2026 Fields Medals awarded to four of world's top mathematicians. The award, nicknamed the Nobel Prize of mathematics, recognizes outstanding achievement - and the promise of future achievement - by mathematicians under 40. During today's opening ceremony at the International Congress of Mathematicians (ICM) in Philadelphia, the International Mathematical Union (IMU) announced the recipients of the 2026 Fields Medals. This year's prizes went to four of the world's top mathematicians: Chinese mathematician Yu Deng of the University of Chicago; American mathematician John Pardon of Stony Brook University in New York; Canadian mathematician Jacob Tsimerman of the University of Toronto; and Chinese mathematician Hong Wang of New York University and France's Institut des Hautes Études Scientifiques (IHES). The Fields Medal is often described as the Nobel Prize of mathematics due to its prestige. Awarded every four years to two to four mathematicians under the age of 40, the medal recognizes outstanding mathematical achievement in existing work and the promise of future achievement. Each winner receives 15,000 Canadian dollars (approximately $10,600) and a gold medal bearing the visage of the Greek mathematician Archimedes. "The four medalists exemplify the depth, originality and vitality of contemporary mathematics, and we are delighted to celebrate their achievements at the International Congress of Mathematicians," says Hiraku Nakajima, president of the IMU. Additional prizes awarded. During the ceremony, the IMU also announced the winners of other top prizes in mathematics. Full citations for these prizes are available on the IMU website. Shayan Oveis Gharan of the University of Washington received the Abacus Medal for mathematical contributions to computer science. Oveis Gharan is a Simons Investigator in Theoretical Computer Science. Graeme Segal of the University of Oxford won the Chern Medal for outstanding lifetime achievement in mathematics. The Carl Friedrich Gauss Prize was awarded to Yurii Nesterov of Belgium's University of Louvain for mathematical contributions with significant applied applications. Hannah Fry of the University of Cambridge was honored with the Leelavati Prize for public outreach. About the fields medalists. Deng was cited "for his work in partial differential equations, including the rigorous derivation of the Boltzmann equation from hard-sphere dynamics for rarefied gases, the derivation of wave kinetic equations from nonlinear dispersive systems, and probabilistic approaches to nonlinear Schrödinger dynamics." He derived one of the most central equations in kinetic theory and fluid dynamics - the Boltzmann equation - from the mathematics of colliding hard spheres. His work is a leap forward in a centuries-long quest by mathematicians and physicists to derive the basic laws of physics from first principles - one of the famous 23 problems put forth by mathematician David Hilbert at the 1900 ICM. John Pardon Pardon was cited for "his achievements in symplectic geometry, including new approaches to virtual fundamental cycles, Fukaya categories of Liouville manifolds and counting holomorphic curves, and for his contributions to other areas of geometry and topology, including group actions on 3-manifolds and knot theory." Pardon determined how to count curves on specific shapes in the field of symplectic geometry, proving the 20-year-old MNOP conjecture, which posited that two different ways of counting curves were in fact the same. Those specific shapes, called Calabi-Yau 3-folds, are thought to model its universe in superstring theory. Pardon's work has implications for representation theory, symplectic topology and quantum physics. Jacob Tsimerman Tsimerman was cited "for his role in the vast extension of the scope of o-minimal techniques within arithmetic and complex algebraic geometry, including the proof of Griffiths' conjecture on the algebraicity of images of the period maps." He started by attacking big problems in number theory, using algebraic geometry to see how shapes could reveal properties of numbers. He then imported a concept known as o-minimality - a logical framework used to "tame" wild mathematical structures - from one of the most abstract fields in mathematics, model theory, into algebraic geometry, with remarkable results. In particular, his results are deeply related to the Hodge conjecture, one of the seven famous million-dollar Millennium Prize Problems. Wang was cited "for her work in harmonic analysis and geometric measure theory, including applications of multiscale and decoupling techniques to the local smoothing conjecture for the planar wave equation, and major advances in Fourier restriction, Falconer distance sets, Furstenberg sets in the plane, and the Kakeya problem in three dimensions." Wang proved the three-dimensional version of a century-old problem that's simple to explain, yet difficult to solve: How much space does it take to turn a needle such that it points in every direction? In two dimensions, one can cleverly slide and rotate a needle in only a tiny area, but a related Kakeya problem in three dimensions proved much harder. Solving this problem has opened the door for a host of theorems and conjectures in harmonic analysis, partial differential equations, geometric measure theory and other fields. The problem remains open for dimensions four and higher. Additional Information The Simons Foundation, in cooperation with the IMU, created videos featuring each of this year's award winners. The embeddable videos can be viewed on YouTube. About the International Congress of Mathematicians The ICM is the most important and prestigious conference in the mathematical community, hosted every four years by the IMU. The 2026 congress, running from July 23 to July 30 in Philadelphia, features hundreds of invited talks, panels and presentations on cutting-edge developments across mathematics. This year's conference is supported by the American Mathematical Society and the Simons Foundation and marks the first ICM in the United States since 1986. About the International Mathematical Union Founded in 1920, the IMU unites more than 80 member countries, represented through their national mathematical societies and academies. Together and through its members, the IMU encourages global collaboration and supports the development of mathematics in all regions of the world. About the American Mathematical Society Founded in 1888 to further mathematical research and scholarship, the American Mathematical Society fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and to everyday life. About the Simons Foundation The Simons Foundation is a private foundation in New York City whose mission is to advance the frontiers of research in mathematics and the basic sciences. Founded in 1994 by Jim and Marilyn Simons, the foundation supports transformative science through grantmaking, in-house research and public engagement. The Simons Foundation provides grants in autism science and neuroscience; life sciences; mathematics and physical sciences; and science, society and culture. The foundation's in-house research division, the Flatiron Institute, develops and deploys computational methods to advance basic scientific research. Media Contacts Vanessa Chung, International Mathematical Union: [email protected] Thomas Sumner, Simons Foundation: [email protected]

The cradle of eukaryotic life. The authors had expected to find eukaryotes throughout the ancient seas. "What's striking to me is how restricted eukaryotes are at this time," Porter said. "The surface water seems like such an obvious place to live, especially if they have to have oxygen; there's lots of oxygen at the surface." Porter and Riedman suspect that eukaryotes first evolved on the seafloor, and perhaps there hadn't been any pressure to move into the water column yet, or any openings to allow them to make the change. They're currently working to uncover when this occurred, which would also open the door to asking how and why. The geographic restriction could also explain a puzzling pattern: Eukaryotes were neither abundant nor diverse for nearly 1 billion years after genetic and fossil evidence suggests they arose. And that would make sense if they were inhabiting a very limited environment. "The fossils that are 800 million years old, and the ones 1.7 billion years old are, for the most part, the same cast of characters," Riedman and Porter explained. But Earth's surface temperatures plunged around 720 million years ago, and it entered the Cryogenian, also known as Snowball Earth. During this period, ice sheets extended from the poles to the equator. The extreme conditions certainly would have caused mass extinctions, the authors explained, which would've opened up previously occupied niches as the planet emerged from its big freeze 635 million years ago. Indeed, the Ediacaran Period that followed marks the first emergence of complex, multicellular life, all of it eukaryotic. An early acquisition. The distribution of fossils also suggests that eukaryotes had probably acquired mitochondria very early on. These specialized energy-generating organelles are a hallmark of all living eukaryotes, and the leading theory posits that they developed from free-living bacteria that were incorporated into an ancestral eukaryotic host cell. In fact, living on the seafloor would've put ancestral eukaryotes in close proximity with other organisms, something that would have facilitated this assimilation. Some scientists hypothesize that mitochondria enabled eukaryotes to develop such complex morphology, which the fossils from the McArthur and Birrindudu basins display even 1.75 billion years ago. While early eukaryote diversity was low in an absolute sense, it's higher than scientists would expect if the group had just gotten going. "So, although these are the oldest eukaryote fossils yet described, the diversity and variety of form achieved by this point suggest they have a deeper history," Porter said. She, Riedman and UCSB PhD student Wentao Zheng are currently looking at microfossils from even older layers in the McArthur Basin, as well as the Animikie Basin of Minnesota, but would like to peer earlier still to uncover how the group reached the sophistication already present in these specimens. Their research is part of a joint project between the Simons Foundation and the Gordon and Betty Moore Foundation investigating the origin of the eukaryotic cell, with additional funding from Nasa's Exobiology program. "Studies like this give us an opportunity to understand these little guys as organisms," Riedman said. "Rather than just viewing them as a name or part of a stamp collection, we can picture where they were living, what they were doing and who they were." This perspective is precisely what's needed to unravel the events that led to its planet's incredible biodiversity, and ultimately its own origins. (ID:50852363)