"To solve a problem, you must first learn how to see it in its most natural setting." — Heisuke Hironaka
Alan Baker (United Kingdom)
British mathematician Alan Baker received the medal for his groundbreaking work in transcendental number theory. Baker developed powerful methods regarding linear forms in logarithms, establishing effective bounds for solutions to Diophantine equations. His techniques solved longstanding open problems in number theory, including the determination of imaginary quadratic fields with class number one, and created practical computational tools to solve equations that had resisted analysis for centuries.
Heisuke Hironaka (Japan)
Japanese mathematician Heisuke Hironaka was honored for one of the most monumental achievements in algebraic geometry: proving the resolution of singularities for algebraic varieties over fields of characteristic zero. Geometric spaces often feature "singularities"—sharp points, folds, or self-intersections where standard calculus breaks down. Hironaka proved that any singular algebraic variety can be systematically transformed into a smooth, non-singular variety without altering its global properties, providing a cornerstone result for modern geometry.
Sergei Novikov (Soviet Union)
Soviet mathematician Sergei Novikov was awarded the medal for his pioneering achievements in algebraic and differential topology. Novikov proved the topological invariance of Pontryagin classes, showing that these important geometric measurements remain stable even when a manifold undergoes non-smooth, continuous deformations. His work revolutionized cobordism theory and surgery theory on high-dimensional manifolds, laying foundational ideas that later connected topology with mathematical physics and integrable systems.
John Griggs Thompson (United States)
American mathematician John Griggs Thompson earned his medal for his structural insights into finite group theory. In collaboration with Walter Feit, Thompson proved the famous Feit–Thompson theorem, establishing that every finite group of odd order is solvable. The proof—spanning over 250 dense pages—was an unprecedented tour de force that provided the essential framework and momentum needed for the eventual complete classification of all finite simple groups.
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