Master of chaos wins $3M math prize for ‘blowing up’ equations

April 18, 2026

5 min read

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Master of chaos wins $3M math prize for ‘blowing up’ equations

For decades, the mathematician Frank Merle has been embracing the messy math behind lasers and fluids

By Joseph Howlett edited by Lee Billings

Frank Merle studies nonlinear equations, which respond in dramatic ways to tiny shifts in their inputs.

IHES/Christophe Peus

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Frank Merle is used to confronting a messy world. He works on the mathematics of highly nonlinear systems—ones that respond in dramatic, unpredictable ways to even the smallest changes. It’s the same math that explains how, under the right conditions, the atmosphere above a barren plain can produce a roiling tornado.

A linear equation is something like y = 2x, which states that the value of y doubles whenever you double the value of x. But most equations are much more sensitive to changes to their input. A highly nonlinear system is defined by equations that can jump from zero to infinity almost out of nowhere. Sussing out whether a system of equations can exhibit this kind of extreme behavior, called a “singularity” or “blowup,” is a difficult task for mathematicians.

Merle has had enormous success taming these blowups in the equations describing lasers, fluids and quantum mechanics. His trick is to embrace the nonlinear. Whereas most researchers before him treated these phenomena gingerly by making tiny tweaks to a well-behaved, linear world, he has focused them, studying their mathematical consequences directly. “I have a slightly different view of the world,” he says. “I see the world as a more catastrophic place to live.”

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By engaging with the chaos, Merle discovered simplicity. Much of his work focuses on special structures, called “solitons,” that persist amid the mayhem of nonlinear systems. Solitons are able to keep their form and energy while they move about in realms where the gnarliest math reigns like a single rogue wave traversing an entire vast, swirling ocean wholly intact. Merle believes that all nonlinear systems can be dealt with by thinking of them as a bunch of these solitons coming together—chaos belying simplicity.

Today Merle received this year’s Breakthrough Prize in Mathematics for his achievements. The prize comes with a $3-million award. Scientific American spoke with Merle about how he managed to tame some of nature’s most tangled sets of equations.

[An edited transcript of the interview follows.]

What does this prize mean to you?

It came as a shock—it took me some time to recover. It’s a great honor. And it’s exciting, because when I found this new way of seeing these problems, most people were not convinced that I could produce something interesting. Then one problem fell and then another one, so of course now there’s a lot of recognition of all this work.

What was your “new way of seeing problems” in nonlinear dynamics?

I was only concentrating on the nonlinear structure. Most of the work before started from something we understand—linear things—and pushed them slightly into the nonlinear. But my starting point was never the linear structure; it was the nonlinear stuff.

And this led you to put solitons front and center.

Yes, because solitons are a totally nonlinear concept. A soliton is a special solution to nonlinear equations, such as fluid equations, that doesn’t send energy away to infinity—it keeps all its energy contained and keeps the same shape.

When you look at physical quantities in nonlinear systems, they seem to oscillate and change chaotically. But if you look long enough, some emergent structure appears that doesn’t depend that much on how things started. This emerging structure is the soliton. From the mathematical point of view, you don’t initially see why it will appear, yet somehow it does.

Solitons seem much simpler than the crazy, chaotic behavior of nonlinear systems. Yet you believe that the behavior of these systems comes down, somehow, to solitons.

Yes, a family of interacting solitons. This is called the “soliton resolution conjecture.”

It’s been the belief since the 1970s, but people then c