Candes, 56, is a professor at Stanford University, while De Lellis, 50, works at the Institute for Advanced Study in Princeton, New Jersey.

One of Candes' most influential achievements was helping develop compressed sensing, a mathematical method that allows computers to accurately reconstruct signals from incomplete data. The breakthrough has had broad applications in signal processing, medical imaging and statistics, according to the Shaw Prize's announcement on Wednesday.

In simple terms, compressed sensing makes it possible to recover accurate information from far fewer measurements than traditional methods require. He later helped develop a more advanced version of the technique that enables low-rank matrices to be reconstructed from partial observations. The work has become widely used in machine learning and data science.

Italian mathematician Camillo De Lellis. Photo courtesy of Institute for Advanced Study

More recently, Candes and his students introduced a statistical filtering method designed to reduce false discoveries in data analysis. The approach is expected to have a major impact on statistics, much like compressed sensing did in imaging technology.

De Lellis, meanwhile, is best known for his work in geometric analysis and fluid dynamics. One of his major achievements involved the Plateau problem, a classic mathematical challenge dating back to the 19th century that studies minimal surfaces, or surfaces that minimize area. Building on a 1,700-page work by U.S. mathematician Frederick Almgren, De Lellis and his students simplified, completed and extended the theory, producing quantitative estimates for more complex geometric settings.

Another major contribution concerns turbulence and the Onsager conjecture, a long-standing problem involving the Euler equations that describe fluid motion.

The conjecture proposes that energy is conserved when fluid flows are sufficiently smooth but may not be conserved when the flow becomes rough enough. Demonstrating this energy loss through so-called "wild" solutions had long been considered one of the field's most difficult challenges.

De Lellis and collaborators developed a breakthrough method known as convex integration to construct such solutions. Their work later helped scientists fully resolve the Onsager conjecture in 2016 and turned convex integration into an important tool in modern fluid dynamics.

Candes was born in France and earned a bachelor's degree from Ecole Polytechnique before completing his doctorate at Stanford. De Lellis was born in Italy and earned his bachelor's degree from the University of Pisa and his doctorate from the Scuola Normale Superiore di Pisa.

Both are members of the American Academy of Arts and Sciences.

French statistician Emmanuel Candes. Photo courtesy of The Shaw Prize

Established by late Hong Kong media mogul Run Run Shaw, the Shaw Prize has been awarded annually since 2004 for outstanding achievements in astronomy, life science and medicine, and mathematical sciences. Each prize includes a medal, a certificate and $1.2 million.

According to the Hong Kong Laureate Forum, many Shaw Prize recipients have later received other prestigious international honors, including 16 Nobel Prizes, 10 Lasker Awards, seven Fields Medals and five Abel Prizes.