How Not to Be Wrong: The Power of Mathematical Thinking

by Jordan Ellenberg

Hilbert’s commitment to logical principle and deduction often led him, like Condorcet, to adopt a surprisingly modern outlook in non-mathematical matters.* At some political cost to himself, he refused to sign the 1914 Declaration to the Cultural World, which defended the kaiser’s war in Europe with a long list of denials, each one starting “It is not true”: “It is not true that Germany violated the neutrality of Belgium,” and so on. Many of the greatest German scientists, like Felix Klein, Wilhelm Roentgen, and Max Planck, signed the declaration. Hilbert said, quite simply, that he was unable to verify to his exacting standards that the assertions in question were not true. A year later, when the faculty at Göttingen balked at offering a position to the great algebraist Emmy Noether, arguing that students could not possibly be asked to learn mathematics from a woman, Hilbert responded: “I do not see how the sex of the candidate is an argument against her admission. We are a university, not a bathhouse.”

Logic can make us aware of our inner biases