Every four years since 1936, the prestigious Fields Medal is awarded to a maximum of four young mathematicians (under 40) for outstanding accomplishments. The awarding organization is the International Congress of the International Mathematical Union.

It’s seen as the “Nobel Prize in Mathematics,” even though it isn’t formally a Nobel. But in one way it’s better: it’s awarded every four years instead of yearly. Since the Nobel Prize in any area can be given to up to three people, the maximum number of Nobelists in four years is twelve—compared to four for the Fields.

The down side, if there is one given the immense prestige the Fields confers, is that it doesn’t come with a lot of dosh—about $15,000 Canadian. In contrast, a Nobel Prize comes with a sum of 10 million Swedish kroner—almost exactly one million U.S. dollars. (If there are two winners it’s split evenly, if three the division is decided by the Swedes.) $15,000 won’t enable you to buy a beach house, as Feynman did with his Nobel money. But money seems of much smaller consequence than the fact that winners are topped for the life with the halo “Fields Medal Winner.” (See the movie “Good Will Hunting.”)

The Fields was just awarded to four people, including only the second woman ever to win. And she’s from Ukraine!

Click to read:

The details and accomplishments of the four are in the article, but here are their names and institutions:

Hugo Duminil-Copin;Institut des Hautes Études Scientifiques, France andUniversity of Geneva, Switzerland

June Huh;Princeton University, US

James Maynard;Oxford University, UK

Maryna Viazovska; École Polytechnique Fédérale de Lausanne, Switzerland

Viazovska is the only woman to win the prize besides Maryam Mirzakhani of Stanford, who won in 2014 and is of Iranian descent.

I’ll highlight Maryna Viazovska to applaud not only the advance of women in math, but as a boon to the much-beleaguered Ukraine. Here’s what the NYT says about her in a summary by Kenneth Chang:

Maryna Viazovska, a Ukrainian who is now a professor at the Swiss Federal Institute of Technology in Lausanne, is known for proofs for higher-dimensional equivalents of the stacking of equal- sized spheres. She is also only the second woman ever to win the Fields Medal.

Of the 60 mathematicians who won Fields Medals before this year, 59 were men. In 2014, a Stanford mathematician, Maryam Mirzakhani, was the first and, until now, the only woman to receive one.

“I feel sad that I’m only the second woman,” Dr. Viazovska said. “But why is that? I don’t know. I hope it will change in the future.”

Dr. Viazovska’s work is a variation of a conjecture by Johannes Kepler more than 400 years ago. Kepler is best known for realizing that the planets move around the sun in elliptical orbits, but he also considered the stacking of cannonballs, asserting that the usual pyramid stacking was the densest way that they could arranged, filling up just over 75 percent of the available space.

Kepler could not prove that statement, however. Neither could anyone else until Thomas Hales, then at the University of Michigan, succeeded in 1998 with a 250-page proof and, controversially, the help of a computer program.

Proving something similar for the packing of equal-size spheres in dimensions higher than three has been impossible so far — with a couple of exceptions.

In 2016, Dr. Viazovska found the answer in eight dimensions, showing that a particularly symmetric packing structure known as E8 was the best possible, filling about one-quarter of the volume. Within a week, she and four other mathematicians showed that a different arrangement known as the Leech lattice was the best possible packing in 24 dimensions. In high dimensions, the filled volume is not very full, with the Leech lattice of 24-dimensional spheres occupying about 0.2 percent of the volume.

What’s so special about eight and 24 dimensions?

“I think that’s a mystery,” Dr. Viazovska said. “It’s just in these dimensions, certain things happen which don’t happen in other dimensions.”

She said that a method that generally gives an upper bound on the packing density turns out to be the exact solution in these cases.

High-dimensional sphere packings are related to the error-correcting techniques used to fix garbles in the transmission of information.

She said that the Russian invasion of Ukraine had taken its toll on her family. “It’s very difficult,” she said.

Her parents still live near Kyiv, Dr. Viazovska said, while her sisters, nephew and niece left and joined her in Switzerland.

Here’s the Fields Medal (caption from Wikipedia, the Latin translation is “Rise above oneself and grasp the world”), and a photo of Viazovska:

Maryna Viazovska, from the *Guardian*:

h/t: Tom

Sub

I remember the Oxford guy from Numberphile.

Congratulations! I’m always fascinated by seemingly simple and intuitively obvious conjectures—such as a triangular stack of cannonballs taking up minimal volume—that are nonetheless so difficult to prove. Obviously true but still a mystery. In eight dimensions, the challenge of a proof is almost unimaginable!.

My good friend the late statistician I.J. Good once told me that “Mathematics isn’t something you understand. It’s something you get used to.”

It’s not even informally a Nobel. An “informal Nobel prize” would be the economics prize. Yes, it’s a prestigious award in its field (but not the only one). A Pulitzer prize is not an informal Nobel. I know what you mean, but it is really only the economics prize which is an informal Nobel.

Three people: either 50/25/25 or a third each. There is actually a scheme; I’ll post details if anyone is interested.

I’d like to know about all four of them. Why ignore the other three just because they’re male?

You know what? I’m getting really tired of comments like this. I did not ignore the other three; I gave their names and a link to the NYT article where their accomplishments were outlined. There was no space to go into detail about all of them, and because the Ukrainian was only the second woman to win, and a Ukrainian to boot, I highlighted her.

Are you telling me that you can’t go to the internet to find the other ones, and it’s my responsibility to enlighten you (it’s not), or are you beefing because I highlighted the woman? Either way, this does not reflect well on you. Why would you want to go after me because I chose one to highlight and gave all their names and links.

A woman achieving this kind of acclaim is very unusual. I did not “ignore” the men, and you can bloody well apologize for your rudeness or go away. Seriously, it’s this kind of hostile nitpicking that sometimes makes writing here a chore. “I’d like to know about all four of them.” THERE’S A BLOODY LINK TO THE ARTICLE AND EACH OF THEIR NAMES LINKS TO THEIR BIOGRAPHY AND ACHIEVEMENTS, and you want me to enlighted you. Jebus!

I remember seeing a video about the 8 and 24-dimensional (and 3-dimensional) sphere packing problem on the regrettably now-defunct YouTube channel PBS Infinite Series. It’s very interesting stuff, and a lot of fun to think about (or to TRY to think about). Thank you for sharing this.

Numberphile videos with :

James Maynard (list) : https://youtube.com/playlist?list=PLt5AfwLFPxWJdwkdjaK1ogByEGiVHdEnM

June Huh on g-conjecture : https://youtu.be/4445Mbw8pYg

Congratulations to all of the winners. Solving the problem of sphere packing in 24-dimensional space is entirely beyond anything I can imagine.

It is perhaps an unfair question, or at least one that some might say should not be asked, but is it possible that the selection of Viazovska was influenced to some degree by the current political situation? Can anyone from the field of mathematics say anything on this? Would she have been a shoo-in or an obvious choice if Ukraine had not been invaded?

It’s perhaps a rather silly comparison, but I had a similar feeling when Ukraine won the European Song Contest this year, as the Ukrainian act was truely aweful. Of course, all the other acts were similarly atrocious, so it’s hard to say one way or the other.

The selections were made in January (before Russia invaded) and the winners were notified then, and sworn to secrecy. I’m a mathematician, or at least can call myself one since I got a doctorate, and her work is seriously top-notch.

Thanks for that!

James, I think that you’re a mathematician! I mean, unless your doctorate is from Corinthian, or Phoenix, or… …or Trump U.

In which case, maybe you can at least get your student loan payments back.