His talk was about ideas, where they come from, how fragile they are. The topic was well received and would have gone down even better had he not argued for their free circulation, in a spirit of collaboration and not competition, and had he not then shown a lawyer’s letter aimed at researchers who published their work not only through the proper channels (that is, steep fee-charging academic journals), but also on a free-to-access digital platform. At which point, coming towards the end of his talk, he almost lost the audience, made up largely of start-up men, entrepreneurs, various manager types, for whom ideas were only as good as the money they earned – the more money, the better the idea.

But as he closed his talk, the audience remembered what they had enjoyed about it and broke into prolonged applause. They indulged his naivety – ordinary ‘nutty professor’ naivety. They only had to look at the long hair and the wacky clothes. A head in the clouds while others on the ground were busy meeting demand, raising capital, inventing tomorrow. But despite all that – and there was really no two ways about it – what a head! It commanded their respect, their magnanimity. They were softened by his high achieving, his being somebody; what did it matter if he didn’t always talk sense? Besides, he’d gone to the same grande école, the same highly selective university in Paris, as many of them; deep down, so they surmised, he was one of them.

Later, over food with friends, I narrated my tête-à-tête with the mathematician and his talk on free ideas before the businessmen. They smiled in all the right places, laughed at the rich men’s expense. What a character, your mathematician, they all said.

I couldn’t have agreed more. Over the years, seeing each other now and then, he and I stayed in touch.

✲

Why the surprise, Cédric had wondered in 2017, at the news of his entry into national politics? Economists already sat on the benches of the Assembly alongside jurists, teachers and farmers. Surely there was space as well for a mathematician? As in fact there had been in the past – the remote past, admittedly: Gaspard Monge, father of optimal transport theory (one of Cédric’s fields of research), had served as minister of the marine under the banner of the Revolution.

Cédric was director of the capital’s mathematics research institute at the time the announcement was made. In this capacity he employed a staff of twenty, organised international symposiums and conferences (when he wasn’t speaking at them), sought out funding. He was also a scientific advisor to the EU. In short, he liked making things run. It satisfied his passion for order and harmony, for taming an unruly world. Back in the nineties, at university, he’d even managed to get himself elected student union president. Having so many clubs, events, councils to organise, schedule and chair, made him feel focused and almost calm.

That period was the beginning of his extraordinary social, and sartorial, transformation. How timid – near paralysed by timidity – he had been back then, how heavy his heart when, leaving his family and Toulon at seventeen to board in the capital, he had gone out into the world. The other freshers, he remembered, seemed to him confident, sophisticated, selfaware. They were not above teasing the odd provincial boy so out of place here. ‘Call that being dressed, do you?’ they guffawed. He glanced down at himself through their eyes and saw the torn blue anorak and shapeless corduroy slacks and beat-up trainers he always wore. He had to do something about them, he suddenly thought – he had to change.

It was not long before he spotted an advertisement in the Métro for historical costumes, with a picture of a ruffle shirt that he thought would lend anyone personality. A few stops from his digs were the city’s flea markets, where he could wander, trying on capes and frock coats and top hats. He recalled then pianists he’d seen on stage (piano playing was a family pastime; one of his brothers would become a composer), how chic they looked. Unflappable. He thought of a young James Clerk Maxwell, nineteenth-century author of immense equations – photographed in a romantic three-piece suit. And so, gradually, merging these and other influences, he decided to dress according to his own secret code; to wear nineteenth-century ruffle shirts and a suit and floppy bow ties, to experiment with style and to embrace his quirks and oddness, instead of trying to fit into fashions which made no sense to him, the way they ceaselessly came and went. It was also during this time that he resolved to grow his hair out, to leave it long as it had been when he was a small boy, before it received the chop for school.

His new style found admirers at the university. They touched an ironic finger to his floppy bow tie, saying, ‘Looking sharp, man!’ and watched his cheeks blush. There was evident pleasure in his face. He was enormously pleased with his new appearance, how it distracted attention from his gawkiness, his limited social skills and lack of small talk. He would take being a hoot any day over being some sad geek. Wherever he went, people came up to compliment him on the get-up. ‘You look like a musketeer,’ they would say, or ‘Chopin’s second cousin,’ and forgetting his nerves he smiled and told them exactly when and where he’d bought each item.

Classmates became his friends – that, too, was thrillingly new. These friends resolved to round him out. ‘You don’t know anything,’ they told their unworldly companion. There was more to life than chess and piano playing and ping-pong (the only sport he’d ever excelled in). They introduced him to pop and rock music, accompanied him to the cinema where he viewed everything from Bergman to Almodóvar. In return, when they were strolling around an arrondissement, or drinking tea in their digs, he told them all about his studies, about Alan Turing’s work on probabilities and James Clerk Maxwell, who, along with Ludwig Boltzmann, gave us statistical mechanics. He told them what he was reading (he was always reading). He couldn’t speak more highly of Maxwell’s Treatise on Electricity and Magnetism and its diagrams which illustrated the invisible lines of force emanating from charged particles. The circular, repeating lines formed beautiful spiderwebs.

The spider brooches, like the pocket watch, would be later additions to his style. By the time they appeared on his lapel in his thirties, he was an increasingly distinguished professor in Lyon. One day, while browsing the shelves of a local gift and decoration shop, a few minutes’ walk from his apartment, he chanced upon the first specimen he ever bought. Encrusted with red glass beads bright in the sun, even dazzling. The thought of wearing it excavated a special pride in him that he could trace all the way back to boyhood. And since he had never done anything by halves, very soon he was collecting spider brooches wherever he travelled.

✲

The presidential contest in 2017 bore no resemblance to any in the history of France’s Fifth Republic. The Left and the Right both imploded during the spring campaign – one mired in discord, the other in scandal. All of which left the dark horse centrist candidate, 39-year-old former finance minister Emmanuel Macron, to surge to victory on the promise of a new politics.

Cédric had cast his vote for the new president and he was pleased when the incoming administration pledged to form a government broad enough to include civil society talents. Candidates from every walk of life, it was announced, would be fielded in the legislative races that were to be held in six weeks’ time. At once Cédric was approached by members of the presidential party urging him to run. They had just the constituency for him, in the Essonne. As he heard them out, his first instinct was to decline, but he was prevented by their polite insistence. He grew hesitant. He asked around. His wife – a biologist he’d met at university – and their two teenagers, a son and daughter, said they would support him whatever decision he reached. Friends were more divided. He tried to convince them, convince himself: he was forty-three, an age when such opportunities did not always come knocking twice. And here was a chance, perhaps, quite possibly, certainly, to use his time and fame for the greater good.

‘Leave mathematics?’ asked his colleagues in disbelief. ‘You’re a pure mathematician and you want to go into politics?’ Several tried to alert him to their misgivings. ‘You’ll be a big catch for them but what’s in it for you? Nothing but hassle, I reckon. And think of your research!’ Politics, they added, was a murky business, little more than glorified horse-trading and cynical calculations. Those and all the handshakes and selfies. Me-me-me. They didn’t have to say that they considered it altogether beneath them.

But Cédric was quite unfazed by their discouragement. He knew full well that many of his fellow mathematicians disdained politics almost as much as the world of television. Just as he also knew that some of these same colleagues would give anything to have their name cited prominently in the journal Acta Mathematica, or to be fêted at a symposium in their honour. Whereas his thoughts were increasingly elsewhere: the future of Europe, and the environment, and the scientific advances promised by artificial intelligence.

He realised then that his mind was already made up.

And so, following a short campaign in a university town favourable to the presidential party, he was comfortably elected and took his seat in the Assembly.

✲

Cédric’s name was in the headlines, both in France and overseas. In the months, then years, that followed – 2018, 2019 – I, like many, read with mounting interest the story they told of his burgeoning career in politics – its various twists and turns – while maintaining a respectful distance. Conscious of the long hours he put in, the many competing demands on his time, it would be several more years before I decided to learn more from the mathematician himself about his political engagement.

I learned that, back in 2013, Cédric had been asked by the think tank EuropaNova, on whose administrative board he sat, to attend a one-on-one meeting at the Elysée Palace. A major international conference at the Sorbonne was in the works, heads of several European governments were expected, and the think tank was counting on a number of France’s ministers to put in an appearance. It was in order to ensure their presence, and to sort other such matters, that Cédric found himself in the office of the deputy chief of staff.

The cordial atmosphere was helped by their closeness in age – the deputy chief of staff was even a little younger than Cédric. He nodded frequently as Cédric spoke. It would be sorted, the man said in turn. The ministers would be found. No problem at all. A strong and united Europe was vital to the nation’s interests. ‘Absolutely,’ Cédric chimed in. And meeting his interlocutor’s blue eyes – bluer for the crisp white shirt and rolled-up sleeves – he proceeded to divulge a knowledge on the topic of the European Union that could have seemed inexhaustible. Furrows of surprise creased the younger man’s forehead as he listened. He had expected the cravat, the spider brooch, but not this. Had he thought to ask the mathematician where all this knowledge, this passion, regarding Europe came from, Cédric would have answered: his family. Italian and Corsican and Greek blood mingled inside him. His mother’s sister lived between Vienna and Brussels, where her Austrian husband was director general of the European Union Military Staff.

Cédric’s emotion, it might have been known, had also to do with his father, with losing his father, a mere few weeks before, to a long and painful illness. The son’s grief still felt deep and raw. His father was only sixty-three. A man of zany energy, with a rebellious streak, much loved by his students of literature and classics in the south of France, and also a devout scholar of Lucretius, the Latin poet-philosopher for whom everything in the universe emerged from the infinite collisions of swerving atoms.

In another time and place the young deputy chief of staff could have engaged Cédric in a lengthy discussion on teaching Lucretius. He had read philosophy at university and would shortly toy with the idea of dropping politics and launching his own e-learning company.

Before he showed Cédric out he asked for his phone number; and the following summer he texted him to say that his edtech project was starting to look serious. He would need to start thinking about the curricula and hoped that the mathematician might make himself available to advise. Though, as it turned out, the future had other plans. A little while after his text message to Cédric, he was appointed finance minister. Within two years he would launch, not a start-up but a political party. The man’s name was Emmanuel Macron.

✲

At the National Assembly the mathematician’s arrival roused a dim animus in certain deputies. The Assembly was no place for someone like him, they fumed – Professor Calculus, the new administration’s useful idiot. His place was particles and nth dimensions, the invisible and incomprehensible. He should have stayed in his lane, they muttered, in his bubble.

One of the deputies who thought so was the leader of the farLeft party Les Insoumises, Jean-Luc Mélenchon. Ah, the maths wizard, Mélenchon thought, now there’s someone who needs setting straight. Would not have the faintest what is inside an employment contract, he thought. Probably imagines workers’ rights sprang up overnight. He said as much to the media.

Cédric was not offended. A silly misunderstanding, or else some clumsy joshing of the novice; the old politician had meant no harm. When Cédric bumped into him in the Assembly’s corridors he smiled and there followed a friendly exchange of words. Another deputy snapped the moment with his phone and shared the photo on social media. And later that day, at the close of the parliamentary session, Mélenchon walked across the chamber in full view and shook Cédric’s hand.

The mathematician-deputy was soon everywhere: on magazine covers and TV, and by the president’s side on state visits to Africa, China and the United States. But he also took his parliamentary work seriously. The other deputies could not help but notice. He raised himself in their esteem by his diligent sitting on several commissions, by his thoughtful proposals of new laws (notably on transparency in public life, and animal welfare), by producing a lengthy and detailed national strategy report on artificial intelligence.

Two hundred and thirty-five pages. Longer even than the dense and elaborate mathematical proof he had written in 2009, which had stretched to a hundred and eighty pages and solved a fifty-year-old open problem. For two years he had laboured to prove that the solution of a nonlinear, spatially periodic, close-to-stable-equilibrium Vlasov equation spontaneously evolves towards another equilibrium. Throughout this long labour he had been ably assisted by a younger colleague, Clément Mouhot, with whom he had gone at the problem from various angles, changing tack every time that they got stuck. Until, in a flash of insight, the missing idea had come to him as though out of nowhere, a spark swerving in a corner of his mind and giving birth to an entire new theorem.

Inevitably Cédric’s fellow deputies lauded his strategy report far more than they read it. They took in the salient points. Accelerate the development of European AI infrastructures. Train more digital specialists in France. Anticipate the impact of artificial intelligence on the workplace. It was the rare Assembly member who could drill down into the detail – neural networks and algorithms and supercomputers – the parts of the report Cédric had enjoyed writing the most.

Mathematics was never far from his mind and sometimes he missed its simple pleasures. For all the importance of writing a parliamentary report, it had nothing on composing a mathematical proof, which was much like composing a poem, Cédric always thought – the same taut phrasing, the same intuitive yet surprising logic behind the unfolding ideas. The same irresistible quest for truth and beauty. Never would he tire of typing the opening incantation let (so and so) be (such and such), or the lovely shapeliness imparted by the if and only ifs. A hundred revisions might separate an initial draft from its final form, a hundred drafts screwed up tight into repellent balls before arriving at the one that would be publishable. He never minded. Each result was its own reward. The main lines of an especially stylish proof could linger in his mind as effortlessly as music.

And music, whether rock or a Prokofiev sonata, had been a constant presence whenever he’d paced back and forth in his study, sitting only to jot equations in a notebook or revise a step in his reasoning. He liked listening to a French folk ballad he’d heard his parents play when he was a boy. A song about passion and letting go: ‘I want to be capable of loving you, for two years, three years, ten,’ the balladeer sings, ‘loving you till the strength to love you fails me … so that I might love someone else.’ Cédric knew all the words, every note and intake of breath; he’d played the song that many times.

Even on those evenings and weekends when he’d been on his own, his wife and children staying with grandparents, he would close the door of his study behind him as he worked, as if not wanting to let the music out. Pacing always in his deep-thinking clothes – some loose T-shirt in summer, in winter a baggy sweater. Up all hours. Endless evenings during those two years working on the theorem, spent with his music (on low when the children were home and sleeping) and laptop and pen and paper, unable to leave this or that formula alone, carried further and further away by his thoughts – perhaps only an earthquake might have shaken him out of them.

‘Marsu,’ his wife might have wished to whisper from the doorway, using the nickname given to him at uni for his bouncy way of pacing around. ‘Do you know what time it is? Hello, hello? Earth to Marsu.’

But she knew well enough when to leave him with his equations.

They were everywhere in his parliamentary work too, Cédric thought, though perhaps he alone in the Assembly saw them in the pie and bar charts displayed in committee presentations, or in the statistics cited during a debate in the lower chamber. He alone might glimpse an intriguing possible link between, say, the nation’s income distribution and the Boltzmann distribution in statistical physics. Some part of him then could feel lonely, having such singular thoughts in the midst of these rowdy politicians who frequently shouted over one another until called to order by the speaker. But another part of him, much the larger, was thoroughly used to thinking apart and at ease doing so. He always had.

✲

Sometimes, coming out of the Assembly into the soothing dark of a late spring evening, Cédric thought he would like nothing better in that instant than to take to the city’s streets as in his student days, to walk his thoughts, or else simply to observe the surrounding facades and faces as he strolled. He loved Paris in these hours when the streets seemed to grow wider and the passers-by were often merry. He relived the stirring nights when he and several university classmates had chased each other through these same cobbled streets into the small hours in a version of the game called hare and hounds; the ‘hounds’ pursuing not a trail of chalk or paper but calls made at successive phone booths, each booth approaching the city centre and the students’ dorms.

He remembered those nights with a double nostalgia, when on the trail of a classmate, getting high on the chase and lured by the approaching solution, he’d experienced the same rush he’d felt as an introverted child engrossed in his favourite detective tales, French translations of The Three Investigators. He’d come a long, long way indeed.

Several of these streets were named after mathematicians: Rue Laplace, Rue Sophie-Germain. It occurred to him that perhaps someday in the future his own name would likewise be given to a street here. There was already a theory of curvature named after him – the Lott-Sturm-Villani theory – a recognition of his ever-growing legacy.

✲

In September 2019, putting an end to a summer of speculation, Cédric made it known that he was running for mayor of Paris. His candidacy was likely doomed from the outset, since he was obliged to go up against his own party.

All summer the government had tried and failed to talk him out of running as an independent. The official candidate – a rather bland apparatchik in a suit, a safe pair of hands – had been selected internally in early July, through the proper channels, a spokesman insisted. It was suggested by some that this decision had come from the top – President Macron had long ago made up his mind. In any event, now was the time to pull together as a party and as a movement, they all said. You owe us your loyalty, they told Cédric, don’t you?

But no, the mathematician did not seem to think in such terms. He hadn’t acquired the politicians’ social codes, or else having done so seemed willing to transgress them when he believed they were unfair.

Cédric had sought the party’s backing for his mayoral run in the beginning, only to finish well and truly stitched up. The party had chosen to disregard all the polls that showed him to be by far the most popular contender with the voters. They had ignored the numerous artists, scientists and public intellectuals who had come out in favour of Cédric’s candidacy. They had gone back on the promise of a new politics which he (and they themselves) had been elected to embody. How then, in all good conscience, could he simply swallow his words and fall in line behind the other man?

The guy’s an idiot, the apparatchik’s team concluded bitterly after months of futile back-and-forth. He’s going to split our vote and gift Paris – a city of two million – to our opponents. No one could say they hadn’t tried to reason with him. To help him digest his disappointment they had made all the right noises about involving him in a manifesto that would be as bold as it would be inclusive. They had alternated between the carrot – Cédric Villani, Minister of Higher Education and Research, how did that sound? – and then the stick: he would risk exclusion from the party if he persevered. When nothing else worked they had asked him to think of his health and his family. Was he really tough enough for such a long and bruising campaign?