Georg von Wallwitz Meine Herren, dies ist keine Badeanstalt. Wie ein Mathematiker das 20. Jahrhundert veränderte
[Meine Herren, dies ist keine Badeanstalt. Wie ein Mathematiker das 20. Jahrhundert veränderte (Gentlemen, this is not a bathhouse: How a Mathematician Changed the Twentieth Century]]

Georg von Wallwitz makes the life, work, and impact of the great mathematician David Hilbert accessible—also for laypersons
 
Everyone knows Albert Einstein. And thanks to the global bestseller Gödel, Escher, Bach, even non-mathematicians have some sense of who Kurt Gödel was. John von Neumann became known as one of the inventors of the first electronic calculating machines. But what world-changing discoveries were made by David Hilbert? What does the Hilbert curve look like? And what is promising about Hilbert formalism? The great mathematician born in Königsberg in 1862 and who died in Göttingen in 1943 is not very well known outside of his discipline. And yet Hilbert has the same status “for the modern natural sciences as Picasso does for art,” writes Georg von Wallwitz, whose biography focuses not only on the mathematician, but also on mathematics itself—so that even laypeople can surmise the revolutions that got underway in Göttingen.

Hilbert was responsible for some of the most important mathematical operations, which left a decisive mark on the twentieth century. His axiomatic method restructured the world of mathematics from the ground up. He transformed Göttingen into a center of intellectual giants in the natural sciences. He discussed with Albert Einstein about his theory of relativity and fostered mathematician Emmy Noether. That alone is reason enough to have a closer look at this extraordinary thinker—and most of all to bang the drum for the power of mathematics to fascinate.

The latter point is perhaps the main objective of the book Meine Herren, dies ist keine Badeanstalt [Gentlemen, this is not a bathhouse]. The title refers to an episode dealing with university policy. When Hilbert wanted Emmy Noether to be appointed to a professorial post in 1915, his efforts failed due to his conservative colleagues who did not want to see a woman assume a professorship. Wallwitz writes that the otherwise reserved mathematician raised an indignant outcry—“Gentlemen, this is not a bathhouse!”—indicating that in the university, in contrast to the bathhouses of the time, gender separation was not appropriate, but rather what counted was mathematical achievement.

Georg von Wallwitz—himself a mathematician, philosopher, fund manager, and author of two books—sheds light on the network of brilliant students and colleagues surrounding Hilbert, which proves to be one of the focuses of this reader-friendly book written in an elegant, casual style. Another focus is Hilbert’s areas of interest in mathematics (and physics). This also has to do with the fact that from an outside perspective, the life of Göttingen’s great mathematician was rather uneventful, as Wallwitz explains.

While studying in Königsberg, his East Prussian hometown, Hilbert became friends with the mathematicians Adolf Hurwitz and Hermann Minkowski. The trio discussed the most recent scientific developments while taking walks. Hilbert would maintain the rhythm of walking and expostulating throughout his life. After getting married, starting a family, and receiving a professorship in Göttingen in 1895, he started working out his life themes: in addition to the invariant and number theories, in particular the axiomatic method, with which mathematics, for the first time since Euclid, would be set on a completely secure, formalized foundation.

After Einstein published the special theory of relativity in 1905, many mathematicians, including Hilbert, pounced on this revolutionary coup. “In the first third of the twentieth century, at least half of mathematics belonged to the physicists, and Hilbert was far too interested in the intellectual trends of his time to refrain from getting his own thing going,” writes von Wallwitz. “Göttingen became—even more so after the First World War—a huge mathematical-physical café house.” Among those present were: the young Norbert Wiener, Max Born, John (at the time still called Johann) von Neumann, Niels [AB1] Bohr, Werner Heisenberg, and of course Einstein, who was supported by Hilbert. Together they calculated the still faulty field equations in Einstein’s theory. There were even short scenes of competition, but reconciliation won out.

“Hilbert wanted an unqualified success; he wanted finally to give physics an axiomatic mantle.” He wanted, according to von Wallwitz, to create a “theory of everything.” The fact that in the end he didn’t discover this theory of everything was due in part to the young Kurt Gödel, who gave Hilbert’s theoretical structure a decisive blow. Georg von Wallwitz manages not only to convey even to laypersons an impression of the mathematical upheaval that took place between Hilbert and Gödel. With an almost physiognomical feel for the “mathematician type,” he also paints an extremely lively portrait of his protagonists.

When this blossoming science landscape was destroyed by the Nazis in 1933, Hilbert had already been retired for several years. His internationalistic formalism was of course light years away from the insanity of “German mathematics.” It would have been interesting to read more about this political turning point in Göttingen, and about the behavior of the scientists around and following Hilbert who did not emigrate. “Hilbert shut down and it became quiet around him,” notes von Wallwitz. In 1942 Hilbert still accepted an honorary membership in the German Mathematicians Association on the occasion of his eightieth birthday.

When Hilbert died in 1943, his death at first received little attention from the international research community. Perhaps people were distracted in this war year, as von Wallwitz explains in detail. He especially succeeded in portraying the global influence of the Hilbert school and arousing curiosity in a subject that changed the world as perhaps no other. As proof just think of your own typing fingers, and the devices beneath them.