Monday, September 13, 2010

Naming Infinity

That's the title of a book by Loren Graham and Jean-Michel Kantor that I finished reading recently. It may be one of the most unusual books I've read, as it focuses on two topics--the mathematics of the infinite and heresy in the Eastern Orthodox Church--that are not typically associated with each other. The story is fascinating and covers the origins of set theory and its early development at the start of the 20th century by French mathematicians. According to the authors, the tendency in France toward positivism and Cartesianism contributed to a bias among French mathematicians against theories that could not be connected to physics. Accordingly, French mathematicians became reluctant to pursue the study of the transfinite. Russia, with its mystical orientation, and particularly what became the Moscow School of Mathematics were a more fertile ground for research in this area. Especially interesting is the role played by Pavel Florensky, a Russian Orthodox monk and mathematician. Florensky represents the link between the Moscow mathematicians, several of them faithful churchgoers, and an obscure sect, the Name Worshippers, within the Russian church. While the authors do not get into the details of the theology of the Name Worshippers, it becomes clear that their beliefs had an effect on the mathematical work of Florensky and perhaps the other Moscow mathematicians. After the revolution and with the growing oppression of the Soviet regime, the overt Christianity that informed these mathematicians' outlooks had to go underground. The exception was the fearless Florensky, who continued to wear his clerical robe even in the presence of leading communists like Trotsky. Florensky ended up in prison camps where he was tortured and eventually killed. The stories and personal travails of many of the other mathematicians are also sad and poignant. But in the midst of totalitarianism, a spirit of faith and mysticism continued to color the Moscow school even in the darkest periods.

The authors are right to conclude modestly that religion does not change mathematics. A Christian mathematician should come to the same conclusions as a positivist mathematician. But the spiritual and philosophical spirit that characterizes a culture can allow ideas to develop that may otherwise be neglected or overlooked. It seems that in this case, at least, it was religion rather than rationalism that proved a more fertile ground for the growth of scientific ideas.


Zach Sherwin said...

Very interesting-- although, I'm curious why you concluded that "it was religion rather than rationalism that proved a more fertile ground for the growth of scientific ideas". Would you consider mathematical research to be scientific? I normally associate science with inductive approaches, whereas mathematics uses per deduction-- I had never considered it a science before (although this is not intended to lessen the legitimacy of the study of mathematics). Do you think I should reconsider this understanding?

michael papazian said...

Yes, I consider mathematical research to be scientific. To be sure, math is not a natural science. People often use "science" as an abbreviation for the natural sciences. But there's a broader sense of science that includes all forms of systematic inquiry, whether that inquiry focuses on nature, society, or in the case of mathematics, structures at their highest level of abstraction, and also whether that inquiry uses exclusively deductive or also inductive forms of inference.

Also, mathematics at Berry is housed in the School of Mathematical and Natural Sciences, so it must be a science.