neighboring Iraq. He showed an affinity for math from a young age, attempting to solve problems in his older brother’s schoolbooks and, during high school, reading borrowed library texts all through night.
Birkar began his undergraduate education at the University of Tehran, where he joined the math club and admired the photographs of Fields medalists adorning its meeting room walls.
“I looked at them and said to myself, ‘Will I ever meet one of these people?’ Birkar tells Hartnett. “At that time in Iran, I couldn’t even know that I’d be able to go to the West.”
In his final year of college, Birkar traveled to England. He applied for political asylum, enrolled at the University of Nottingham upon receiving approval and set out to pursue a career in algebraic geometry, a field that The New York Times’ Kenneth Chang describes as an investigation of the “connections between numbers and shapes.” Paolo Cascini, a colleague who works at Imperial College London, tells The Guardian’s Nicola Davis and Naaman Zhou that, in layman’s terms, Birkar’s work focuses on the classification of geometric shapes and description of their building blocks.
Figalli, the optimal transport expert, started his academic career as a Classics student, Quanta’s Hartnett writes. He was drawn to math during high school after realizing that many problems’ solutions were not always straight-forward but required invention and ongoing innovation. This concept stands at the core of optimal transport, which allows mathematicians to compare shapes by thinking about the most efficient way of converting one into the other.
Venkatesh, the Princeton mathematician renowned for his expertise in an array of subjects, has long been labeled a prodigy: He started college at age 13, Quanta’s Erica Klarreich notes, and graduate school at age 16.
The Fields Medal is often awarded to individuals who solve seemingly unsolvable problems, Venkatesh tells Klarreich, so he was surprised to be recognized for his recent speculative work, which focuses on the Langlands program, a network of connections between number theory, geometry and analysis.
“A lot of the time when you do math, you’re stuck, but at the same time there are all these moments where you feel privileged that you get to work with it,” Venkatesh said during the awards ceremony. “You have this sensation of transcendence, [and] you feel like you’ve been part of something really meaningful.”