Hilbert

David Hilbert was a German mathematician whose work and ideas helped define 20th-century mathematics. Born in Königsberg, East Prussia, in 1862, he spent much of his career at the University of Göttingen, where he orchestrated advances across geometry, algebra, analysis, and mathematical logic. His influence extended beyond specific results to a broad program of axiomatization and formal rigor.

Hilbert championed an axiomatic method as the foundation of mathematical reasoning. His Foundations of Geometry (Grundlagen der Geometrie, 1899) offered a systematic, axiomatic treatment of Euclidean geometry and helped shape modern formalism in mathematics. He also contributed to functional analysis through the concept of what is now called a Hilbert space—a complete inner product space central to analysis, quantum mechanics, and many areas of mathematics. In algebra, his Hilbert basis theorem established that polynomial ideals over a field are finitely generated, and his Hilbert Nullstellensatz linked algebraic equations to geometric objects.

In 1900, Hilbert presented a list of 23 unsolved problems at the International Congress of Mathematicians in Paris, outlining goals that guided research for much of the century. His work on the foundations of mathematics laid the groundwork for the formalist approach, while Gödel’s incompleteness theorems later showed intrinsic limits to completing such a program. Hilbert’s legacy rests in shaping rigorous methods, inspiring generations of mathematicians, and providing foundational concepts that remain central across multiple disciplines. He died in Göttingen in 1943.