David Hilbert

David Hilbert, born in 1862 in what is now Kaliningrad or nearby Znamensk, was a German mathematician and philosopher of mathematics whose influence on the field is hard to overstate. His work spanned invariant theory, the calculus of variations, commutative algebra, algebraic number theory, the foundations of geometry, operator spectral theory and its use in integral equations, mathematical physics, and the foundations of mathematics—especially proof theory. He championed Georg Cantor’s set theory and transfinite numbers. In 1900, Hilbert set the agenda for 20th-century mathematics by presenting a famous list of problems. Along with his students, he helped bring rigor to modern mathematical physics and co-founded proof theory and mathematical logic.

Hilbert was the first of two children, born to Otto, a county judge, and Maria Therese Hilbert, a merchant’s daughter with interests in philosophy, astronomy, and prime numbers. His father taught him Prussian virtues. The family moved to Königsberg when Otto became a city judge. Hilbert started school at age eight, two years later than usual. He attended the Friedrichskolleg Gymnasium—the same school Immanuel Kant had attended—but was unhappy there and transferred to the science-oriented Wilhelm Gymnasium, graduating in early 1880. That autumn, he entered the University of Königsberg. In early 1882, Hermann Minkowski, two years younger and also from Königsberg, returned from Berlin and enrolled; the two formed a lifelong friendship. In 1884, Adolf Hurwitz arrived from Göttingen as an associate professor, sparking a fruitful scientific exchange among the three.

Hilbert earned his doctorate in 1885 under Ferdinand von Lindemann, with a dissertation on invariant properties of special binary forms. He stayed at Königsberg as a senior lecturer until 1895, when Felix Klein helped him secure a mathematics professorship at the University of Göttingen. Under Hilbert and Klein, Göttingen became the world’s leading mathematics center. Hilbert remained there for the rest of his life. Among his 69 doctoral students were Hermann Weyl, chess champion Emanuel Lasker, Ernst Zermelo, Carl Gustav Hempel, Otto Blumenthal, Felix Bernstein, Richard Courant, Erich Hecke, Hugo Steinhaus, and Wilhelm Ackermann. John von Neumann served as his assistant. Hilbert’s social circle included Emmy Noether and Alonzo Church. From 1902 to 1939, he edited the leading journal *Mathematische Annalen*. He was elected to the U.S. National Academy of Sciences in 1907.

In 1892, Hilbert married Käthe Jerosch, an outspoken merchant’s daughter. They had one child, Franz, born in 1893, who suffered from mental illness throughout his life. After Franz was admitted to a psychiatric clinic, Hilbert said he must consider himself as having no son, which caused Käthe much sorrow. Hilbert considered Minkowski his best and truest friend. Raised a Calvinist in the Prussian Evangelical Church, he later left the church and became agnostic, arguing that mathematical truth does not depend on God or a priori assumptions. He once remarked that only an idiot would think scientific truth needs martyrdom—religion might, but science proves itself in time.

In his later years, Hilbert had close ties with the Berlin Group, whose leading founders had studied under him in Göttingen. Around 1925, he developed pernicious anemia, a then-untreatable vitamin deficiency causing exhaustion. He died in 1943.