2026 · Analysis & PDEsHong Wang
A collection containing a unit line segment in every direction can have zero volume, yet its fractal dimension remains constrained.
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The laureates
Sixty-eight people. A world of ideas.
Discover the mathematicians behind a century of new perspectives.
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Newest first · scroll to explore2026 · Analysis & PDEs
2026 · Number theoryJacob Tsimerman
An idea from mathematical logic helps distinguish exceptional arithmetic patterns from the ordinary points of complicated geometric parameter spaces.
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2026 · Geometry & topologyJohn Pardon
Symplectic geometry extracts information from families of curves, but those families can be too singular for ordinary counting to work.
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2026 · Analysis & PDEsYu Deng
How can reversible collisions of countless tiny particles produce the statistical equation used to describe the evolution of a gas?
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2022 · Probability & dynamicsHugo Duminil-Copin
Random connections or microscopic spins can suddenly organize at a critical threshold, creating large-scale behavior invisible in any single component.
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2022 · Number theoryJames Maynard
Primes become rarer as numbers grow, yet carefully designed sieve weights reveal infinitely many intervals containing several of them together.
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2022 · CombinatoricsJune Huh
Numbers obtained by counting finite configurations often rise and fall regularly; geometric ideas explain why certain patterns cannot fluctuate arbitrarily.
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2022 · Geometry & topologyMaryna Viazovska
The E8 lattice looks extraordinarily efficient, but proving optimality requires ruling out every competing arrangement, including irregular and nonperiodic packings.
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2018 · Number theoryAkshay Venkatesh
Number-theoretic objects can become points or trajectories in a geometric space, allowing dynamics to reveal patterns that direct calculation hides.
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2018 · Analysis & PDEsAlessio Figalli
Optimal transport compares distributions by moving mass between them, turning a question about cheapest routes into deep information about geometric regularity.
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2018 · Algebraic geometryCaucher Birkar
Polynomial equations define endlessly many spaces; birational geometry searches for building blocks and asks how complicated those blocks can become.
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2018 · Algebraic geometryPeter Scholze
Perfectoid spaces let mathematicians transfer difficult geometric questions between characteristic zero and characteristic p, where different tools become available.
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2014 · Probability & dynamicsArtur Avila
A simple repeated rule can produce stability or chaos; renormalization compares its behavior at different scales to uncover the deeper organization.
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2014 · Number theoryManjul Bhargava
Integer equations can look unrelated one by one; organizing them as geometric objects makes it possible to study their average behavior.
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2014 · Analysis & PDEsMartin Hairer
Some random-growth equations contain products too irregular for ordinary calculus; regularity structures provide a precise language for making them meaningful.
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2014 · Geometry & topologyMaryam Mirzakhani
A curved surface contains infinitely many closed geodesics; understanding the family of all surface geometries reveals a surprising law for simple loops.
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2010 · Analysis & PDEsCédric Villani
Particles need not stop moving for a collective electric field to fade; phase mixing can produce damping without ordinary friction.
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2010 · Probability & dynamicsElon Lindenstrauss
An orbit may look unpredictable, yet several compatible symmetries can sharply limit its possible statistical behavior and constrain arithmetic patterns.
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