Politics, Religion, and Prime Obsession

I never intended Prime Obsession to have any particular point of view about matters outside the mathematical and historical, but several readers none the less commented on the book's slight — and, I intended, utterly non-controversial — political, religious, and philosophical content.  Here I have posted as many of those comments as seemed interesting to me, with my own responses to them.

For the record, and as a patient reader can easily confirm from my print and web journalism posted elsewhere on this website, my own views on politics and religion are as follows. 

• Politics:  I am a conservative, in both the American (limited government, low taxation, local autonomy, self-support, judicial restraint) and European (respect for custom and tradition, skepticism towards ambitious schemes for perfecting human society or human nature) senses. 

• Religion:  I am a mild, not very observant, Anglican (Episcopalian in the U.S.) Christian, inclined to think that human societies are, on balance, better off with religion than without it, and that individual human beings are, on balance, better off with the religion they grew up in than with any other, or with none. 

I am not especially passionate or dogmatic in either sphere.  The above is a merest sketch of my positions, and would need a lot of qualifications to give a full picture.  (Which, if you want it, you can get by reading my journalism.)  I certainly do not need to be told that "custom and tradition" have in various times and places included foot-binding, race slavery, human sacrifice, the exclusion of women from professions, and the criminalization of private adult sexual behavior, none of which I approve of.  Nor do I need to be instructed in the many crimes and horrors that have been inspired by religious faith.  I am a well-read and thoughtful person, who has lived for several decades in the world and traveled widely.  I am always willing to read communications from readers, but I shall not respond to people who tell me, as if they were sensationally original observations, things that occurred to me before I was twenty years old.

Q.  Your day job is as a writer of political and cultural comment for National Review and other heavyweight conservative publications.  Is there any politics in Prime Obsession?  Does the book have a "view"?

A.  No.  The only politics in Prime Obsession occurs where my coverage of historical events obliges me to mention the political situation of the relevant time and place.  I give a sketchy account of the Dreyfus affair, for example, by way of background to the life of the mathematician Jacques Hadamard, who was a second cousin of Alfred Dreyfus's wife Lucie, née Lucie Hadamard.  Similarly, I show how the rise of the Nazis in Germany destroyed Göttingen university as a center of mathematical excellence.  I deal with these issues in a documentary and factual way, without passing any opinions.  To the degree that my views are visible at all in Prime Obsession, they are, I think, un-controversial — pro-Dreyfus, anti-Nazi.  I don't think there are any references to recent (post-WW2) politics at all.

This book is about the Riemann Hypothesis, and the mathematicians who worked on, or towards, it.  If you are on the political Left, you might of course object on general principles to putting money into the pockets of an author who cleaves to the opposite persuasion.  In that case you should not buy my book.  There is, however, nothing in the book itself to offend you — unless, I suppose, you are a Nazi or an anti-Dreyfusard.

Q.  What was Bernhard Riemann's politics?  Wasn't he a bit of a reactionary?

A.  Riemann's politics seem to have been conventionally monarchical-conservative.  That spell of guard duty with the student loyalists during his Berlin days (Chapter 2.vii) was the only overt political act of his life, and there is no evidence that his views changed much in the following 18 years.  I should be surprised to learn, if it were a thing that could be learned, that Riemann spent more than 0.001 percent of his time thinking about politics.

Q.  Do mathematicians as a whole have any political tendency?

A.  Historically, I cannot see one.  You can find great mathematicians of all political persuasions.  Cauchy was an extreme reactionary, Galois a radical, and so on.  There are two mathematicians in my book who were sincere Nazis:  Bieberbach and Teichmüller.  Neither was of the first rank, but both were much better mathematicians that you (almost certainly) or me (indubitably). 

From hanging around with mathematicians while working on Prime Obsession, I should guess that an American mathematician in our own time is more likely to vote Democrat than Republican.  That, however, is true of academics in general.  A liberal would argue that this demonstrates the superior intellectual content of Democratic policies; a conservative would argue that it demonstrates the ivory-tower nature of those policies — the fact that they have as little application to everyday life as, well, analytic number theory. 

The most general statement I am willing to make in this area is the following:  If you are going to do mathematics at the highest level, you will not have much time or brain-power left to think about anything else in a serious way. 

If I am right about that, one would expect that the principal characteristic of the politics of professional mathematicians would be un-seriousness.  Either a mathematician will, like Riemann, never bother to question the political ideas he heard in his childhood home; or else, if he develops strong political opinions of his own, those opinions are likely to be wacky and extreme.  The ease with which confirming examples of the latter type spring to mind suggests to me that I am on to something here.  Look at the glimpse of Hardy's politics I give in Chapter 14.iii of Prime Obsession, for instance.  Bieberbach and Teichmüller can be mentioned again in this context, too.  And let us not forget that Theodore Kaczynski, the Unabomber, holds a Ph.D. in math from the University of Michigan, and taught math at Berkeley...

Q.  You mention Riemann's piety several times in the book.  Do you believe it was a factor in his mathematical achievements?

A.  Yes.  Behind any great human accomplishment there must be some kind of energizing principle.  This must particularly be the case for a person like Riemann, weak and in poor health all his life.  Religious belief is one kind — not the only kind, but one that has been sufficiently prominent in the history of human accomplishment to suggest that it may be the best kind — of energizing principle.  For much more on this topic, I refer the reader to Charles Murray's book Human Accomplishment.  The following is taken from Chapter 19 of that book.

The vertical dimension [of a diagram Murray has introduced into his text] labeled purpose of this life also combines two thoughts:  The sense that life in general has a purpose, as opposed to being pointless, and the sense that this life is uniquely important, and is not just one of an ongoing sequence of lives. ...  Creative elites in a culture with a strong sense of duty are more likely to work hard, and be better able to carry on an existing stream of accomplishment, than in a culture where the creative elites see life as a matter of amusement.  But for the ignition of creativity, an additional sense of vocation is required....  With regard to purpose, my position does not require that the secular life be a life without purpose.  Rather, I argue that it is harder to find that purpose if one is an atheist or an agnostic than if one is a believer.  It is harder still to maintain attention to that purpose over years of effort.  Devotion to a human cause, whether social justice, the environment, the search for truth, or an abstract humanism, is by its nature less compelling than devotion to God.  Here, Christianity has its most potent advantage...  [M]y position is not at odds with the obvious fact that great human accomplishment has been produced outside Christian cultures and, for that matter, in cultures where the creative elites are secular.  I am treating Christian religious belief as one of the variables that help to explain how human accomplishment in the arts and sciences has been ignited...

There is much, much more on this topic in Murray's book, which I recommend to anyone who wishes to pursue this line of thought.  Murray describes his own religious position as follows:  "I was raised as a mainstream Presbyterian, was drawn to Buddhism during the six years I lived in Asia (and still am), currently attend Quaker meeting, and can best be described as an agnostic."

[The following multi-part question from a single reader is included here more than anything else as an illustration of the kind of thing writers have to put up with.]

Q1.  How could you place Sophie Germain among the greatest dozen mathematicians living around 1800?  What did she do to deserve that distinction?  If Bolzano could make the list, why was Pfaff, Gauss's teacher, left off?  Or among the geometers, Brianchon, Steiner, Poinsot, Gergonne; or Ruffini, a truly phenomenal amateur algebraist?  I am also puzzled by the name of Argand but Germain?  Did you have to yield to some form of, how shall I say it politely, political pressure and make a "more correct list" to get the book published?

Q2.  If you had space to mention the fanatic racialist beliefs of the otherwise talented Teichmüller, who died as a young idealistic soldier for the 3rd Reich, as relevant to the subject matter how come you did not find Hadamard's pro-Soviet views as objectionable?  While I see no relation between Hadamard's political idiocy and his contribution to number theory, if you do, fine.  Nevertheless, now that you were talking about it, this would have been a very nice opportunity to explain to the American reader how stupid some great mathematicians can be, and Hadamard was great, while Teichmüller only "talented" but not "great."  After all, you know better than most of your readers the thoroughly evil nature of Soviet Bolshevism with which quite a few intellectuals were flirting while millions were butchered in the gulags.  Honest Nazi Idealism was and is no worse than Honest Communist Idealism, just don't ask me to define what that "Honest" is.  Not all intellectuals, nor all great mathematicians, were pro-Soviet: von Neumann was virulently anti-Bolshevik, for example.

Q3.  I think the low-point in the book was dropping a casual line about Hardy's sexual, or rather potentially homosexual, interests.  I found it wholly irrelevant to the subject and, hence, tasteless.  Now Turing was a pervert and you might have said that his homosexuality did indeed eventually interfere with his creativity: instead of facing public embarrassment for his activities, he committed suicide preventing him from further work on the Hypothesis.  But Hardy?  Will you next write a variational analysis on the Britney-Madonna curvatures for the National Enquirer?

Q4.  It was most unfair to dismiss Erdős, one of the most creative mathematicians of the last century, as eccentric.  I know many mathematicians who worked with him and have nothing but kind words about Erdős's generous and collaborative spirit.  Over some sixty years, he worked with hundreds of people and never had any priority problem with anybody except for Selberg.  If anybody, Selberg is an eccentric.  And how is that possible psychologically that Erdős managed to work with almost as many people as the known zeros of Zeta function until the 60's without ever, ever, getting involved in a controversy over credit, except for one instance, while Selberg who never worked with anybody except for one instance..., well, you finish the sentence.  Mathematics is not just the PNT and to be famous and remembered, Erdős does not need the "elementary proof" to his name, Selberg does; and, probably, they both knew that ...

A1.  As I say in Chapter 6.vi, lists of this kind are always liable to start a fist-fight.  Any number of arguments similar to that of my correspondent's could be made, with different names inserted.  I don't think, however, that any of them would invalidate the general point I am making about the rise of the Germans in math during the 19th century.  I can't be bothered to argue this, or any other, correspondent's particular points.  There would be no end to it, and I have a great many other things to do.  Was I put under any pressure by my publisher to be "politically correct"?  Not really.  There were one or two small issues in copy editing, of which none loomed any larger than the following.  The copy editor suggested that Littlewood's remark quoted in Endnote 51 ("Mathematics is very hard work, and dons tend to be above the average in health and vigor.  Below a certain threshold a man cracks up...") would be improved by changing "man" to "person."  I replied that Littlewood was a great mathematician, a giant in the field I was writing about, and that however regrettable it might be that he did not meet early 21st-century standards of punctilious political correctness, it would be grossly disrespectful for me, a mere journalist, to interfere with his quoted words.  The quote remained in its original form, and I heard no more on this point.

(Added later:  Two different readers have now objected to my use of "B.C.E." in dating, so perhaps this is worth a note.  "B.C.E." stands for "Before the Common Era."  The two plaintiffs would have preferred me to use "B.C." — "Before Christ."  Well, the "B.C.E." usage is mine.  It was not imposed on my by my publisher.  I actually began with "B.C." in my early drafts, from sheer habit.  Then it occurred to me that my publisher might ask me to change it to "B.C.E."  It is the kind of change publishers do ask authors to make nowadays.  I therefore had to think the matter through — to decide how I would react if they did ask me to change "B.C." to "B.C.E."  I decided that I wouldn't much mind, and would make this change if requested.  It then occurred to me that, since I didn't much mind, and was willing to make the change if requested, I might as well avoid the whole silly business and make it right there in my manuscript.  So I did.)

A2.  Nazi Germany and Soviet Russia were both totalitarian tyrannies that committed monstrous crimes.  They were, however, different in so many respects, some quite fundamental, that I think it is pointless to argue that this one was worse or better than that one.  I agree, however, with my correspondent's implication that the crimes of the Soviets are far too little known and understood, by comparison with those of the Nazis; and that this is in part a reflection of the fact that many mid-20th-century Western intellectuals were, like Hadamard, taken in by Soviet propaganda.  (Though it is also a reflection of the other fact that Nazi Germany was defeated in battle and occupied by the victors, while Soviet Russia was not.)  However, Teichmüller was a uniformed, active, and obedient member of the ruling party in Nazi Germany, while Hadamard was merely a distant observer of, and mild sympathizer with, the U.S.S.R.  He did not even join the French Communist Party (though his daughter did).  I cannot see any equivalence here.

A3.  My correspondent is referring to the following remarks I included in Chapter 14.iii of Prime Obsession:  "In the manner of our age, there has recently been some speculation that Hardy may have been homosexual.  I refer the curious reader to Robert Kanigel's biography of Hardy's protégé Srinivasa Ramanujan, The Man Who Knew Infinity, which contains a full discussion of this point.  The answer seems to be:  probably not, except perhaps in the innermost sense."  Now, I believe that a fair-minded reader would deduce from that passage that (a) I don't care for this kind of speculation myself, (b) for the benefit of readers who do, I took the trouble to supply a suitable reference source, (c) I don't think Hardy was an active homosexual.  I don't see how I could have said less than this, without completely avoiding a point that would naturally — though in my opinion, as I think I made clear, regrettably — occur to a reader in our time.  That Alan Turing's homosexuality did indeed "interfere with his creativity" and so on is surely plain from what I wrote in Chapter 16.v.

A4.  I have covered the case of Erdős in my FAQs page (the note to page 125 of Prime Obsession).  I too have met many mathematicians who knew and worked with Erdős, and I have also discussed the matter face to face with Atle Selberg.  As best I can judge, Erdős was a very fine mathematician who was much loved by his colleagues.  However, the consensus among mathematicians is that he was at fault in the Selberg affair, though probably from sheer unworldliness rather than ambition or malice — there seems to have been no trace of either ambition or malice in his personality.  Since I do not pass an opinion on any of this in Prime Obsession, these are all secondary remarks.  I do, however, use the word "eccentric" to describe Erdős.  If this usage is, as my overheated correspondent claims, "unfair," then I do not know what possible application the word "eccentric" can have.  If Erdős was not eccentric, nobody has ever been, nor ever will be, eccentric.  Here is something I wrote when reviewing the Erdős biographies that came out after his death.

Erdős was born in 1913 (a prime number, I cannot forbear noting, both forward and backward) and died a prime number of years later in 1996 (a prime backward and upside down — though not, alas, forward). All but the first two of those years were given up to mathematics — every day, every hour.  He did nothing else; he wished to do nothing else. He had no possessions, no regular job, no home, no sex life, no interests outside math.  All his friends were mathematicians. When they took him to movies or concerts, he fell asleep.  He never watched TV or read fiction. His letters go like this: "Am in Sydney. Next week, Budapest. Let p be any odd prime..."  He never spent a second trying to acquire any more money than his very frugal lifestyle required.  When larger sums of money came to him, he gave them away as prizes for solving mathematical problems.

It is possible that this is just a linguistic misunderstanding of the transatlantic sort.  The word "eccentric" has no pejorative connotations in British English.  To the contrary, eccentric people are rather admired in Britain.  Amazon.co.uk lists at least two books in praise of great ("magnificent" says one of the titles!) British eccentrics.  I thought — and, as a matter of fact, still think — that the word has no pejorative connotations in American English, either; but perhaps my correspondent does not know this.  Or perhaps I am mistaken; in which case I hope someone will tell me which word American English prefers in this context.