Hilbert on Theology and Its Discontents
Hilbert on Theology and Its Discontents
The Origin Myth of Modern Mathematics
This chapter examines the myth surrounding Paul Gordan's response to David Hilbert's finiteness theorems. A proof introduced by Hilbert in 1888 became the paradigm of modern axiomatic mathematics. In the myth, Gordan denounced Hilbert's proof, and his anathema rebounded against himself when he said, “This is not Mathematics, it is Theology!” After providing the background to the various interpretations that Gordan's comment has generated, the chapter considers the so-called “Gordan's problem”—to find finite complete systems of invariants for forms. It then discusses Hilbert's theorem and Gordan's reaction to Hilbert's fuller version of the invariant theorem, as well as Gordan's mythic quotation. It also explores the role played by Gordan's one and only doctoral student, Emmy Noether, in the Gordan–Hilbert controversy and concludes by emphasizing Gordan's story as an example of the deliberate use of narrative in mathematics.
Keywords: myth, Paul Gordan, David Hilbert, finiteness theorems, proof, mathematics, theology, axiomatic mathematics, Emmy Noether, narrative
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