NAMING INFINITY

NAMING INFINITY
By Loren Graham & Jean-Michel Kantor
Belknap Press of Harvard University Press, 2009
ISBN 978-0-674-03293-4

Review by George R. Pasley

Here is a fascinating book authored by two historians of science who survey the lives and thoughts of mathematicians involved in the origins Descriptive Set Theory during the first three decades of the Twentieth Century.

Why would I read such a book, and why should you? The books subtitle caught my eye, and aptly sums up the plot of the book,”A True Story of Religious Mysticism and Mathematical Creativity”.

The book purports to be written for mathematical lay persons, and perhaps it is, but I found the math almost impossible to comprehend. Well, maybe that is as it should be, for the mathematicians were all involved in studying infinity, something which is undefined except to say what it is not. None-the-less, the authors did manage to describe, both analytically and poetically, the struggles, conflicts, and insights contributed by all persons involved.

Specifically, Graham and Kantor describe how a trio of French mathematicians (Emil Borel, Henri Lebesgue, & Rene-Louise Baire), raised in a world of ultra-rationalism, made certain insights into Set Theory but then “lost their nerve” when their insights pushed them further and further away from their philosophical worldview. Their teaching, however, influenced a trio of Russian mathematicians (Dmitri Egorov, Nikolai Luzin, & Pavel Florensky) whose specific religious inclinations allowed them to make an imaginative leap where cold rationalism could not go. Florensky in fact was a priest of the Russian Orthodox Church, though the particular mystical practice (Name Worshipping) of the trio was considered heretical. Egorov and Luzin founded a school of mathematics, the Moscow School of Mathematics, whose prestige and influence world-wide is still great.

That the Russian trio lived and taught during the Russian Revolution, with Florensky being executed and Egorov dying as a result of imprisonment, and Luzin suffering in academic exile, and that the French trio suffered a host of mental breakdowns, makes the story tragic, compelling, and dramatic. Brief snippets are also provided to a host of the supporting players, some of whom could be the subjects of quite dramatic biographies.

The authors admit to being secularists. The book is not an attempt to solve the science-religion debates. But their final words are pragmatic, tolerant, and open to possibility. Quoting legendary secular mathematician Grothendieck, who insisted mathematicians do not need religion, Graham and Kantor reply:”Our belief, as we have shown here, is that it sometimes can help.”

August 19, 2009
Ketchikan, AK