Energy is conserved when fluid flows smoothly, but may not be when it becomes chaotic enough.
Once a year, the Shaw Prize turns its gaze toward the kind of mathematical thinking that quietly rewires how civilization understands the world. This year, it found two such thinkers: Emmanuel Candes of Stanford, who taught us that incomplete data can still reveal the whole truth, and Camillo De Lellis of the Institute for Advanced Study, who dove into the turbulent heart of fluid motion and emerged with new tools for an ancient problem. Their $1.2 million shared prize is less a reward than a recognition — that pure mathematical inquiry, pursued with patience, eventually touches everything from hospital imaging to the physics of chaos.
- The central tension in both laureates' work is the same: how do you find order — in data, in surfaces, in turbulent fluids — when the information you have is radically incomplete or chaotic?
- Candes' compressed sensing upended decades of signal processing orthodoxy, proving mathematically that you do not need to measure everything to reconstruct it accurately — a disruption that rippled through MRI technology, smartphone cameras, and machine learning alike.
- De Lellis inherited a 1,700-page manuscript on minimal surfaces and, rather than being overwhelmed, simplified and extended it — then turned to turbulence and helped crack the Onsager conjecture, a problem that had haunted fluid dynamics for generations.
- The tool De Lellis and collaborators forged — convex integration — is now a foundational method in modern fluid dynamics research, demonstrating how a single theoretical breakthrough can restructure an entire scientific discipline.
- The Shaw Prize's track record as a predictor of future Nobel and Fields Medal recipients signals that the world is watching: the mathematics being honored today is likely to shape science for decades to come.
Emmanuel Candes was in his Stanford office when the call came confirming the Shaw Prize in Mathematical Sciences — a $1.2 million annual honor with a reputation for identifying work that reshapes entire fields. At fifty-six, the French statistician had spent his career pursuing a deceptively elegant question: how much data do you actually need to see the full picture?
His answer became compressed sensing — a theoretical framework proving that accurate reconstruction is possible from far fewer measurements than classical methods demanded. The implications spread quickly: MRI machines now produce clear images with less scanning time, cameras reconstruct photographs from partial information, and data scientists find patterns in vast datasets without exhaustive measurement. Candes later extended the idea to reconstructing low-rank matrices from partial observations, a technique now central to machine learning, and developed statistical methods to eliminate false discoveries in data analysis — a problem that had long undermined research across disciplines.
Sharing the prize was Camillo De Lellis, an Italian mathematician at the Institute for Advanced Study in Princeton. His work occupies different terrain — the geometry of surfaces and the physics of fluids — but is equally foundational. He took on a 1,700-page manuscript left by Frederick Almgren on the Plateau problem, which asks what shape a surface takes when it minimizes area. De Lellis and his students simplified, completed, and extended Almgren's work, producing quantitative estimates that allowed the entire field to advance.
De Lellis is perhaps best known for resolving the Onsager conjecture, a decades-old puzzle in fluid dynamics proposing that energy conservation breaks down in sufficiently chaotic flows. To prove it, he and collaborators developed convex integration — a method for constructing turbulent, "wild" solutions to the Euler equations — completing the conjecture's proof in 2016 and transforming convex integration into an essential tool for modern fluid dynamics.
Both laureates carry the marks of rigorous European training — Candes from École Polytechnique and Stanford, De Lellis from the University of Pisa and the Scuola Normale Superiore. The Shaw Prize, established by Hong Kong media figure Run Run Shaw and awarded annually since 2004, has proven a reliable forecaster of lasting scientific impact: sixteen past recipients have gone on to win Nobel Prizes, and seven have received Fields Medals. The prize is, in this sense, less a conclusion than a signal — that the mathematics being honored today will continue to echo through science for years to come.
Emmanuel Candes was sitting in his office at Stanford when the news arrived: he had won the Shaw Prize in Mathematical Sciences, a $1.2 million honor that arrives once a year to recognize the kind of mathematical work that changes how the world actually functions. At fifty-six, the French statistician had spent decades chasing a deceptively simple question: what if you didn't need all the data to see the whole picture?
The answer, which he helped develop, is called compressed sensing. It sounds abstract until you realize what it means in practice. A hospital MRI machine can now produce clear images using far fewer measurements than the old methods required. A smartphone camera can reconstruct a photograph from incomplete information. A data scientist can find patterns in massive datasets without needing to measure everything. Candes didn't invent this alone, but his theoretical work gave it a foundation. Later, he extended the idea further, showing how to reconstruct low-rank matrices from partial observations—a technique that became essential to machine learning and modern data science. Most recently, he and his students developed a statistical filtering method designed to catch and eliminate false discoveries in data analysis, a problem that has plagued research across disciplines. The Shaw Prize committee recognized all of this as work that reshaped signal processing, data science, and statistics itself.
Sharing the prize was Camillo De Lellis, a fifty-year-old Italian mathematician at the Institute for Advanced Study in Princeton. His path through mathematics took him into the geometry of surfaces and the physics of fluids—territories that seem far removed from Candes' world of data and signals, yet equally fundamental. De Lellis inherited a 1,700-page manuscript written by American mathematician Frederick Almgren on the Plateau problem, a question mathematicians had been wrestling with since the nineteenth century. The problem asks: what is the shape of a minimal surface, a surface that takes up the least possible area? De Lellis and his students didn't just read Almgren's work—they simplified it, completed it, extended it, and produced quantitative estimates that made the theory work in more complex settings. It was the kind of foundational cleanup that rarely makes headlines but that allows an entire field to move forward.
But De Lellis is perhaps best known for his work on turbulence and the Onsager conjecture, a problem that had haunted fluid dynamics for decades. The conjecture, named after physicist Lars Onsager, proposes something counterintuitive: that energy is conserved when fluid flows smoothly, but may not be conserved when the flow becomes chaotic enough. Proving this meant constructing what mathematicians call "wild" solutions to the Euler equations—solutions that describe fluid motion in such rough, turbulent ways that energy itself seems to vanish. For years, this was considered nearly impossible. De Lellis and his collaborators developed a method called convex integration that made it possible. Their breakthrough helped resolve the Onsager conjecture completely in 2016 and, in the process, turned convex integration into an indispensable tool for modern fluid dynamics research.
Both men carry the marks of rigorous European mathematical training. Candes earned his bachelor's degree from École Polytechnique in France before coming to Stanford for his doctorate. De Lellis studied at the University of Pisa and the Scuola Normale Superiore di Pisa in Italy. Both are members of the American Academy of Arts and Sciences. The Shaw Prize itself, established by Hong Kong media mogul Run Run Shaw, has been awarded annually since 2004 to recognize outstanding work in astronomy, life science and medicine, and mathematical sciences. The prize comes with a medal, a certificate, and the $1.2 million award. The track record is striking: sixteen Shaw Prize recipients have gone on to win Nobel Prizes, ten have received Lasker Awards, seven have won Fields Medals, and five have claimed Abel Prizes. The prize has become a reliable predictor of work that will shape science for decades to come.
Citas Notables
Compressed sensing makes it possible to recover accurate information from far fewer measurements than traditional methods require.— Shaw Prize announcement on Candes' work
De Lellis and collaborators developed convex integration to construct solutions demonstrating energy loss in turbulent flows, resolving the Onsager conjecture.— Shaw Prize committee recognition of De Lellis's contributions
La Conversación del Hearth Otra perspectiva de la historia
Why does compressed sensing matter outside of mathematics departments? What does it actually do?
It lets you see the whole picture from fragments. An MRI scan that used to require a thousand measurements now needs three hundred. A medical imaging system becomes faster, cheaper, less radiation exposure. In data science, it means you can find real patterns without drowning in noise. It's the difference between needing everything and needing enough.
And De Lellis's work on turbulence—that's more abstract, isn't it? How does solving a conjecture about fluid motion change anything?
Not abstract at all. Understanding when energy disappears in turbulent flow matters for everything from aircraft design to climate modeling to predicting how pollutants spread through water. The Onsager conjecture was a wall. De Lellis and his collaborators didn't just prove it was true—they built a new mathematical tool, convex integration, that let them do it. Now that tool is being used to solve other problems in fluid dynamics that seemed impossible before.
These are two very different mathematicians working in completely different areas. Why are they winning the same prize?
Because both did the foundational work that lets entire fields move forward. Candes didn't just solve a problem—he created a method that became essential to medical imaging, machine learning, statistics. De Lellis didn't just answer a question—he built tools that are now standard in his field. The Shaw Prize recognizes that kind of transformative contribution, whether it's in data or fluids.
What comes next for work like this?
Candes' filtering method for false discoveries is just beginning to reshape how scientists validate their findings across disciplines. De Lellis's convex integration is being applied to problems in geometry and physics that people didn't know how to approach before. The real impact often comes years later, when younger mathematicians and scientists build on what these two have done.