A Richer Picture of Mathematics by David E. Rowe

Author:David E. Rowe
Language: eng
Format: epub
Publisher: Springer International Publishing, Cham

Plans for Hilbert’s Paris Lecture

Minkowski’s role as Hilbert’s silent collaborator during the production of the Zahlbericht ought not to be exaggerated, but he certainly did offer his friend a great deal of intellectual and moral support. The same pattern can be observed a few years later when Hilbert called on his advice again during a time when both were making plans to attend the Second International Congress of Mathematician in Paris. It was on this occasion, of course, that Hilbert delivered his famous lecture on “Mathematical Problems” (Hilbert 1901), a performance that soon brought him lasting fame. Had it not been for Minkowski’s wise counsel, however, he might well have chosen a more controversial, but less ambitious topic for this lecture. Once again, Minkowski’s letters shed considerable light on the motivations and behaviors of both friends.

As the newly-elected president of the DMV, Hilbert received an invitation in December 1899 to deliver a plenary address in Paris on a theme of his choosing (see Chap. 16). This was a splendid opportunity, or at least so Hilbert thought, to throw down the gauntlet to the dominant mathematician of the era, Henri Poincaré. At the previous ICM, held in Zurich in 1897, Poincaré had been designated as one of the plenary speakers, and for this occasion he took as his theme the role of physical conceptions in guiding fertile mathematical research. With that speech still in mind, Hilbert thought he should counter by singing a hymn of praise to pure mathematics. No doubt he also recalled how Jacobi had once rebuked his French contemporary, Joseph Fourier, for failing to recognize that the highest and only true purpose of mathematics resided in nothing other than the quest for truth; this alone redounded honor on the human spirit (Klein 1926, 114).

But Minkowski strongly counseled his friend to abandon this plan (Minkowski to Hilbert, 5 January 1900, Minkowski 1973, 119). After rereading Poincaré’s text, he found that its assertions in no way compromised the integrity of pure mathematics. Furthermore, he felt that the Frenchman’s views were formulated so cautiously that Hilbert and he could easily subscribe to them. Moreover, he recalled how Poincaré had not even been present in Zurich, so his text was actually read by another party. Consequently, Minkowski was sure that there was little point in drawing attention to Poincaré’s opinions, since few would remember what he had written for that occasion. He then contrasted this rather dull speech with the stirring lecture delivered by Ludwig Boltzmann at the annual meeting of German scientists held in Munich just 4 months earlier (Boltzmann 1900).

Hilbert clearly took this all to heart, even if he never said so. Indeed, he had returned from that Munich meeting in high spirits, writing to Hurwitz that this event was the best attended and most stimulating of all the DMV meetings held thus far.6 Furthermore, he was clearly pleased by the response to his two talks (one on the axioms of arithmetic, the other on Dirichlet’s principle). Still, these could

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