Previous post: Who will get Fields medals in less than two hours?
Of course, if you are interested, you know already: Artur Avila, Manjul Bhargava, Martin Hairer, Maryam Mirzakhani.
I named in my previous post all except Martin Hairer, who is working in a too distant area in which too many people are working. I was put off tracks by the claim that M. Mirzkhani definitely will not get the medal. Before this rumor (less than a week ago) I would estimate her chances as about 60%. The award has no effect on my opinion about her work: her results are very good and interesting, but not "stunning", as it is said in the citation. Many people in related areas and even in the same area made comparable or much deeper and unexpected contributions.
I do not consider my estimates of somebody chances as predictions when the estimate is 60% or even 80%.
But I made three predictions, and they turned out the be correct: Artur Avila will be a winner; one of the winners will be a woman; one of the winners will be from Stanford. The first two of them were rather easy to made. But why Stanford? The idea materialized in my mind out of blue sky only few days ago; there was no new information, neither rumors, nor mathematical news.
Instead of a medal Jacob Lurie recently got a prize worth of 3 millions. I hope that he realizes that the decision of the Fields medal committee not to give him a medal tells much more about the committee than about the depth and importance of his work.
Next post: To appear
Showing posts with label monetary rewards for research. Show all posts
Showing posts with label monetary rewards for research. Show all posts
Wednesday, August 13, 2014
Tuesday, August 12, 2014
Who will get Fields medals in less than two hours?
Previous post: About expository writing: a reply to posic
At 10:30 p.m. US Eastern Summer time, the winner of this (2014) year Fields medals will be announced in Seoul.
I would like to post my current guess, mostly to have a record of it with the date and time stamp from Google, at least for myself.
As I wrote about one year ago, I believe that I would be able to predict the actual winners if I would know the composition of the Fields medals committee. But I don't. I am not particularly interested in the names of the winners, so I did not attempted to find out the actual winners, who are known for at least three months already, and who are known to the press for at least two weeks already (if the practice of the last two congresses was continued). So, my guess is a guess and not based on any inside sources.
And the winner are (expected to be):
Artur Avila - my confidence is over 95-99%.
One of the winners will be a woman - my confidence is over 95%. This is a pure politics. This deserves a separate discussion. The main obstruction to the Fields medal for a woman is not the discrimination, but the absurd age restriction. Most likely, she is
Sophie Morel - my confidence is over 80%. There are political consideration against her. For example, she would be the 3rd medalist who was a student of Gérard Laumon.
Jacob Lurie - my confidence is about 60%. This is my favorite candidate. He will get it if Harvard has enough political clout now. So, it is a measure of the influence of the Harvard Department of Mathematics, and not of the level of J. Lurie as a mathematician.
Manjul Bhargava - my confidence is less than 50%. If Sophie Morel gets a medal, his chances are much lower than otherwise: two mathematicians from the same university (Princeton).
Following the tradition firmly established since 1990, one of the medals should go a "Russian" mathematician, no matter where she or he is working know and where she or he completed Ph.D. I don't see any suitable candidate. Some people were naming Alexei Borodin, but I was firmly told that he will not get one.
A couple of days ago a strange, apparently unmotivated idea come to my mind: one of the winners will be from Stanford. Some people were naming Maryam Mirzakhani, but, again, a couple of days ago was firmly told that she is not the winner. Her work is interesting and close to my own interests. In my personal opinion, she has some very good results, but nothing of the Fields medal level. I would estimate the number of mathematician of about her level or higher, working in closely related areas, as at least 2-3 dozens. Of course, I am not aware about her most recent unpublished (at least on the web) work.
Next post: And who actually got Fields medals?
At 10:30 p.m. US Eastern Summer time, the winner of this (2014) year Fields medals will be announced in Seoul.
I would like to post my current guess, mostly to have a record of it with the date and time stamp from Google, at least for myself.
As I wrote about one year ago, I believe that I would be able to predict the actual winners if I would know the composition of the Fields medals committee. But I don't. I am not particularly interested in the names of the winners, so I did not attempted to find out the actual winners, who are known for at least three months already, and who are known to the press for at least two weeks already (if the practice of the last two congresses was continued). So, my guess is a guess and not based on any inside sources.
And the winner are (expected to be):
Artur Avila - my confidence is over 95-99%.
One of the winners will be a woman - my confidence is over 95%. This is a pure politics. This deserves a separate discussion. The main obstruction to the Fields medal for a woman is not the discrimination, but the absurd age restriction. Most likely, she is
Sophie Morel - my confidence is over 80%. There are political consideration against her. For example, she would be the 3rd medalist who was a student of Gérard Laumon.
Jacob Lurie - my confidence is about 60%. This is my favorite candidate. He will get it if Harvard has enough political clout now. So, it is a measure of the influence of the Harvard Department of Mathematics, and not of the level of J. Lurie as a mathematician.
Manjul Bhargava - my confidence is less than 50%. If Sophie Morel gets a medal, his chances are much lower than otherwise: two mathematicians from the same university (Princeton).
Following the tradition firmly established since 1990, one of the medals should go a "Russian" mathematician, no matter where she or he is working know and where she or he completed Ph.D. I don't see any suitable candidate. Some people were naming Alexei Borodin, but I was firmly told that he will not get one.
A couple of days ago a strange, apparently unmotivated idea come to my mind: one of the winners will be from Stanford. Some people were naming Maryam Mirzakhani, but, again, a couple of days ago was firmly told that she is not the winner. Her work is interesting and close to my own interests. In my personal opinion, she has some very good results, but nothing of the Fields medal level. I would estimate the number of mathematician of about her level or higher, working in closely related areas, as at least 2-3 dozens. Of course, I am not aware about her most recent unpublished (at least on the web) work.
Next post: And who actually got Fields medals?
Thursday, January 2, 2014
Graduate level textbooks I
Previous post: The role of the problems
Back in August Tamas Gabal asked me about my favorite graduate level textbooks in mathematics; later Ravi joined this request. I thought that the task will be very simple, but it turned out to be not. In addition, my teaching duties during the Fall term consumed much more energy than I could predict and even to imagine.
In this post I will try to explain why compiling a list of good books is so difficult. It is much easier to say from time to time “This book is great! You should read it.” Still, I will try to compile a list or lists of the books I like in the following post(s).
If one is looking for good collection of graduate level textbooks, there is no need to go further than the Springer series “Graduate Texts in Mathematics”. The books in the Springer “Universitext” series are more varied in their level (some are upper level undergraduate, others are research monographs), but one can find among them a lot of good textbooks. There is a more recent series “Graduate Studies in Mathematics” by the AMS. From my point of view, this series includes some excellent books, but is too varied both in terms of the level and in terms of quality. If you are looking for something on the border between an advanced graduate level textbook and a research monograph, the Cambridge University Press series “Cambridge Studies in Advanced Mathematics” is excellent. The bizarre economics and ideology of the modern scientific publishing resulted in the fact almost all good books in mathematics (including textbooks) is published by one of these 3 publishers: AMS, Springer, and Cambridge University Press. You will not miss much if will not go any further (but you will miss some book, certainly).
I cannot suggest a sequence of good books to study any sufficiently broad area, even not necessarily a sequence of my favorite books. If you want to be a research mathematician, you will have to learn a lot from bad books and badly written papers. It would do a lot of good for mathematics if afterwards you will write a good book about things you learned from badly written books and papers. Unfortunately, writing a book is not a really good idea at the early stages of the career of a mathematician nowadays. Expository writing is hardly valued. On the one hand, expository writing does not help to get grants and grants is the only thing valued by administrators at the level of deans and higher. It seems that the chairs of the mathematics departments started to follow this approach. Deans and chairs are the ones who have the last word in any hiring or promotion decision. Sometimes a mathematician is essentially forced to write a book in order to continue research. For example, the foundation of a theory may be absent from the literature, or some “known to everybody” results may require clarification. But this is rare.
Some freedom of what to do, in particular, the freedom to write books, arrives only with a tenured position. Still, a colleague of me gave me many years ago the following advise: “Do not write any books until you retire”. Right now I am not sure that any mathematical books will be written or used when I retire. I actually had abandoned a couple of projects because I don’t see any efficient and decent way to distribute mathematical books. I don’t think that charging $100.00 for a textbook is decent given that the cost of production is about $5.00—$20.00 per copy.
On the other hand, there is a lot of good textbook introducing into a particular sufficiently narrow branch of mathematics. It hardly make sense to list all of them. All this leads me to chosing “my favorite” as the guiding principle. And, after all, this is what Tamas Gabal asked me to do.
Next post: Graduate level textbooks II
Back in August Tamas Gabal asked me about my favorite graduate level textbooks in mathematics; later Ravi joined this request. I thought that the task will be very simple, but it turned out to be not. In addition, my teaching duties during the Fall term consumed much more energy than I could predict and even to imagine.
In this post I will try to explain why compiling a list of good books is so difficult. It is much easier to say from time to time “This book is great! You should read it.” Still, I will try to compile a list or lists of the books I like in the following post(s).
If one is looking for good collection of graduate level textbooks, there is no need to go further than the Springer series “Graduate Texts in Mathematics”. The books in the Springer “Universitext” series are more varied in their level (some are upper level undergraduate, others are research monographs), but one can find among them a lot of good textbooks. There is a more recent series “Graduate Studies in Mathematics” by the AMS. From my point of view, this series includes some excellent books, but is too varied both in terms of the level and in terms of quality. If you are looking for something on the border between an advanced graduate level textbook and a research monograph, the Cambridge University Press series “Cambridge Studies in Advanced Mathematics” is excellent. The bizarre economics and ideology of the modern scientific publishing resulted in the fact almost all good books in mathematics (including textbooks) is published by one of these 3 publishers: AMS, Springer, and Cambridge University Press. You will not miss much if will not go any further (but you will miss some book, certainly).
I cannot suggest a sequence of good books to study any sufficiently broad area, even not necessarily a sequence of my favorite books. If you want to be a research mathematician, you will have to learn a lot from bad books and badly written papers. It would do a lot of good for mathematics if afterwards you will write a good book about things you learned from badly written books and papers. Unfortunately, writing a book is not a really good idea at the early stages of the career of a mathematician nowadays. Expository writing is hardly valued. On the one hand, expository writing does not help to get grants and grants is the only thing valued by administrators at the level of deans and higher. It seems that the chairs of the mathematics departments started to follow this approach. Deans and chairs are the ones who have the last word in any hiring or promotion decision. Sometimes a mathematician is essentially forced to write a book in order to continue research. For example, the foundation of a theory may be absent from the literature, or some “known to everybody” results may require clarification. But this is rare.
Some freedom of what to do, in particular, the freedom to write books, arrives only with a tenured position. Still, a colleague of me gave me many years ago the following advise: “Do not write any books until you retire”. Right now I am not sure that any mathematical books will be written or used when I retire. I actually had abandoned a couple of projects because I don’t see any efficient and decent way to distribute mathematical books. I don’t think that charging $100.00 for a textbook is decent given that the cost of production is about $5.00—$20.00 per copy.
On the other hand, there is a lot of good textbook introducing into a particular sufficiently narrow branch of mathematics. It hardly make sense to list all of them. All this leads me to chosing “my favorite” as the guiding principle. And, after all, this is what Tamas Gabal asked me to do.
Next post: Graduate level textbooks II
Wednesday, March 27, 2013
The value of insights and the identity of the author
Previous post: Hard, soft, and Bott periodicity - Reply to T. Gowers.
This is partially a reply to a comment by Emmanuel Kowalski.
There is a phenomenon which I can hardly explain. For example, E. Kowalski said in the linked comment that he cannot comment on my statements (it seems that he is not addressing me at all, he is just commenting) without making assumptions about me, i.e. without using ad hominem arguments. Why he cannot write about my ideas without knowing my personal details?
It seems that E. Kowalski suspects that my opinions are somehow deducible from my personal life circumstances, my biography, etc.
In fact, it is possible that I have more experience due to my biography than most of other mathematicians. This is even partially the case, but only partially, and this does not affect my opinions about mathematical theories. These aspects of my life experience are quite obvious already in the discussion in the Gowers's blog.
But my opponents do not seem to adhere to this theory, which is obviously favoring me. Rather, it seems that they believe I am not knowledgeable enough or plain stupid. Would this be the case, my conclusions would be, most likely, wrong and, moreover, it would be quite easy to refute them without making any assumptions about me.
In fact, one of the main reasons for my semi-anonymity is that I would like to see my arguments and opinions evaluated on their intrinsic merits, without knowing if am I married or not, how good or bad is my employer - name anything you would like to know.
This phenomenon is not limited to my opponents. Somebody, apparently sympathetic to me, wrote: I’d be very interested in any small mathematical insight you might be willing to share, if you’re whom I conjecture you are". So, even my mathematical insights are interesting or not depending on who I am. For me, the interest of a mathematical (or “meta-mathematical”, like this discussion) insight does not depend on whom it belongs.
Of course, sometimes the authorship matters. But assumptions about the author still do not. Let us imagine that it is 1976 today (many other years will work also). Then any person interested in algebra, algebraic topology, or Grothendieck algebraic geometry knows that all papers by D. Quillen to date are very interesting and often contain incredibly deep insights. It is only natural to be interested in any new paper by Quillen. I don’t know anybody working now and comparable in this respect to 1976 Quillen; this is the reason for an exercise in time travel.
At the same time, if I see an interesting result, theory, insight, it does not matter for me if it is published in Annals or in Amer. Math. Monthly, who is the author, and what problems in life she or he has, if any.
In both situations the insights of a person lead to her or his reputation. The reputation itself does not make all insights of this person interesting. Only in rare cases the reputation may suggest that it is worthwhile to pay attention to works of a person.
Unfortunately, this seems to be not true nowadays at least in the West. The relatively recent cult of Fields medals makes the work and the area of any new winner instantly interesting. In the past the presenters of the awarded medals used to stress that there is at least 30-40 young mathematicians with comparable achievements. Not anymore. In the US, one will be monetarily rewarded for a trivial paper in Annals, but never for an expository paper (and no books, please, I was told many years ago), no matter how deep its insights. Papers in a European journal are treated by default as second rate papers. An insight of a person working in Ivy League is more valuable that a much deeper insight of a person working in Alabama. And so on.
Finally, I would like to make an offer to Emmanuel Kowalski (only to him).
Dear Emmanuel Kowalski,
You may ask me in comments here anything you would like to know. I do not promise to answer all the questions. I will evaluate to what extent my answers will help to sort out my real life identity, and will not answer to the questions which are really helpful in this respect. In particular, I will not tell what my area of research is. I will not answer to the questions which I will deem to be too personal. But if finding out my identity is not your goal, here is your chance to replace your assumptions by the actual knowledge.
Next post: Combinatorics is not a new way of looking at mathematics.
This is partially a reply to a comment by Emmanuel Kowalski.
There is a phenomenon which I can hardly explain. For example, E. Kowalski said in the linked comment that he cannot comment on my statements (it seems that he is not addressing me at all, he is just commenting) without making assumptions about me, i.e. without using ad hominem arguments. Why he cannot write about my ideas without knowing my personal details?
It seems that E. Kowalski suspects that my opinions are somehow deducible from my personal life circumstances, my biography, etc.
In fact, it is possible that I have more experience due to my biography than most of other mathematicians. This is even partially the case, but only partially, and this does not affect my opinions about mathematical theories. These aspects of my life experience are quite obvious already in the discussion in the Gowers's blog.
But my opponents do not seem to adhere to this theory, which is obviously favoring me. Rather, it seems that they believe I am not knowledgeable enough or plain stupid. Would this be the case, my conclusions would be, most likely, wrong and, moreover, it would be quite easy to refute them without making any assumptions about me.
In fact, one of the main reasons for my semi-anonymity is that I would like to see my arguments and opinions evaluated on their intrinsic merits, without knowing if am I married or not, how good or bad is my employer - name anything you would like to know.
This phenomenon is not limited to my opponents. Somebody, apparently sympathetic to me, wrote: I’d be very interested in any small mathematical insight you might be willing to share, if you’re whom I conjecture you are". So, even my mathematical insights are interesting or not depending on who I am. For me, the interest of a mathematical (or “meta-mathematical”, like this discussion) insight does not depend on whom it belongs.
Of course, sometimes the authorship matters. But assumptions about the author still do not. Let us imagine that it is 1976 today (many other years will work also). Then any person interested in algebra, algebraic topology, or Grothendieck algebraic geometry knows that all papers by D. Quillen to date are very interesting and often contain incredibly deep insights. It is only natural to be interested in any new paper by Quillen. I don’t know anybody working now and comparable in this respect to 1976 Quillen; this is the reason for an exercise in time travel.
At the same time, if I see an interesting result, theory, insight, it does not matter for me if it is published in Annals or in Amer. Math. Monthly, who is the author, and what problems in life she or he has, if any.
In both situations the insights of a person lead to her or his reputation. The reputation itself does not make all insights of this person interesting. Only in rare cases the reputation may suggest that it is worthwhile to pay attention to works of a person.
Unfortunately, this seems to be not true nowadays at least in the West. The relatively recent cult of Fields medals makes the work and the area of any new winner instantly interesting. In the past the presenters of the awarded medals used to stress that there is at least 30-40 young mathematicians with comparable achievements. Not anymore. In the US, one will be monetarily rewarded for a trivial paper in Annals, but never for an expository paper (and no books, please, I was told many years ago), no matter how deep its insights. Papers in a European journal are treated by default as second rate papers. An insight of a person working in Ivy League is more valuable that a much deeper insight of a person working in Alabama. And so on.
Finally, I would like to make an offer to Emmanuel Kowalski (only to him).
Dear Emmanuel Kowalski,
You may ask me in comments here anything you would like to know. I do not promise to answer all the questions. I will evaluate to what extent my answers will help to sort out my real life identity, and will not answer to the questions which are really helpful in this respect. In particular, I will not tell what my area of research is. I will not answer to the questions which I will deem to be too personal. But if finding out my identity is not your goal, here is your chance to replace your assumptions by the actual knowledge.
Next post: Combinatorics is not a new way of looking at mathematics.
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