2013年1月1日 星期二

Nikolai Luzin

Nikolai Luzin

Maths and the monks

How the name-glorifiers’ influence rippled through intellectual history

ON THE wall of the maths department of Moscow University, there used to be a family tree tracing links—who mentored whom—between dozens of Russian and Soviet mathematicians and scientists of the 20th century. Towards the bottom are some leaders of the Soviet space and nuclear programmes. Near the top is Nikolai Luzin, a brilliant, tortured mathematician, straddling the tsarist and Soviet eras, who was also a devout follower of the name-glorifying movement.
Two scholars—Jean-Michel Kantor, a French mathematician, and Loren Graham, an American philosopher of science—see this as more than a biographical detail. As name-glorifying gathered pace in the twilight of the tsarist world, mathematicians were wrestling with the question of infinity, and with the idea of a set which had an infinite number of constituents. Were all infinite sets the same, or was it possible to speak of multiple infinities, even an infinite number of infinities? French mathematicians got stuck on this question; their Russian counterparts untied the knot and stimulated such rich lines of enquiry as string theory, topology and the possibility of multiple universes.

In their book, “Naming Infinity”, Mr Kantor and Mr Graham argue that Luzin’s religious beliefs—and those of his close friend, the idiosyncratic priest, mathematician and name-glorifier Pavel Florensky—help explain these breakthroughs. As people who believed in the spiritual power of the name of God, the glorifiers felt bold enough to grapple with, and in some sense, pin down the concept of infinity. Their religious faith may have helped them find a path through the old debate between nominalism—the idea that names or sets are just a handy way of bunching things together—and realism, which holds that categories have an objective existence. (Plato was a realist; a famous nominalist was Lewis Carroll’s Humpty Dumpty, who declared that “When I use a word, it means just what I choose it to mean…”)
Like his theological mentors, Luzin got on the wrong side of authority. In 1936, he was tried for treason; two of his pupils (blackmailed because they were gay) denounced him. He escaped execution but Florensky, tried separately, did not. Until the Soviet Union collapsed, files on Luzin were hard to get. Mentioning him can still cause discomfort in Russian academic circles, where his fate is a dark memory. This year he was rehabilitated by Russia’s Academy of Sciences. Perhaps the monks who inspired him will have a similar vindication.

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