Cycling around Munster, (long) after the siege.

Back in May I was visiting Giles in Munster. Aside from meditating on what exactly a symmetry restricted group should be, and going to see Detective Pikachu, we did a fair amount of cycling back and forth across the city. Munster enjoys a reputation (perhaps self-proclaimed) of being the cycling capital of Germany, and with all the cycle paths and low levels of automobile use it is not hard to fall in love with the place and wonder why we aren’t all living is such a fashion.

If you are observant enough while wandering around the city, you will notice three metal cages hanging from the steeple of St Lambert’s church. Those cages once held the mutilated remains of religious radicals who had been so jazzed up by the Reformation that they had declared Munster the New Jerusalem and announced the imminent apocalypse, Jesus’s return, and all the rest of it. So deplorable was their rule of the city (and embarrassing) that both Catholics and Lutherans united to lay siege to the Munster to bring an end to New Jerusalem.

This photo of Muenster Cathedral (St. Paulus Dom) St Lambert’s Church is courtesy of TripAdvisor

Giles was good enough to lend me his copy of New Jerusalem: The short life and terrible death of Christendom’s most defiant sect, by Paul Ham. (A good alternative source is this episode of In Our Time on the Siege of Munster, although the reintroduction polygamy is not even given a mention). It makes for quite remarkable reading. To a contemporary reader the most obvious parallel is to ISIS. I would go so far as to say that everything you could find in the rise and fall of ISIS you can also find in the history of New Jerusalem. Down to the beheadings.

The founding of New Jerusalem was the culmination of the work of many personalities. They were all united in the Anabaptist cause: abandoning infant baptism as a perversion of the “true” gospel by the church in Rome. While the followers of Luther took a more pragmatic, and even conservative, approach to religious reform, these “re-baptisers” were revolutionaries outside any kind of religious establishment who were provocative to the point of inciting violence. (Baptism is no small point; you will still find many protestant churches today which require adult baptism for membership.)

Melchior Hoffman, an Anabaptist preacher, prefigured the events in Munster when he declared Strasbourg to be the New Jerusalem, and the site of the apocalypse the following year, 1533. The authorities back then took such rantings seriously enough that they threw him in a dungeon, where he could safely be forgotten. Then came John Matthais, a self proclaimed prophet, who received the divine revelation (or simply decided, depending on your point of view) that Hoffman had got the time and place wrong, and that Munster was in fact the right location. Initially it seemed that this prophesy was realized, as in February 1534 the city was taken into Anabaptist control. This turn of events was seen as an embarrassment, nuisance, and danger to the various authorities involved. Ultimately it fell to Bishop Waldeck — more a nobleman or prince than an actual religious leader — to marshal an army and lay siege to the city. Due to the commitment and tenacity of those under siege, Munster’s excellent fortifications, and the drunkenness of the mercenaries that Waldeck employed, the whole sorry business lasted a year and a half.

John Matthais would go on to have himself cut to pieces by the armies of Bishop Waldec in possibly the most ill advised cavalry charge in history. It is Matthais’ second in command, John of Leiden, who takes over control of New Jerusalem and ruled it through most of the rebellion. Leiden’s rule quickly becomes a tyranny marked with the reintroduction of polygamy and summary executions by decapitation. The whole episode was marked with a strange combination of farce and grim horror.

While ISIS is the most obvious modern parallel, with its explicitly apocalyptic mission, reading the accounts of meetings between radical preachers and Luther calls to mind the general dangers of political radicalism.

Instead, Rothman set off on the well-worn pilgrimage to Wittenberg, as reform-minded novitiates tended to. There, Luther and Melanchthon deigned to meet this impassioned young man, as they had met Hoffman and so many other zealous young preachers. They noted his intelligence and eloquence, yet something about Rothmann troubled them. His passions were unguarded, and untutored. His self-righteousness lacked the grace of humility. They concluded that he was probably mentally unfit for the job. As Melanchthon observed, Rothmann might turn out to be exceptionally good or exceptionally bad.

New Jerusalem, Chapter 7 — Paul Ham

I find the reformation, or at least what little I understand about it, deeply fascinating. It is on the list of subjects that, once you understand a little of what it meant and continues to mean, you are staggered by the degree with which you misunderstood so much of what is going on in the world today.

(For whatever it is worth, Detective Pikachu was fun but completely disposable.)

Gromov, cheese, pretending to quit mathematics, and French.

In December last year, the Notices of the AMS ran a collection of reminiscences in memory of Marcel Burger (1927-2016), the late French differential geometer. He was also a former director of the Institut des Haute Etudes Scientific and, according to the Wikipedia, played a major role in getting Gromov positions in Paris and at the IHES in the 80s. Gromov contributed to the article, listing Berger’s mathematical achievements, before sharing a more personal anecdote:

Within my own field Gromov has had a profound influence. His essay Hyperbolic Groups led to the term “combinatorial group theory” being more or less abandoned and replaced with “geometric group theory”. As a graduate student I found the monograph frequently cited as the origin for an astounding range of ideas. At some point I had trouble finding a copy of the paper online and for a brief moment wondered if the paper itself were just an urban myth or elaborate hoax.

Gromov’s foray into group theory is just one episode in a long career. His first major breakthrough was in partial differential equations; the “h-principal” which, according to Larry Guth, was analogous to observing that you don’t need to give an explicit description of how to put a wool sweater into a box in order to know that you can actually put it into the box. It is actually a little hard, at least for myself, to get a full grasp on Gromov’s other contributions as they span unfamiliar fields of mathematics, but I recommend this nice What is… article, written by the late Marcel Berger, describing Gromov’s contribution to the understanding of isosystolic inequalities.

There is the perception about great mathematicians that, while they are no doubt very clever, somehow they have lost a little of the common sense that the rest of us possess. I’m naturally inclined to discount such thinking; I am far happier believing that we are all fool enough to take absence of common sense, on certain occasions. However, it is hard to dismiss the  idea entirely given the following admission by Gromov, in his personal autobiographical recollections he wrote on receipt of the Abel prize in 2009:

The passage speaks for itself, but I wish to emphasize that Gromov’s discovery of the correct pronunciation of French verb endings came after ten years of living in Paris. You don’t have to have extensive experience learning foreign languages to appreciate how remarkable an oversight this is. It certainly puts his remarks in other interviews about dedicating one’s life to mathematical pursuits in a rather strong light.

If you read the entire autobiographical essay you will find it rather short on biography. The best biographical details I have found came from this La Monde article written on his being awarded the Abel prize. Even then the details seems to be coming second hand. The most interesting parts concern his leaving the Soviet Union:

I wanted to leave the Soviet Union from the age of 14. […] I could not stand the country. The political pressure there was very unpleasant, and it did not come only from the top. […] The professors had to teach in such a way as to show respect for the regime. We felt the pressure of always having to express our submission to the system. One could not do that without deforming one’s personality and each mathematician that I knew ended up, at a certain age, developing a neurosis accompanied  by severe disorders. In my opinion, they had become sick. I did not want to reach that point.

Gromov, according to Georges Ripka, via La Monde (apologies for my translation)

As the article goes on to explain, Gromov decided his best chance to escape was to hide his mathematical talent. He quit math, quit his university, and burned all his academic bridges. He stopped producing mathematics. Or at least writing it. He joined some meteorological institute and did research on paper pulp. Eventually, he was granted permission to emigrate to Israel, but on landing in Rome in 1974 he set off for the States instead, where Jim Simons secured him a position at Stony Brook.

(As a side note, this is Jim Simons of Renaissance Technology and Simons foundations fame. Simons, aside from his mathematical contributions, is probably one of the most important mathematicians alive in terms of funding, supporting, and propagandizing for mathematics. He is considered influential enough for the New Yorker to profile. Alongside Gromov, he is one of the names that every mathematicians should know.)