Here we go again...

Tolerance of evil.

Leo Tolstoy on Mathematics

In 1862, Leo Tolstoy published “War and Peace,” an epic national novel of Russia that uses individual and singular moments in peace and war to explore human universals and timeless themes. So now, as I begin page 937 (out of 1,386), or Part 11, Chapter 1, I decide to bring Tolstoy’s thoughts on mathematics (circa 1862) to bear on the FCP crowd.

After the catastrophic and near pyrrhic Russian victory over Napoleon’s forces at the Battle of Borodino just outside Moscov (Tolstoy has it taking place in late August 1812), Tolstoy ruminates on the eternity that is the universe, and how humans are incapable (or nearly incapable) of dealing with infinite, but are very capable in dealing with small segments of quantities in an historical or mathematical way. To connect the analogy with the battle, or with humanity: “The progress of humanity…” that is, after literally tens of thousands of Russian and French soldiers are annihilated, “…arising from an innumerable multitude of individual wills, is continuous in motion.” Thousands have died. But hundreds of thousands continue living. Humanity pushes on, and on, and on. But understanding this grand push requires one to study the singular.

And on mathematics, Tolstoy says, “By taking smaller and smaller units of motion we merely approach the solution of the problem, but we never attain it. It is only by assuming an infinitely small magnitude, and a progression rising from it up to a tenth, and taking the sum of that geometrical progression, that we can arrive at the solution of the problem. A new branch of mathematics [again, this written in 1862], dealing with infinitely small quantities, gives now in other more complex problems of dynamics solutions of problems that seemed insoluble.”

(page 937 of Tolstoy, “War and Peace,” Constance Garnett translations, Modern Library, 2002 printing.)

So feel free to use that as the opener in you next mathematical conference paper (just footnote me as your pro-bono, self-appointed historical and literary consultant).