In the post Graduate level textbooks I I mentioned an advice given to me by a colleague many years ago:

*"Do not write any books until you retire"*. posic commented on this:

"Do not write any books until you retire"?! One is tempted to generalize to "do not do any mathematics until you retire". Or, indeed, to "do not do anything you find interesting, important or meaningful until you retire"...

Gone are the days when Gian-Carlo Rota wrote "You are most likely to be remembered for your expository work" as one of his famous "Ten lessons I wish I had been taught". Not that I so much like this motivation, that is one's desire to have oneself remembered at any expense, but compared to people doing mathematics from the main motivation of getting tenure, grants, etc., it was, at least, leaving ground for some cautious hope. Presently I do not see any.

I am sorry for the long delay with a reply. Here are some thoughts.

The advice of my colleague does not admit such generalizations. He based it on the opposite grounds: he wanted me to do something more interesting than writing books.

He made a couple of common mistakes. First, he has no way to know what is interesting to other people, including myself. A lot of people do find writing expository works (at any level, from elementary school to the current research) to be very interesting. Actually, I do. At the same time, many mathematicians complain about lack of necessary expository writings. Some direction of research died because the discoverers are not able to write in an understandable manner, and others were discouraged to write expositions. At the same time, writing down some ideas is a creative work at a level higher than most of

*“Annals of Mathematics”*papers.

Second, he followed a prejudice common at least in the US: expository writing is a second-rate activity compared to proving theorems. This prejudice is so strong that proving “empty” theorems is valued more than excellent expository writing. Apparently, this is a result of external with respect to mathematics influences. The main among them is the government funding of pure mathematics. There is essentially only one agency in the US providing some funds for pure mathematics, namely, the NSF. The role of few private institutions is negligible. It is not surprising that NSF has its own preferences, and the pure mathematics is not its main concern. Moreover, it is very likely that NSF is even not allowed by law to fund expository writing (I did not attempted to check this).

G.-C. Rota is right. He almost always right, especially if you at least try to read between the lines. Actually, the most cited (and by a wide margin) work of the mentioned colleague is a purely expository short monograph. So, he does not put his money where his mouth is.

Actually, I am not inclined to read G.-C. Rota so literally. He is a too sophisticated thinker for this. Whatever he says, he says it with a tongue in cheek. He wanted to encourage expository writing. The motivation he offered isn’t really the fame. It is the usefulness. You will be remembered most for things most useful for other people. For many expository writing will be much more useful than publishing a dozen of “research” papers.

I think that it will come as no surprise to you that the government agencies, supposedly to work on behalf of the people, demand a lot of work hardly useful to anybody, and do not support really useful (at least to some people) activities. I also believe that only few other mathematicians will agree.

Doing mathematics for getting tenure or its equivalent is essentially doing mathematics for having an opportunity to do mathematics. There are no other ways. If you know a way to do mathematics without an equivalent of a tenured academic position in the US, please, tell me. I do have tenure, but I am quite interested.

This is not so with "grants, etc.", especially if you have tenure. Working for grants is a sort of corruption. Unfortunately, it is so widespread. Well, some people, for example G.W. Mackey, predicted this at the very beginning of the government funding. They turned out to be correct.

G.-C. Rote wrote these words quite a while ago. Things did not improve since then. The expository writing is valued even less than at the time. Nobody cares if he/she or you will be remembered 100 years from now, or if a current paper will be remembered 10 years from now. Everything is tailored for the medicine and biology. Reportedly, almost no papers there are remembered or cited after 2 years. Anyhow, the infamous impact factor of a journal takes into account only the citations during the first 2 years after the publication. The journals are judged by their impact factor, the papers are judged by the journals where they are published, and academics are judged by the quantity (in the number of papers, not pages) and the "quality" of their publications.

Apparently, mathematicians are content with the current situation and are afraid of any changes more than cosmetic ones. Is there a hope?

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ReplyDeleteWell, I can only speak for myself. I do not believe there is, or can be, or indeed should be, any regular way to "have an opportunity to do mathematics". Neither grants nor tenured positions are such an opportunity; in my view. Rather, they are an opportunity to solve one's everyday problems and have a moderately pleasant life based on declaring oneself to be a research mathematician and producing enough worthless or nearly worthless writing and oral presentation imitating mathematical research in accordance with the presently prevailing fashion of imitating mathematical research, in order to be awarded the desired material goods by the crowd of people specializing in the imitation of mathematical research. Of course, both the grants and the tenured positions can be also used, at least in principle, as a way of doing genuine mathematics and not an imitation; so can perhaps many other things. But they are not a regular way to provide oneself with such an opportunity. Nothing is.

ReplyDeleteIn my case, I started doing research in mathematics as an undergraduate student in Moscow, then continued as a graduate student in Moscow, and then as a graduate student in the US. Then I did several years of postdocs in the US and in Europe, interrupted by a year in Moscow (where I lived off what little remained of my savings after buying a small apartment in the outskirts of the city with the IAS postdoc stipend money, paid of course by the NSF).

Having only one refereed publication (with two coathors) for the five years after Ph.D. (and four refereed publications for the seven years before Ph.D.), I had no other choice but to return home after the postdocs in Europe ended. There I remained essentially unemployed for 4.5 years, living off what little remained of my savings after exchanging the small apartment for a slightly bigger one with the MPIM stipend money added, plus very little income from high-level teaching and small grants, but mostly off the financial help of my relatives (mostly of my mother, who had three simultaneous teaching jobs in three different higher education institutions in Moscow at some point, as however did quite a few people in Russia at the time). I was married with a little daughter, and my wife was also working and making some money.

Then I started writing and publishing again, and soon a new 190-page long preprint (eventually published as a 370-page long research monograph) was on the arXiv, and I won a competition for individual grants, obtaining a rather large stipend for 3 years (later extended for another year), and soon also got a researcher job in one of the Moscow research institutes. Three and a half years later, I also had a regular teaching job at the best (by large margin) pure mathematics department in the city. It also paid rather well; my savings were once again growing rapidly.

None of these was anything like a tenured position, of course. On paper, these were fixed-term contracts for 1, or sometimes 3, or, at most, 5 years. In reality, the probability of the contract being formally not extended always seemed to be rather small, but the actual wage payments consisted mostly not of the base salaries but of salary supplements, which were guaranteed for at most 2 years, or not guaranteed at all. The rules for obtaining or calculating these salary supplements were changing all the time, and the actual payments sometimes fluctuated wildly.

ReplyDeleteDuring the 6 years that I was employed in Moscow in this way, in addition to the preceding 1.5 years of unemployment, I wrote something like 1250 pages of mathematical research work, in 12 separated pieces, 6 of which (of some 650 pages of total length) have been published in refereed journals or book series, and the other 6 still only exist as arXiv preprints (4 of them largely finished and 2 pretty much unfinished). Summarizing this kind of a research career in a short formula, I would say that for the first 10 years of my life I was a child, for another 10 years I was learning the subject (including how to do research and write short papers), for the next 10 years I was making the major conceptual breakthroughs of my work (while publishing almost nothing), and then during the last 10 years I was polishing the techniques and writing up the expositions.

So, looking at things in retrospective and based on what I actually did and which choices I actually made, I think it is fair to say that it was never much of a concern for me to have an opportunity to do mathematics, and now I do not have it. Rather, I wanted to have some important mathematics done, and now I have. My faith in longevity of my mathematical ideas is much, much stronger than that in my own survival. But then, mathematics exists for more than 2000 years, and I never heard of a mathematician who lived past 120, tenure or no tenure.

Still, there are different ways of living, and different ways of dying. The present situation in Russia is a clear-cut catastrophy in my view, so I had to leave the country and move elsewhere. Being Jewish, I am now in Israel, attempting to obtain the "ole hadash" (newly repatriated person) status. (My wife, whom I de facto, but not yet de jure, divorced almost a year ago, still lives in that Moscow apartment together with our daughter.) Shortly before leaving for Tel Aviv, I was told by a colleague in Moscow that I should expect my position in Israel to be much worse than it used to be in Moscow, and that I may well end up collecting garbage on the beach. So my choice can be said to have been made based on the preference of collecting garbage on an Israeli beach rather than cutting timber in a Kolyma prison camp.

At the age of 41, with quite an amount of important work done in the past (including and up to the very recent past) and very little perspectives or expected opportunities in the future -- do I have any hope? Yes, but it is not a hope in the short-term future of mathematics, not to speak of the present or future of the present-day mathematicians. Rather, I hope that the gems of the 20th and early 21st century mathematics will survive the impending collapse of our civilization, just as the gems of Greek mathematics survived the collapse of the antiquity. Perhaps even one or two of my best ideas will be found among the less important of these surviving gems.

@posic: people in Russia nowadays are just plain crazy. Your colleague deserves a spite right into face.

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