Abel Prize Winners: Complete List of Laureates, 2003-2026

Kashiwara spent 5 decades building algebraic analysis: the study of differential equations by algebraic means. His D-modules treat a system of differential equations as an algebraic object you can manipulate, classify, and glue, which turned analytic problems into algebra. His crystal bases then gave representation theory a combinatorial skeleton: infinite symmetry structures reduced to graphs you can literally draw. He is the first Japanese laureate.

Talagrand made randomness predictable. His concentration-of-measure inequalities explain why systems built from many independent random pieces, spin glasses and airline delays alike, behave far more regularly than intuition suggests: a function of many independent variables that depends only a little on each one is nearly constant. Statistics, machine learning theory, and mathematical physics lean on that fact daily.

Caffarelli is the master of regularity: proving that solutions to nonlinear partial differential equations are smoother than they have any obvious right to be. His signature terrain is free-boundary problems, where the domain itself is unknown, like the moving edge of melting ice, and the Monge-Ampère equation that underlies optimal transport.

Sullivan was cited for topology in its broadest sense: algebraic, geometric, and dynamical. Rational homotopy theory is one famous piece, a way to compute the essential shape of a space using only fraction-valued data, but the award spans his whole habit of importing tools across fields, down to his later work on the topology of fluid flow.

Lovász connected graph theory to optimization and computing: the LLL lattice-reduction algorithm he co-created now underpins parts of cryptography, and his structural results made huge networks mathematically tractable. He shared the 2021 prize for turning theoretical computer science into a central field of mathematics.

Furstenberg showed that ergodic theory, the mathematics of long-run evolution, could prove hard static facts, including a celebrated dynamical proof of Szemerédi’s theorem on arithmetic progressions. Watching systems evolve became a way to settle questions that never mention time.

The first woman to receive the Abel Prize, for geometric PDEs, gauge theory, and integrable systems. Her full story, and why her bubbling technique became standard equipment in geometric analysis, is in its own section below.

Langlands proposed in a 1967 letter what became the Langlands program: a web of conjectures connecting representation theory and number theory so ambitious it’s routinely called a grand unified theory of mathematics. Wiles’ Fermat proof walked through one corner of it; whole careers now live inside it.

Meyer built the mathematical theory of wavelets: decomposing signals into little waves at multiple scales. It’s the rare Abel-level theory you carry in your pocket, running inside image compression and signal processing, and it helped process the LIGO gravitational-wave detections.

Wiles proved Fermat’s Last Theorem, the most famous unsolved problem in mathematics for 358 years, via the modularity conjecture for semistable elliptic curves. Seven years of secret work, a flawed 1993 announcement, and a repaired proof in 1994 make it the best mathematical drama of the century.

Nash, famous publicly for game theory and A Beautiful Mind, did his deepest mathematics in PDEs: embedding theorems and regularity results that analysts rank above his Nobel-winning economics. He and his wife Alicia died in a car accident days after the Oslo ceremony; the prize was awarded while he lived.

Sinai gave chaos its mathematics. Sinai billiards, Kolmogorov-Sinai entropy, and his ergodic theory measure exactly how unpredictable a deterministic system is, which is why statistical mechanics can trust probability at all.

Deligne completed the proof of the Weil conjectures, the deepest link between counting solutions of equations over finite fields and the topology of shapes. Grothendieck built the machine; Deligne drove it somewhere nobody else could.

Szemerédi proved that any set of integers with positive density contains arbitrarily long arithmetic progressions, and his regularity lemma showed that every huge graph looks approximately structured. Modern combinatorics, and a good part of computer science, stands on those two results.

Milnor discovered exotic spheres: 7-dimensional spheres that are topologically identical to the standard one but smoothly different. That single 1956 example split topology into new fields and set the agenda for decades.

Tate built so much of modern number theory’s scaffolding that his name is attached everywhere: Tate modules, Tate cohomology, the Tate conjecture. The award citation is one line because the full list would be a syllabus.

Gromov reinvented geometry several times: groups viewed as geometric objects, spaces compared as wholes, and the h-principle that turns impossible-looking constructions into flexible ones. Ask a geometer which Gromov idea they use; the answer is usually several.

Thompson proved with Feit that every finite group of odd order is solvable, the 255-page theorem that launched the classification of finite simple groups, arguably mathematics’ largest collaborative proof.

The first Indian-born Abel laureate, for the unified theory of large deviations: the mathematics of rare events. The full story, from Chennai to Courant, is in its own section below.

Carleson settled a 1913 question by proving that the Fourier series of a square-integrable function converges almost everywhere. Analysts had expected a counterexample; he delivered the theorem instead, and his corona theorem and dynamics work were nearly as influential.

Lax shaped both the theory and the computation of partial differential equations: shock waves, scattering theory, and the Lax equivalence theorem that tells you when a numerical scheme can be trusted. Every serious PDE simulation still runs across his ideas.

Atiyah co-proved the index theorem with Singer: the number of solutions to a differential equation, computed from pure topology. He spent the rest of a famous career walking the bridge it built between geometry and quantum physics.

The first laureate. Serre reshaped topology, algebraic geometry, and number theory across a 7-decade career, and remains the youngest Fields Medalist ever at 27. Starting the Abel list with Serre set the bar exactly where the founders wanted it.