Paris: On a Wednesday night in December, amid civic strife over proposed pension reforms, Cedric Villani, a prize-winning mathematician and a deputy in the French National Assembly, packed the Trianon Theatre and made the case that he should be elected mayor when Parisians go to the polls in March.

Cedric Villani (right) poses for a selfie while campaigning for mayor in Paris on Jan 25, 2020. Credit:The New York Times

"Is a scientist in politics incongruous?" he asked. "I do not believe that. Science can provide solutions to the greatest challenges of our time."

Mathematician-politicians are not unknown; the first elected mayor of Paris, in 1789, was Jean-Sylvain Bailly, a mathematician, astronomer and revolutionary. In the United States, the pro-science political action committee 314 Action has helped hundreds of candidates with STEM backgrounds run for office.

Such candidates promise to add a certain je ne sais quoi to the political fray — something intangible at the nexus of rigor, rationality, creativity and perseverance. Villani, with the campaign slogan "Le Nouveau Paris," envisions the City of Light as the city of the future: "Trust science to invent new urban lives."

Villani himself recently underwent a subtle reinvention — taking scissors to his signature Chopin pageboy with iterative trimmings that eventually resulted in bangs. The new hairstyle did not go unnoticed. "My adversaries have made a good job of portraying this as the fact that I was hiding something, that I was pretending," Villani said during an interview a couple of days prior at campaign headquarters, a third-floor flat with old oak floors and clean-slate white walls, one block over from Notre Dame.

Sitting on a sofa, he wore his usual three-piece suit and a spider brooch perched on the lapel. Shoes off, he was in sock feet — his preferred state for thinking and meetings and talks — although these days it's a rare indulgence.

"This is the laboratory of a new political bet," he said. "People here believe that it is not by following the rules of the political parties that you can improve the future."

Scientifically, Villani does not lack for credentials. After winning the Fields Medal in 2010, he became a pundit for sexy math. As a member of Parliament, he led a task force on artificial intelligence that produced the widely discussed report For a Meaningful Artificial Intelligence: Towards a French and European Strategy.

Some of the biggest challenges facing Paris, in his view, lie at the intersection of democracy and information technology. His top priorities include a plan to revamp municipal boundaries that would incorporate the suburbs within one metropolis, the environmental crisis and Paris' traffic problem. "I will use all means to make traffic flow and finally to escape from the traffic jams that undermine the daily lives of so many people," he vowed at the Trianon.

Perhaps it bodes well that one of Villani's areas of expertise is "optimal transport," investigating the most efficient allocation of starting points to end points. For instance, as Villani considered in a 976-page book on the subject —Optimal Transport: Old and New— there is the grand challenge each morning of transporting quantities of bread from bakeries to cafes. "The problem is to find in practice where each unit of bread should go, in such a way as to minimise the total transport cost," he wrote.

"I've been tackling complex problems my whole life before entering politics," he said in the northern autumn, when he confirmed his intentions to go it alone as a dissident candidate. (In July, he was passed over as the official candidate for President Emmanuel Macron's En Marche party.) On January 26, the president received Villani for a meeting at the Elysee Palace and asked him to make common cause with the party candidate, but Villani refused.

"My campaign for Paris continues in complete independence," he announced in a statement. As he noted in a text: "There is currently absolutely no reason to withdraw that I could possibly see."

Macron's party then expelled Villani, who has already picked up support. Isabelle Saporta, an environmental journalist, moved to run under Villani's flag, joining a growing climate coalition. "Getting involved with a very great mathematician, an out-of-party man, seduces me," she told Le Monde.

A mathematically optimized politician

As a mathematician, Villani has been nonpracticing since 2017, when he became an MP for Essonne, near Paris. The political play did not take his mathematical colleagues entirely by surprise. He loves the spotlight and is known as the Lady Gaga of mathematics. But they were sad to see him go.

"To have reached that level of mathematics, it certainly implies that you are in love with mathematics," said Michel Broue, a mathematician at the University of Paris. "And if you love it, it's terrible to leave it."

"Cedric always loves a challenge," said Sylvia Serfaty, who teaches at New York University's Courant Institute and studied with Villani at Ecole Normale Superieure in Paris in the 1990s. "The Fields Medal was a challenge for him. He did it, he got it. So once that was done, I think he was also just needing a new challenge."

He entered European politics about a decade ago, and moving in those circles, he met Macron, with whom he shared a "neither left nor right" mantra. Nonetheless, when courted to run for Macron's party, Villani declined, twice. He was director of the Henri Poincaré Institute and had big plans. Then, a few weeks before the presidential election in 2017 came the "fake news," as he called it, proclaiming that he was indeed a candidate. "I saw that the idea was popular," Villani said — so he reconsidered.

He asked the advice of Jean-Pierre Bourguignon, a former director of Institut des Hautes Etudes Scientifiques and the outgoing president of the European Research Council. Bourguignon told him it was a bad idea. "I feared that his weight as a scientist would be jeopardized by becoming a political statesman," he said. "I was concerned that he would diminish his impact, rather than increase it."

Villani is still wrapping his head around the transition. Sitting on the sofa, peering at his smartphone, he noted that the title of his latest book —Immersion: From Science to Parliament — has multiple meanings. "Immersion" describes his deep dive into politics (he considered titling it "Plunge"). And "with a little mischief," he wrote in the introduction, immersion also refers to a mathematical operation "by which one 'transports' a geometric object, without changing its intrinsic nature, into the heart of a new ambient geometry."

A combinatorial puzzle

Some of the attributes that made Villani a successful mathematician — his relentless energy, for one — no doubt helped him adapt to the political realm. But other aspects of his past might work against him.

"He comes from a world which is regulated by truth, or trying to approach truth," said Clement Mouhot, at the University of Cambridge, formerly a doctoral student with Villani and a key collaborator.

"Truth is more polemical in social sciences, but in mathematics it's not polemical. He has moved into another world which is regulated by other principles. Probably he sometimes gets it right, he sometimes gets it wrong."

He got it right in responding to crude questions from a TV presenter who asked whether Villani was autistic. "What would it change anyway?" Villani replied.

But with politics come ideological triangulations, alliances and counter-alliances. In 2014, Villani supported the incumbent, Mayor Anne Hidalgo, a Socialist, but her "method was lacking rigor, and results were not at the level of ambitions," he said.

Currently, Hidalgo is ahead in the polls, but by some accounts the race is still open, with no candidate having a decisive edge.

Scrolling through his smartphone in December, he marveled at the unfathomable complexities. "The combinatorics is amazing," he said. (Combinatorics is a branch of math concerned with combinations and permutations.) "It's really like a puzzle. You can meet a politician one day, and three weeks later, it will be a different speech. Three weeks later again, it will be another one, and then another one."

Paris mayor Anne Hidalgo gives a press conference ahead of squaring off against Cedric Villani at the March 15 poll. Credit:AP

A call came in that he couldn't ignore. "May I? This is a bit of an emergency." It was a former MP who had promised her support, calling with the news that she would no longer be in the Villani camp: She was moving to the En Marche camp, in an act of revenge against the Socialists.

"Wow, wow, wow, wow, wow," Villani replied. "That's politics," he said, afterward. "Politics is where rationality and irrationality meet. As well as passion."

Villani's bet and conviction is that bringing science into politics is important — at this moment, particularly. "It's my job to bring more rationality but never forget the irrational side," he said.

"There have been several times in the history of France in which science and politics were mixed together. It was always times of great social redistribution. One of these times was the French Revolution," he said. "One of these times was the Front Populaire, in the '30s. It would be a dream if it would be another one of these periods coming"— a dream problem, with increasing degrees of difficulty.

"He is not happy when things are easy," said Raphael Rouquier, another graduate of the Ecole Normale Superieure, now at the University of California, Los Angeles. "Politics is where he will have the hardest problems to deal with, so I am absolutely convinced that he is in politics for the long haul." Ultimately, he speculated, Villani wants to be president of the republic.

Villani, having put his shoes back on, dismissed that idea with a laugh. "This Paris election is so complicated, it is taking all my heart and brain," he said.

The New York Times

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