This week’s quotation is anecdotal, but it captures a sensation many of us will recognise. The context is that Paul Gordan, an eminent German mathematician who had spent much of his life working on invariant theory, had just encountered a brilliant but perplexing piece of work by the younger but even greater mathematician David Hilbert. Hilbert had apparently proved for the first time that certain problems, on which Gordan had worked for twenty years, could be solved — but without providing any clue how to solve them. Gordan’s cry, according to his colleague Max Noether, was
This is not mathematics; it is theology!
In fact, the story behind this exclamation isn’t even as simple as that. Despite the impression it gives, Gordan seems to have accepted Hilbert’s work; there’s even an argument that far from being derogatory, he may have been paying Hilbert’s mathematics the highest compliment available. If that sounds peculiar, imagine trying to explain why mathematics isn’t a religion, to somebody who doesn’t believe in either…
It may be that Max Noether simply made the story up, or at least embellished it — the story was first told a quarter of a century later, during a eulogy to Gordan, and it could have been part of an elaborate in-joke. (To illustrate the tangled world that these people inhabited: these days Paul Gordan is best known for the sole PhD student he supervised: the great Emmy Noether, daughter of Max and one of the people who developed Hilbert’s ideas past the point that Hilbert reached.)
In the article “Theology and its Discontents” in the book Circles Disturbed, from which I’ve lifted this information, Colin McLarty discusses the anecdote and the myths surrounding it, and incidentally suggests another interpretation: “Paul Gordan was a very funny man”. Possibly we shouldn’t read too much into an ironic comment by a mathematician who’d just seen two decades’ work outflanked, and was big enough to take it with a rueful smile.