Figalli celebrated alongside co-winners Caucher Birkar, Peter Scholze and Akshay Venkatesh in the Rio de Janeiro ceremony of the prize, which is awarded every four years.
But he had an unlikely start to his career.
"Until high school, his only concern was playing football," the International Congress of Mathematicians (ICM), which oversees the prize, said in its announcement.
That changed after Figalli entered the International Mathematical Olympiad, awakening a fascination for math that today has seen him become a leader in calculating variations and partial differential equations.
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Figalli, now 34 and at ETH Zurich, said the prize "gives automatic visibility and opens up doors to us." In addition to pursuing his own high-level research, he says encouraging young mathematicians "is something of a duty."
But he joked that the one equation still baffling him is how to spend more time with his professor wife.
"I have work for the next 30 or 40 years. But there is one problem I really hope to solve soon: that is me and my wife living in the same city," Figalli said.
The Fields medal recognizes the outstanding mathematical achievements of candidates who were under 40 years old at the start of the year. At least two and preferably four people are honored each time. In 2014, Maryam Mirzakhani, from Iran, became the award's first and so far only female winner. She died in 2017.
Another of the 2018 winners, Kurdish refugee turned Cambridge University math professor Caucher Birkar, had his gold medal stolen minutes after receiving it. Less than an hour had passed since Birkar, a 40-year-old specialist in algebraic geometry, had been handed his 14 karat gold medal when his briefcase went missing. The organizer behind the event, the International Congress of Mathematics, said it "profoundly regrets" the incident.
But Birkar celebrated his achievement as a victory f or Kurds, saying: "I'm hoping this news will put a smile on the faces of those 40 million people," he said.
As for Germany's Scholze, who was awarded the Fields medal for his work in arithmetic algebraic geometry, he says there'll never be an end to the challenges he faces.
"There are an infinite number of problems," said Scholze, who is at the University of Bonn and is only 30 years old. "Whenever you solve a problem, there are 10 more coming."
The fourth laureate, Venkatesh, is an Indian-born, Australian-raised prodigy who began his undergraduate degree in mathematics and physics at the University of Western Australia when he was just 13.
Now 36 and at Stanford University in the United States, Venkatesh specializes in number theory and describes his work in terms more often associated with the artistic fields.
"A lot of the time, when you do math, you're stuck. But you feel privileged to work with it: you have a feeling of transcendence and feel like you've been part of something really meaningful," Venkatesh said.