4-40. David Hilbert

David Hilbert (1862–1943) was widely recognized as the foremost mathematician active in Germany in the first decades of the twentieth century. Hilbert taught mathematics at the University of Königsberg from 1886 until 1895, when he accepted a chair at the University of Göttingen. At the latter institution, Hilbert and his fellow mathematician Felix Klein combined forces to transform Göttingen into the world’s first center for cutting-edge research in pure and applied mathematics (Rowe 2008).

After solving the extant problems of invariant theory as a young man, Hilbert worked on algebraic numbers, and on the foundations of geometry, providing an axiomatization of Euclidean geometry satisfying his requirements of independence and consistency (but failing for that of completeness, in the sense of Tarski). The formal approach was influential both in mathematics and in broader circles; Hilbert and his students applied it – with varying degrees of success – to the domains of mechanics, mathematical physics, and to the foundations of mathematics. Hilbert also made fundamental contributions to the theory of integral equations, upon which the concept of a Hilbert space was elaborated, beginning in 1904.

Much of the correspondence between Hilbert and Poincaré concerns the organization of a cycle of lectures delivered by Poincaré in Göttingen from April 22 to 28, 1909, under the auspices of the Wolfskehl Foundation. Hilbert opened the cycle with a short speech, an English translation of which was published by David Rowe (1986). For an overview of Poincaré’s lectures, see Gray (2013, 416), and Rowe (2018, chap. 16); for a discussion of the third and sixth lectures, on the propagation of Hertzian waves and on the “new mechanics” based on Lorentz covariance, respectively, see Walter (2019).

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Notes

• 1 See Dieudonné (1981). Overviews of Hilbert’s career are provided by Reid (1986) and Corry (2004).