NBA History of Science Seminar – Niels Bohr Archive

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Niels Bohr Archive > Calendar > 1999-2011 > Graham and Kantor

NBA History of Science Seminar

Loren Graham and Jean-Michel Kantor, "Naming God, naming Infinity: A True Story of Religious Mysticism and Mathematical Creativity."

This story combines mathematics and religious heresy, a tale in which Russian mathematicians who were religious mystics (Dmitri Egorov, Nikolai Luzin) triumphed over French mathematicians (Émile Borel, René Baire, Henri Lebesgue) who were secular rationalists.

Loren Graham, MIT

In the early twentieth century mathematicians, following the work of Georg Cantor in set theory, faced a major problem: it was possible to conceive of sets of infinite numbers, sets which resisted rigorous definitions. But was it mathematically sound to work with such sets?

Two groups of mathematicians intensively studied this question, the French in Paris and the Russians in Moscow. The French, rigorous rationalists, doubted that such sets were justified; the Russians, religious heretics emboldened by their faith, freely created such sets. 

Jean-Michel Kantor, Institut de Mathématiques de Jussieu, Paris

The Russians noted that they could not give a definition of either "God" or their new sets, but they nonetheless had faith in the reality of both. They answered the question "How do we know such sets of infinite numbers exist?" in a similar way to "How do we know God exists?": "We know both exist," they maintained, "because we can name both and treat them as real." These Russian mathematicians were called "Name Worshippers" and were a part of a religious heresy spreading in Russia.

The French considered such an attitude mystical nonsense, and they lost their nerve to go forward. The Russians plunged ahead and created a new field of mathematics, establishing at the same time the famous Moscow School of Mathematics. And they changed the face of the mathematical world.