Footnotes:
1The learned reader will notice that this letter is modelled on the ``J'accuse'' written by Zola in 1898.
Dear sir,
The facts that are recalled here have been in your knowledge for almost a year now. These facts involve stealing of results, putting graduate students to work for powerful members of the mathematical community without the students knowledge, and lastly and mainly all kinds of unethical behaviour in relation with the Fields Medals. But your reaction to these facts has been inexistent. Thus, history could recall you as the president under which mandate the International Mathematical Union (IMU) went a way towards disreputability that could perfectly end up with the reputation that mathematics has gained itself as a serious science during the last millennia. As I see it, the loss of credibility that the IMU could suffer could affect all of us mathematicians, and this loss has been induced by the incorrect, even unethical, behaviour of people appointed by you or by your predecessors.
The most visible act of the IMU is the International Congress of Mathematicians (ICM), and in it a central part is the awarding of the Fields Medals. It is true that the IMU takes part in many other activities, but they are not so visible. Thus, anything that diminishes the credibility of the Fields Medals as awards representing the excellence in mathematics will decrease the credibility of the IMU, and, even worse, the credibility of mathematics as a science. Any award has a degree of subjectivity in it, and one could discuss whether it is convenient, or even good, for mathematics to have such an award to be given to the people that certain committee decides are the best mathematicians of their time. I, as a scientist, consider that the only price that is worth its value is the general recognition of the future mathematicians. But this is not the place for such a discussion, for we are not here to talk about certain degree of subjectivity, but of simple and plain fraud. And fraud in its most visible act is not a thing the IMU should tolerate if it wants to preserve its credibility.
The people that I am going to mention have, alone or with the help of others, transformed the IMU Fields Medals committee into a market for their own ambitions, overriding the (arguable) scientific criteria with a market of favours that deprives the mathematical community of what it expects from them. They have done so in many bastard ways, each worse than the previous. Since they have dared to do so, I will dare to explain it, even if by doing so I am putting my professional career in jeopardy. Because I have seen behaviours inside the mathematical community that I would never have expected to see. Since this is the community into which I would like to spend the rest of my life, I would not feel comfortable if these ways of acting prevailed. Because for me it would be easier to keep silent, but then I would become accomplice. And it is to you and the world, dear president, that these facts have to be explained.
Here are the facts:
In 1992, during my graduate studies, I took a course named `Nonlinear functional analysis', given by Ernest Fontich. As an end of term exercise I was given the job of finding an inverse function theorem which covered at the same time those appearing in [Zeh,75] and [L-Z,1979]. Later I came to know that the same exercise had been given (and done with different degrees of success) to several students both at my university and at the Autonomous University of Barcelona during the previous years.
My resolution of the problem must have been successful as, after Fontich gave it to Carles Simó, which is the head of the Applied Mathematics section, it ended up in the hands of Jean Christophe Yoccoz. Yoccoz was, by that time, always told as one of those few that were close, but not quite, to obtain a Fields Medal, as one can read in some reviews of that time. Yoccoz had been looking, unsuccessfully, for such a theorem in order to prove some results on the behaviour of one dimensional dynamical systems. The fact that some of the Ph. D. students in Barcelona were put to work on a problem which was precisely what Yoccoz needed strikes me as something quite peculiar.
I wasn't told any of this, not even that my exercise had circulated. Thus Fontich (and hereby Simó) were giving exercises to their pupils for purposes different to the one of evaluating them. Or, more precisely, they were put to work for other people without their knowledge.
Thus in 1994, under the presidency of Jacques-Louis Lions, the I.M.U. awarded Fields Medals to P. L. Lions, J. Bourgain, Zelmanov, and J. C. Yoccoz. Incidentally, the president of the committee was David Mumford. To understand this choice, it is clarifying to read [Sch,1977], p. 320. There, one can read that ``...Pierre-Louis Lions et Jean-Chistophe Yoccoz (de la même promotion de Normale, et même camarades de taupe), [...]. J'ai déjà fait remarquer que la recherche, en raison du système universitaire, avait tendance en France à devenir héréditaire: les deux derniers sont les fils du physicien Yoccoz et du mathématicien Jacques-Louis Lions''. (There was some discussion about a similar question when, during the last European Congress in Mathematics, five of the ten awards that were given went to French mathematicians. Curiously, the president of the awards committee was Jacques-Louis Lions.)
Thus, and in short, under the presidency of J.P. Lions, Fields Medals were awarded to his son and one of the best friends of his son. Moreover, this best friend obtained some of the results for which he was awarded the Medal thanks to the work of graduate students who were put to work on problems that he could not solve by himself. Moreover, the student (that is, yours truly) has never been given any recognition for that work.
Now for the 1998 Fields Medals. As a result of the aforementioned work, but also as a result of my doctoral dissertation, I was given one of the 1998 Fields Medals. When the Fields Medals committee met on Friday March 27th, 1998, and for whatever the reasons, the Fields Medals they chose were R. E. Borcherds, W. T. Gowers, M. Kontsevich, and J. Gudayol. To understand the following, I must explain how the Fields Medals awarding process works. Once the Fields Medals committee of the IMU has decided who is to be awarded the Medals, the winners are kept in secret until the International Congress of Mathematicians (ICM), usually held in August. This is the theory, since most well informed mathematicians know the names of the winners by the next day. Meanwhile, each winner is assigned a godfather with the task of formally announcing the candidate that he has won a Fields Medal and instructing him on what is to be expected from him. The decision on who is to be given a Fields Medal needs to be taken months in advance in order to provide the candidates with time enough to prepare the talk they are supposed to give during the ICM.
The godfather that was assigned to me was J. C. Yoccoz. By then, we were in the same University, the Universit� de Paris-Sud. In my case, the announcement (if it had ever happened) would not have been merely formal, as C. Sim� (and others) had failed to warn me that I was being considered as a candidate. This, together with the fact that I had not been warned about the way in which Yoccoz had won his Medal (that is, thanks in part to my work) caused that I did not expect him at all. When he found himself unexpected, his pride forbid him to fulfil the mission the FM committee had given to him. Instead, he waited until mid July and, when I returned to Barcelona to spend there my holidays, he talked to the president of the committee, Yuri Manin, and told him some lies, which he (Manin), without even trying to get in touch with me, believed. The result of that was that Manin, with or without the help other members of the committee, decided to take the Medal away from me. Curiously enough, the Medal ended up in the hands of McMullen, friend and collaborator of Yoccoz.
It has to be known that one of the Fields Medalists that the committee had chosen was M. Kontsevich, who is one of the main collaborators of Yuri Manin. Thus, and from the moment in which it was known that Kontsevich was one of the candidates, Manin was, for ethical reasons, unfit for the chair of the committee, since he obviously lacked the necessary objectivity. In other words, and to put it plainly, when Manin was evaluating the work of Kontsevich he was in fact evaluating his own work.
The setup of the fake Fields Medal awarded to C. McMullen was difficult, though. First, the list of the medalists had been widely circulated. The organisation of the ICM had made press releases that, even though had no names in them, made a close description of the FM to be. Moreover, the candidate they found did not fill the age requirements (the FM have to be under 40). Some things could not be set up, though. McMullen had to give a talk in a sectorial meeting during the conference (whereas Fields Medalists never do) that could not be unscheduled. Steve Smale had to patronize McMullen in the same way that Yoccoz was assumed to patronize me, but for whatever the reason (I give Smale some credit on that) he (Smale) does not appear on the picture.
My position in the mathematical community has been difficult ever since that that series of events fell upon me. Moreover, when I decided to explain these facts, I was expelled from work and, by preventing me from finding another job, from the mathematical community. Hence freedom of expression in the mathematical community is, nowadays, an empty expression. Those who hold the power in the mathematical community and use it in many dubious ways can not be criticized freely.
This letter is rather long, dear president, and it is time to finish:
By making such accusations, I am aware that I am risking myself an accusation of libel. I am willing to take that. But, in any case, if there is anyone out there who can testify for me or supply me with any proof, he will be welcome.
As I have explained, at least half of the latest Fields Medals (and with them power in the mathematical community) of the past eight years are at least dubious on ethical grounds. Moreover, not only they are dubious, but the events that are related to such Medals can (and in my case, have) damage seriously the careers of otherwise perfectly able mathematicians. Thus not only these medals fail to fulfil properly the mission they are supposed to fulfil, but they have become a thing with which is dangerous to get involved. Since this is the present situation, I would like to end by asking you a question, on the occasion of the 2002 ICM. Are these Fields Medals worth giving?
Yours sincerely,
Barcelona, August 16th, 2002.
1The learned reader will notice that this letter is modelled on the ``J'accuse'' written by Zola in 1898.