Re: Vanity and Ambition in Mathematics
Thanks for your feedback.
Note that my suggestion is that
It’s noticeably less common for mathematicians of the highest caliber to engage in status games than members of the general population do.
This is consistent with your remark:
It makes sense that while mathematicians are thinking about math they need to focus completely on the subject to do good work, and don’t have time to be concerned with status.
as the very best mathematicians typically spend a lot more time fully focused on math than is typical among mathematicians. I find it plausible that such focus tends to spill over into nonmathematical activity as well. In Henri Poincare’s “Ethics and Science,” Poincare wrote
Can science become the creator or the inspirer of feelings? What science cannot do, will the love of science be able to do?
Science keeps us in constant relation with something which is greater than ourselves; it offers us a spectacle which is constantly renewing itself and growing always more vast. Behind the great vision it affords us, it leads us to guess at something greater still; this spectacle is a joy to us, but it is a joy in which we forget ourselves and thus it is morally sound.
He who has tasted of this, who has seen, if only from afar, the splendid harmony of the natural laws will be better disposed than another to pay little attention to his petty, egoistic interests. He will have an ideal which he will value more than himself, and that is the only ground on which we can build an ethics. He will work for this ideal without sparing himself and without expecting any of those vulgar rewards which are everything to some persons; and when he has assumed the habit of disinterestedness, this habit will follow him everywhere; his entire life will remain as if flavored with it.
For a counterpoint to my suggestion, I’d point to Grothendieck’s remark in “Recoltes et Semailles” (quoted in my “Vanity and Ambition in Mathematics” article):
The truth of the matter is that it is universally the case that, in the real motives of the scientist, of which he himself is often unaware in his work, vanity and ambition will play as large a role as they do in all other professions. The forms that these assume can be in turn subtle or grotesque, depending on the individual. Nor do I exempt myself.
Concerning your remarks:
Every mathematician worth his or her salt knows of Hironaka, Langlands, Gromov, Thurston and Grothendieck. So these are not typical mathematicians: they are our heroes, our gods.
It is nice having humble gods. But still, they’re not stupid: they know they’re our gods.
I think that expressions of humility that great mathematicians exhibit may be genuine. The historical standard for quality is very high and exposure to the work of great mathematicians of the past and the historical sweep of the subject can be humbling. In a 1940 letter of André Weil on Analogy in Mathematics, Weil wrote
Of course, I am not foolish enough to compare myself to Riemann; but to add a little bit, whatever it is, to Riemann, that would already be, as they say in Greek, to do something {[faire quelque chose]}, even if in order to do it you have the silent help of Galois, Poincaré and Artin.
In “Commencement address at the University of Toronto, June 1993”, Robert Langlands wrote:
It is difficult for those with no experience to understand that most mathematical issues are, in spite of the efforts of our great predecessors, in large part unresolved. Although not so chaotic or undisciplined as the world around us, mathematics does reveal itself in shapes and patterns that, like those of light and sound, can never be seized once and for all. To impose order on them requires often heroic efforts.
Moreover, although mathematics is an art that is anterior to the classical Mediterranean civilizations, it moves slowly. We are not so far from the number theory of Fermat in the seventeenth century, nor from the mechanics of fluids and solids of Euler in the eighteenth.
Re: Vanity and Ambition in Mathematics
I am intrigued by Sinick’s suggestion that mathematicians have a “markedly lower than usual interest in status” than most people. I don’t believe it, and I tried to explain why in a comment over there.
John, could you give a link to your comment, please?
There are two aspects that seem obvious to me. One the one hand, it’s obvious that we mathematicians crave respect from our peers: gaining the respect from smart people we respect is arguably a major drive that keeps us going.
But we are also very lucky in that status always takes a back seat to logical correctness. It is a wonderful thing that if a graduate student points out a flaw in the argument of the illustrious Professor, the point must be quickly (and is usually graciously) admitted. I don’t see how you can be a mathematician without being fanatically committed to logical truth: only a fool clings to status over a mathematical truth which will soon enough become obvious to all!
Indeed, we mathematicians are fantastically lucky that we can so easily come to agreement (compared to philosophy or politics say), on account of the strict rules of our game. This makes real and rapid progress in our field possible, in a way unlike any other field.
Re: Vanity and Ambition in Mathematics
As I understand it, the quote from Jonah was about the *comparison* to other fields of activity. In this, I tend to agree. Obviously, political considerations will be part of most human affairs and you can bring up your favorite example of the arrogance of Professor X. But still, on the whole, my feeling is that the landscape of mathematics is remarkably even.
I have quite a few anecdotal bits of evidence, but the ones that come closest to being concrete I get by comparing notes with my father, who works in literature.
I often organize mathematical events and my father organizes literary events. When we discuss these things, he is regularly amazed at how easy it is for an ordinary person like me to invite distinguished mathematicians when compared to the enormous production involved in inviting distinguished writers. The latter often employ agents, and demand tens of thousands of USD for a single lecture. I’ve remarked elsewhere that this kind of display often creates the wrong impression that writers are better off than mathematicians, even though the average active writer would starve without another job. To make this into a quantitative statement would obviously take careful work, but my impression is that the *difference* of (actual and self-perceived) status among practioners of literature, as well much of the arts, is markedly larger than in mathematics.
Here is another story (intended to be funny, mostly): My father was once involved in an attempt to invite Professor N to Korea, a philosopher, and perhaps one of the most distinguished within the liberal/radical school in the US. As mentioned, people are quite used by now to the demand for high fees, airfare, and so forth. In this case, the philosopher asked the organizers to make sure that the hotel had an exercise room. This was done. After a while, inquiry was made about a specific piece of equipment. This seemed a bit strange, but the hosts obliged. And then, they were asked to make sure about the specific brand…(things got a bit strained at this point). As I said, we all know examples of the antics of mathematician X. But my feeling is it’s not too well-known among my colleagues how extreme things can be in other professions.
If I would venture as guess as to the reasons for this difference, the nature of the work itself may indeed play a role. But at least one important (and related) factor seems to involve the size of the cognizant community. Even a Fields medallist (and the medal itself) is virtually unknown outside of the mathematicial community. Famous writers, artists, and philosophers, on the other hand, often have a presence in the public media.
Re: Vanity and Ambition in Mathematics
Thanks for your feedback.
Note that my suggestion is that
This is consistent with your remark:
as the very best mathematicians typically spend a lot more time fully focused on math than is typical among mathematicians. I find it plausible that such focus tends to spill over into nonmathematical activity as well. In Henri Poincare’s “Ethics and Science,” Poincare wrote
For a counterpoint to my suggestion, I’d point to Grothendieck’s remark in “Recoltes et Semailles” (quoted in my “Vanity and Ambition in Mathematics” article):
Concerning your remarks:
I think that expressions of humility that great mathematicians exhibit may be genuine. The historical standard for quality is very high and exposure to the work of great mathematicians of the past and the historical sweep of the subject can be humbling. In a 1940 letter of André Weil on Analogy in Mathematics, Weil wrote
In “Commencement address at the University of Toronto, June 1993”, Robert Langlands wrote: