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- The Fields Medal recognizes outstanding mathematical achievement and future promise.
- Funded by a trust established by J.C. Fields, with additional support for 2026 from the Fields Institute.
- Awarded for work in partial differential equations, including derivation of the Boltzmann equation and wave kinetic equations.
- Recognizes achievements in symplectic geometry, including virtual fundamental cycles and Fukaya categories.
- Honors contributions to o-minimality and proofs of conjectures like the Andre-Oort conjecture.
- Awarded for work in harmonic analysis and geometric measure theory, including the local smoothing conjecture and Kakeya problem.