Martyrdom of a Mathematician

I finished reading Naming Infinity a while ago, but I never did get a chance to wrap up my blogging on the book. The end really is quite tragic, and all the more so because it's a true story.

There is so much to say about all that Dmitri Egorov, Nikolai Luzin, and Pavel Florensky did for mathematics and science, and how their faith influenced their work. But since I have to choose what to focus on in a little blog post, I will choose to talk about how they were treated on account of their faith.

Pavel Florensky and Dmitri Egorov both died for their faith. It's a complicated story, and they both went down distinctly different paths, but in the end they both had the same problem--they were openly Christian under a militantly atheist regime.

Pavel Florensky was a Russian Orthodox priest, but he was also a scientist and inventor, and he is part of this story because he was very close friends with both Egorov and Nikolai Luzin, the other member of this "Russian trio."

I suppose it didn't help him that he insisted on wearing his white priest's cassock while delivering his scientific papers. You can kind of guess how the Soviet police eventually got to him--they "proved" that he was the leader of a counter-revolutionary organization, which of course he had never heard of. They shipped him off to a prison camp where he continued scientific research, but I guess they didn't even want him doing science as a prisoner.

In 1937, Florensky was sentenced to be shot. He was executed on December of that year. Recent evidence suggests the details of this death were not pleasant:

According to this information, in December 1937 Florensky was brought from the Solovetsk Islands to Leningrad, where for a while he was in a prison cell in the "Big House," the headquarters of the Leningrad secret police.... Then, according to this new evidence, Florensky was forced to undress, his hands and feet were bound, and he was taken along with several hundred other people in a convoy of trucks to the Rzhevsky Artillery Range, near the town of Toksovo, about 20 miles south of Leningrad. There, we are told, they were all shot.

What causes certain regimes to have such an irrational hatred of religion (or any dissenting view) so as to treat someone in this way?

Egorov didn't fare much better. What's crazy is that he simply insisted that his religious views were a private affair, and that all views should be tolerated in the university. Nevertheless, when he was arrested in 1930 the charge included "mixing mathematics and religion." Can you imagine living in a country where that's a crime?

While in prison Egorov prayed daily, including practicing the "Jesus Prayer," despite persecution from the guards. He eventually died there in prison due to digestive failure (which had already been a problem before being sent to prison, where his health only deteriorated). His last words are reported to have been, "Save me, O God, by Thy name!" from Psalm 54--which according to the authors of this book were "appropriate to his Name Worshipping creed."

Nikolai Luzin was not martyred for his faith, but he came pretty close. In the tragic "Luzin affair," he was basically put on trial for his faith--the crime was being tied to anything considered anti-Soviet, including the old monarcy and Christianity. Kind of ironic, considering Luzin at one time had been a sympathizer with the revolutionaries.

It's really depressing to see a lot of those big names of mathematics listed among the people who attacked Luzin, such as Alexandrov, Khinchin, Sobolev, Kolmogorov, Liusternik, and Pontriagin. Most of these are names I've heard at one time or another in my analysis classes.

But that's part of why I write this. Who knows what will ultimately draw us to such evil? It may be that a compelling ideology will grip our hearts so tightly that we lose all sanity. It appears as if a whole country was led into insanity by such an ideology. I don't think any amount of intelligence or wisdom can prevent it. Evil cuts through all of our hearts.

In the end Luzin was spared, thanks to the intervention of a famous physicist of the time, Peter Kapitsa. It's still not entirely clear why Stalin spared Luzin in this instance. He got rid of plenty of other people who were just as valuable as scientists. Perhaps we'll never really know.

What a change it is to think about mathematicians as people who suffered for their beliefs! All you typically hear is about how these child geniuses grew up to prove amazing theorems; but rarely is it ever mentioned that mathematicians have been people who struggled through real trials.

And it puts things into perspective. My friends in grad school were talking about this, and one of us said, "Next time we start to complain about departmental politics, I guess we should keep this in mind." We are so blessed to live in a country where freedom is a given.

But finally, this story really is an inspiration to me, in that it makes me contemplate how to integrate my faith completely with my occupation. It's interesting to read the author's of this book struggle with this idea:

"In concluding that mysticism helped Russian mathematicians in the development of descriptive set theory, we have had to overcome our own natural predispositions. Both of us are secular in our outlooks--far from being Name Worshippers ourselves. We did not start out writing this book in order to come down on the side of religion in the infamous science-religion debates that have occupied so large a place in recent public discussions."

As Jesus Christ put it, Wisdom is vindicated by her deeds. There really is no need to endlessly debate over religion and science. The faithful simply ought to pursue knowledge with all their heart, and they will bear fruit.

That's my goal in life--a unified pursuit of knowledge. Incidentally, that's why I've been loving Florensky's Pillar and Ground of the Truth. Maybe I'll start blogging about that soon.

Mystical Mathematicians

The essence of mathematics lies in its freedom.

Georg Cantor

I continue on in my reading of Naming Infinity, that book about religious mysticism and mathematical creativity.

Chapters 4 and 5 introduce some of the most fascinating mathematicians I've ever read about. Two of them are familiar names from my graduate level Real Analysis class during my first year: Dmitri Egorov and Nikolai Luzin.

Egorov seems more of a distant character than Luzin. He's described as "a very reserved and modest man, so much so that it would be easy to believe that he lived only for mathematics." But if one looks at his actions, one finds a man driven by strong principles and devout religious faith. This becomes a bit more of an issue later, after the Communist take-over in Russia.

Luzin is Egorov's student, a bright, idealistic intellectual who sympathizes with political radicals of his day--at least as a younger man. What really fascinates me is Luzin's story of conversion from atheism to Christianity. It's a story of real crisis, both intellectually and emotionally.

"From 1905 to 1908 Luzin underwent a psychological crisis so severe that several times he contemplated suicide. One precipitating event was the unsuccessful revolution of 1905, an event that was sobering for many left-wing members of the intellegentsia.... Luzin was shaken not only by the shedding of blood but also by personally witnessing poverty and suffering.

...

Earlier, he had embraced science, materialism, and secularism as the answer to Russia's problems. Now he doubted that these were any answers at all."

Thankfully, Luzin is deeply acquainted with Pavel Florensky, the third member of this "Russian trio." Florensky studies mathematics with Luzin in Moscow and then later becomes an Orthodox priest. The two of them remain very good friends, and later during the time of Luzin's personal crisis, this friendship becomes extremely important, as the two correspond concerning Luzin's troubled thoughts. Luzin writes to Florensky,

"You found me a mere child at the University, knowing nothing. I don't know how it happened, but I cannot be satisfied any more with the analytic functions and Taylor series.... To see the misery of people, to see the torment of life....--this is an unbearable sight....I cannot live by science alone.... I have nothing, no worldview, and no education.

...

"If I do not find a path to seek the truth...I will not go on living."

Florensky himself is a convert to Christianity, having converted from atheism at the age of 17. Despite having been raised in a secular environment, he believes that one of the sources of Russia's problems is that so many of its brightest minds (like Luzin) are attracted to atheism.

Florensky therefore provides Luzin with a "path to seek the truth" from his own religious insight. Luzin reads Florensky's thesis "On Religious Truth" (a version of which I happen to have at the moment, thanks to a kind uncle who seems to have every book in the world).

This reading combined with a continued friendship with Florensky leads to a full conversion. In 1908 Luzin writes to Florensky, "I felt as if I had leaned on a pillar...I owe my interest in life to you."

Luzin and Florensky press forward from here into a study of mathematics shaped by a shared interest in Christian mysticism. Florensky becomes an avid supporter of the "Name Worshiping" movement which goes back to chapter 1. Luzin surely knows about this development, even if he never becomes an active participant in the movement.

When it comes to mathematics, Luzin and Egorov are the real experts, it seems, but when it comes to fusing religious, philosophical, scientific, and mathematical thought together, Florensky is the real genius. Some quotes from the book illustrate:

"Florensky was convinced that intellectually the nineteenth century, just ending, had been a disaster, and he wanted to identify and discredit what he saw as the 'governing principle' of its calamitous effects. He saw that principle in the concept of 'continuity,' the belief that one could not make the transition from one point to another without passing through all the intermediate points.

...

Florensky faulted his own field, mathematics, for creating this unfortunate monolith. Because of the strength of differential calculus, with its many practical applications, he maintained that mathematicians and philosophers tended to ignore those problems that could not be analyzed in this way--the essentially discontinuous phenomena. Only continuous functions were differentiable, so only those kinds of functions attracted attention... Differentiable functions were 'deterministic,' and emphasis on them led to what Florensky saw as an unhealthy determinism throughout political and philosophical thought in general, most clearly in Marxism.

...

Florensky was convinced that mathematics was a product of the free creativity of human beings and that it had a religious significance. Humans could exercise free will and put mathematics and philosophy in perspective.... Mathematicians could create beings--sets--just by naming them.... The naming of sets was a mathematical act, just as, according to the Name Worshipers, the naming of God was a religious one....

I can't tell you how motivating it is to read about Florensky's religious and mathematical thought, and his influence on Egorov and Luzin. Today's mathematicians often seem inclined to divorce philosophical concerns from mathematics, but that is a sad state of affairs, one from which these early 20th century Russians can liberate us.

I am also deeply moved by the personal struggles of these mathematicians, and how they had to respond to the crisis of their time. I, with them, am persuaded that the best response to the crises of our time is deeper religious thought, not more secular thought.

As much as I am a fan of interacting with secularism in a healthy and open-minded manner, I think that ultimately secular thought lacks the resources we humans need to move forward. Not that religion doesn't often hold us back; but I think the best cure for stale religion is fresh religious thought. Man, does one ever find that in Florensky.

Still more to come... This book has been really good so far!

Infinity and Insanity

I've just finished reading chapters 2 and 3 of Naming Infinity, a book about mathematics, religious mysticism, and the problem of infinity.

Part of the main thesis of the book is that mathematical advances in the early 20th century were profoundly shaped by cultural and philosophical background. Overall, the book tries to compare the very different approaches of the French and the Russians, contrasting the very rationalist with the very mystical.

Chapter 2, however, starts with the Germans. In a way, I suppose the German mathematicians in this chapter (and the next) come across as in between France and Russia, both in geography and in philosophical approach. The whole mess about set theory starts with the work of Georg Cantor, who proves that there are multiple types of infinity.

Entering into Chapter 3, we read that Cantor eventually suffers from mental illness in connection with his studies of infinity. He keeps trying to prove something called the continuum hypothesis, which, as it turns out, is not really provable within the axioms of set theory. Poor guy is chasing a phantom.

People respond to Cantor's set theory with mixed reactions. One German that is willing to go to bat for him is David Hilbert, who is busy trying to advance an axiomatic approach to mathematics. Also he has a terrific hat in the picture I found on Wikipedia.

This axiomatic approach is culturally much different from the French approach, which stresses the need for a connection between physical reality and mathematics. In 1900 Hilbert proposes that the continuum hypothesis is one of the most important problems in mathematics--a pure mathematical problem, needing no grounding in physics or other sciences.

It is in this mathematical climate that we meet the three star French mathematicians of the book: Emile Borel, Rene Baire, and Henri Lebesgue. All three are very different people, except they do seem to share in common that they were not born into privilege--their mathematical talents caused them to rise to prominence in France.

The French have a cultural commitment to rationalism, inherited from Descartes, as well as positivism, a product of late 19th century philosophy. Under this philosophy, "once science liberates itself from all metaphysical influences and enters the 'positive stage,' its goal is no longer a metaphysical quest for truth or a rational theory purporting to represent reality. Instead, science is composed of laws (correlations of observable facts) that can be used by the scientists without regard to the nature of reality."

Contrast this with Cantor, whose struggles with infinity are deeply metaphysical and even religious. This is a foretaste of how the Russians will deal with the issues of set theory. But in the meantime, this "French trio" sets out with their own brilliance, eventually hitting a wall of mystery and frustration.

Despite the fact that Borel, Baire, and Lebesgue all make deep discoveries that move the study of infinity forward, eventually they all reject some basic notions of infinite set theory.

Ernst Zermelo (another mischievous German) comes up with this notion of the "axiom of choice," which all three of the French trio reject.

Kind of bizarre for me to read, really, because the very first day of Real Analysis in grad school was using the axiom of choice to generate a set that isn't Lebesgue measurable. History is full of irony.

In any case, Borel goes all hard-core and starts saying that the only entities that really exist in mathematics are those that can be constructed in finite steps. He abandons his older pursuits and focuses on more "useful" mathematics. Lebesgue can't quite divorce himself from the study of the continuum, but he's rather stuck without certain philosophical tools.

Baire becomes another victim of mental illness in this story of infinity. His already unstable mind isn't helped by the fact that he can't seem to find any way forward through the "intellectual abyss" created by the problem of the infinite.

Meanwhile, lurking around the corner seems to be a glimmer of progress in these Name-Worshiping Russian mathematicians who are about to be introduced in Chapter 4. Their secret seems to lie in being open to precisely what the French are closed off to: allowing metaphysics to mix with mathematics.

This has been a good read so far. It's keeping me awake at night, to be sure. It also makes me hope I don't go crazy. Why is there such a strong connection between mathematics and insanity, anyway?

One thing I'm seeing in these first few chapters is that perhaps there really is a need in all of us to embrace mystery, and accept what we cannot understand. Maybe it really can drive a mind insane to try to iron out all the details of a rational system that may simply have boundaries that we can never see.

Mathematics and mystery... at first they don't seem to go hand in hand, but the more I think about it, the more I think they do.

Anyway, I'm excited to continue on through this book!