Kepler Asked. Newton Argued. She Answered.
Maryna Viazovska cracked a problem Kepler posed in 1611, became the second woman ever to win mathematics’ highest honour — and did it while her country was being invaded.
By Teona Abuladze · 7 min read
Start with something you can see from your kitchen.
Stack oranges in a pyramid. That arrangement — the one every greengrocer arrives at without thinking — fills about 74% of the space. In 1611 Johannes Kepler wrote it down in a small essay on snowflakes and asserted, essentially without justification, that no arrangement could ever do better.
He was right. It took 387 years for anyone to prove it. The three-dimensional case was finally settled by Thomas Hales in 1998, with a proof so vast it needed computers to check.
That is how hard this problem is. And three dimensions is the easy one.
The dimensions nobody could touch
Mathematicians don’t stop at three. Sphere packing matters in higher dimensions because it isn’t really about fruit — it’s about information. Error-correcting codes, the mathematics that keeps your phone call intelligible and your data intact, are packing problems in disguise.
But every dimension behaves differently, and the optimal answer changes completely depending on which one you’re in. Four dimensions: unsolved. Five, six, seven: unsolved. Most of them remain unsolved today.
Then there is dimension eight, where something strange lives: a structure called the E8 lattice, so symmetric and so perfect that mathematicians had suspected for decades it must be the answer. Suspected. Nobody could prove it.
In 2016, Maryna Viazovska did — in a paper of about 23 pages.
There is a detail here that mathematicians still talk about. A method had existed since 2003 that could crack these dimensions if someone could construct one specific, extremely elusive function. For thirteen years, nobody could. Viazovska built it, using modular forms — an area of number theory that looked entirely unrelated to stacking spheres.
Then, within a week of her paper appearing, she and four collaborators used the same idea to solve dimension 24 as well.
Two of the great open problems in geometry. Weeks apart.
Four centuries of failure. Then a 23-page paper.
What the viral posts get wrong
You may have seen this story going around: she solved what Kepler and Newton couldn’t.
The truth is more interesting than the meme, so let’s be exact.
Kepler stated the conjecture in 1611 — that part is right, and the four-hundred-year framing is fair. Newton, though, wasn’t stuck on this problem. He argued with his colleague David Gregory in the 1690s about a related question — how many spheres can touch one central sphere, the so-called kissing number. Newton said twelve; Gregory thought thirteen might fit. Newton was correct, and it took until 1953 to prove it.
So it isn’t quite that Newton failed where she succeeded. What’s true is stranger and better: this family of problems, which looks like something a child could ask, has defeated some of the finest minds in the history of science for four hundred years — and Viazovska walked into the eighth dimension and closed it.
The war
In February 2022, weeks after she learned she had won the Fields Medal — mathematics’ highest honour, awarded once every four years to a handful of people under forty — Russia invaded Ukraine.
Viazovska was born in Kyiv in 1984 and studied at Taras Shevchenko National University. She now holds the Chair of Number Theory at EPFL in Switzerland. But her family was still there.
She did what many women in that position did: she got them out. Her mother and her sisters. She helped organise the escape, then helped resettle them — while preparing to accept a prize that would put her in the history books.
Her nephew Maksym, six years old, began sleepwalking after the first days of the invasion. She has spoken about that plainly: extreme stress and extreme fear in children are not free, and the bill arrives later.
She has also spoken about what the war has done to Ukrainian education — a quarter of students gone from Kyiv University, children scattered across Europe learning in languages that aren’t theirs.
And then she said the thing that belongs on a wall:
“Tyrants cannot stop us from doing mathematics. There is at least something they cannot take away from us.”
The second woman in eighty-six years
Viazovska is only the second woman to receive a Fields Medal in the award’s history. The first was Maryam Mirzakhani, in 2014, who died of cancer three years later at forty.
Two women. Since 1936.
Sit with that number, because it isn’t a statement about female mathematical ability — it’s a statement about who was permitted into the rooms where this work happens, who was funded, who was mentored, who was believed. Viazovska is from a generation and a country where a girl could go to maths olympiads and be taken seriously, and it shows.
She is also, quietly, evidence against the way we usually tell these stories. She is married to a fellow physicist, her schoolmate; they have two children. She runs, she draws. She did the most celebrated mathematics of the decade while raising a family and, later, while getting her relatives out of a war zone.
Nobody asks the male medallists how they managed it.
Why she belongs in this magazine
Because when people ask — and they still ask — where are the great women, then?, this is the answer, alive, working, forty-one years old.
Not a woman erased by history like Elizabeth Magie. Not a woman whose credit was taken. A woman who solved it, was recognised for it in her lifetime, and stood on the stage in Helsinki to collect the medal while her country burned.
The oranges in your kitchen have been arranged the same way for four hundred years, and for four hundred years nobody could prove it had to be so. Then a woman from Kyiv proved it — in a dimension you cannot picture, using tools nobody expected, in a matter of weeks.
Shansi means chance. She took hers. Watch what happens when women are given theirs.
Sources: International Mathematical Union; Quanta Magazine; Scientific American; Nature; Max Planck Institute for Mathematics; Annals of Mathematics.
