John Pardon Wins the 2026 Fields Medal for Work in Symplectic Geometry

Yeseveral eminent mathematicians inform completely different variations of the similar story about John Pardon.

Fifteen years in the past, János Kollár was seated subsequent to Pardon at a Phi Beta Kappa dinner. Kollár held an endowed chair as a full professor at Princeton University, the place he’d been educating for over a decade after stints at the University of Utah and at Harvard University as a member of its Society of Fellows, arguably the nation’s most prestigious postdoctoral fellowship. Which is to say, Kollár shouldn’t be dangerous at math. Pardon was an undergraduate, a couple of months into his senior yr.

Kollár had gotten caught on a query in the area of topology. At the dinner, he talked about it to Pardon in passing. Two weeks later, I obtained an electronic mail from Pardon — with the answer. “And it’s not just that he solved the question I needed, but he gave a much more general case in a very nice way,” Kollár recalled. I’ve discovered working with the 21-year-old a pleasure. It felt, he stated, “like working with a postdoc who had very good ideas.”

When Pardon graduated the following May, he was at the prime of the Princeton class. In his valedictory tackle, he requested his fellow graduates, rhetorically, “When is the last time you had a truly original idea?” He proceeded to reply his personal query: “The single most basic form of expression that humans draw upon is imitation of others, and so I think having an original idea may qualify you as being partially insane.”

By younger Pardon’s definition, present-day Pardon, who turned 37 in June, is greater than slightly loopy, in that he has had not one however many unique concepts. For these, the International Mathematical Union has now awarded him the Fields Medal, the most prestigious prize in arithmetic. “He started off solving well-known spectacular problems,” he stated Tobias Ekholm of Uppsala University. “At a slightly older age, he’s doing this same spectacular work, but he has this ability: He solves a famous problem but does it in a way that creates a framework, a whole new package, that will be useful to other people.”

Pardon, now at Stony Brook University in New York, shouldn’t be significantly prolific. “His publication list is not very long,” he stated Kai Cieliebak of the University of Augsburg. “But every paper he wrote is some kind of breakthrough paper. All of them appeared in very top high-level journals.” Furthermore, Cieliebak stated, Pardon “has done work in really a whole number of, to my understanding, completely separate areas of mathematics. Probably somewhere in his brain these things might be connected.” As his former scholar Mohan Swaminathannow at the Tata Institute of Fundamental Research, put it, “If John has a problem, he goes really deep and learns whatever is necessary for it.”

Pardon is tall and quiet. He has a delicate, unassuming have an effect on and a popularity for kindness. He’s prone to be the greatest mathematician in any room he walks into, however he wears this frivolously. He’s useful to colleagues, sporadically answering graduate college students’ questions on the on-line bulletin board MathOverflow. He generally weighs in on different topics as properly, with an invariable well mannered decisiveness. When one person, exasperated by their lack of ability to make restaurant-quality pancakes, requested for assist, Pardon provided recommendation: “The difference between ‘fluffy and fall-apart crumbly’ and ‘thinner, chewy, and sort of dense,’” he wrote, “is precisely governed by baking powder/soda. … If you want thin and chewy, omit the baking powder.” Pardon is as prone to ask for assist as he’s to supply it — airline ticketing, Schengen visas, and Wi-Fi passwords are as irritating and complicated to him as they’re to anybody. He is a father of two sons. He performs the cello properly and discovered to talk Chinese fluently in faculty, finally profitable a Chinese-language debate event held in Singapore.

Pardon declined to talk on the document for this profile. Many individuals who know him comment on his reluctance to say absolutely anything, least of all about himself. “He will only say something when he feels it is definitely correct,” he stated. Shaoyun Baia mathematician at the Massachusetts Institute of Technology who obtained his doctorate underneath Pardon.

“He refrains from saying too much,” he stated. Thomas Massoni of Stanford University, one other former scholar. “He knows so much that you really have to go fishing for his knowledge.” Multiple college students recounted conferences with him the place they needed to do nearly all the speaking — however he was all the time accessible, glad to fulfill with them, and a affected person listener. Ace Barış Kartalwho labored with Pardon whereas doing a postdoctoral fellowship, stated, “He is silent, but he says very useful things.”

“I think John knows who he is and probably doesn’t want to come across as a cartoon of ‘Here’s a boy genius who’s done such-and-such a thing,’” he stated David Gabaia former chairman of the Princeton arithmetic division. This is an actual, cheap concern. Nevertheless, when mathematicians talk about him, it is arduous to keep away from the conclusion that he’s a once-in-a-generation mathematical expertise.

Like a generational expertise in sports activities — Ohtani, Jordan, Messi — Pardon seems to be enjoying a unique recreation than his colleagues, all of whom are themselves exceptionally expert. But his achievements aren’t as simple to understand as a star athlete’s. Without years of research, it is powerful to grasp simply how shocking Pardon’s proof of a conjecture about six-dimensional manifolds actually is. An earlier Fields Medal had been awarded in half simply for making the conjecture.

So, with each intention of avoiding caricature, this is a glimpse of Pardon’s work in knot concept, topology, and symplectic geometry.

Knot a Problem

Pardon was already the star of Princeton’s math division when he sat subsequent to Kollár at that dinner throughout his senior yr. He’d grown up in North Carolina, and by the time he was in highschool, he was taking math programs at Duke University, the place his father was a math professor.

Once in faculty, he got down to remedy an open drawback in knot concept that he’d first encountered in highschool. So I’ve side awning his Stony Brook colleague Simon Donaldsonnow at Imperial College London, he had kind of given up on it by the finish of his junior yr. But a line of assault occurred to him whereas he was strolling in an English park that summer season. A number of months later, he had his proof.

Knot concept is a type of areas of arithmetic which can be simply what they sound like, but additionally by some means deeper and extra sophisticated than they appear. It is the research of knots — actually, given a size of rope, how are you going to tie it? (Mathematicians usually splice the ends of the rope collectively.) But this query generalizes to greater dimensions and otherwise structured areas, and in the finish, the construction of knots is a strong instrument for understanding the geometry and topology of the areas in which they are often embedded.

In 1983, the distinguished mathematician Mikhael Gromov made a conjecture a few property of knots known as the distortion. Consider two factors on a knot. You can measure the distance between them in two alternative ways. Either you possibly can journey alongside the rope itself, as if you have been a tiny ant, or you possibly can take a straight-line shortcut throughout area, as a (small) crow flies. It’s simple to intuit that the size you journey alongside the rope will all the time be not less than so long as the straight-line distance. For any given knot, there shall be a pair of factors for which the ratio between the distance alongside the rope and the straight-line distance is the largest. That ratio is the knot’s distortion.