2014 Fields Medals

I thought this wasn’t supposed to be announced until late this evening New York time, but the Fields Medal announcement is now online. The winners are:

  • Artur Avila
  • Manjul Bhargava
  • Martin Hairer
  • Maryam Mirzakhani

Mirzakhani is the first woman to win a Fields medal. Congratulations to all four.

I’m not at all knowledgeable about the work of this year’s medalists, for this you can consult the press releases on the ICM page.

Update: Quanta magazine has profiles of the winners. Avila, Bhargava, Hairer, Mirzakhani.

: For ICM blogging, clearly the place to go is the blog of a Fields Medalist.

Update: According to Tim Gowers, the Fields Medal Committee was: Daubechies, Ambrosio, Eisenbud, Fukaya, Ghys, Dick Gross, Kirwan, Kollar, Kontsevich, Struwe, Zeitouni and Günter Ziegler.

Update: For two very different sorts of blog posts about the Fields Medal, see Terry Tao and Mathbabe.

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53 Responses to 2014 Fields Medals

  1. Bill says:

    Peter, it’s Avila, not Avial. Do you know who was on the committee? Strange for them to announce it before the opening ceremony.

  2. Peter Woit says:

    Typo fixed. I haven’t seen the committee list, don’t know if it’s public yet. Yes, it is strange for this to be posted before the opening ceremony. Also strange is that from the history it looks like this was posted on Wikipedia yesterday, even before the early ICM page went up.

  3. Als says:

    Great choice.

    I think some category theorists are going to be a bit disappointed for Lurie, but he did get a 3 million dollars consolation prize…

  4. Daniel McLaury says:

    Given that the page was written in the past tense (“the winners were announced”), this is pretty obviously an accident.

    What’s interesting to me is that Quanta clearly had all those profiles ready to go in advance. Who else must they have written profiles for?

  5. Peter Woit says:

    In cases like this journalists are often contacted in advance and told in confidence what will be announced, as long as they agree to “embargo” their stories and not release them publicly until a specified time. I’m sure this is how the Quanta stories came about.

    The odd thing here is that one would have guessed that things were embargoed until the public announcement in Seoul (10:30pm today here in New York). It’s unclear whether it was intentional or not that the news got out earlier than this.

  6. Peter Woit says:

    Googling “Fields Medal” and “embargo” turns up various things, for instance this from the 2006 version
    where news was given to the press on August 15, embargoed until the time of the ceremony on August 22.
    For the Seoul ICM, a cached journalist registration form shows up, which says that names of Fields Medalists are embargoed until the ceremony.

  7. The official website was probably primed to go and the page released at something like midnight Seoul time. I got the first message about this 3.30 am local, and I’m in the same time zone as South Korea. It may have been a planned thing, or a small bungle on behalf of a programmer who set the day of release, but not the time. And then other news sources could follow suit, since the cat was out of the bag.

  8. Bill says:

    Quanta profiles are way over the top for my taste, even though I liked some of the comments from the winners about how they focus on the problems. Another thought that came to mind – billiards everywhere (especially, if you include this year’s Abel prize). No updates on the committee yet on the IMU website.

  9. Ethan says:

    Congratulations to all the winners, indeed!

    One question that I have though is how relevant is these days the Fields Medal compared to other awards that exist right now in Mathematics.

    Certainly, at the time the medal was introduced, there were no other high profile awards in Mathematics. These days, there are many other awards which do not have the insidious 40 years old limit.

    The discrimination that these medals help perpetuate, ageism, is preposterous. To cite perhaps the most visible case -although there are others-, Andrew Wiles didn’t get a Fields Medals for proving Fermat’s last theorem, only because of the age limit.

    The New York Times had an article about how the Fields Medal got to gain its status as the “Nobel Prize of Mathematics” http://www.nytimes.com/2014/08/10/opinion/sunday/how-math-got-its-nobel-.html?_r=0 . Not sure if the argument is valid though, because there are tales of how John Nash was disappointed when he didn’t get one back in the 1950s.

    Any thoughts?

  10. Peter Woit says:

    The combination of no Nobel prize and the age limit have always made the Fields medal kind of unusual. The prize was always well-known among mathematicians, especially after the fifties, but little-known outside mathematics. I don’t think the Smale story referred to in the NYT had that big an impact.
    So far the existence of other prizes doesn’t seem to have changed much. The Abel prize is set up to be a Nobel equivalent, but it gets given to people late in their careers. The Fields medal always had a significant impact since it was identifying not the grand old men of the field, but the young stars. Unclear yet what the effect of the Milner/Zuckerberg prize with its big payday will be.

    Over the past 20 years I see two conflicting trends: the first is that society and academia is ever more star-driven, so more and more attention gets paid to awards and those identified as stars.

    The second though is that something has changed in math research, with a lot more research mathematicians working on more and more specialized problems. The first time I went to an ICM was Berkeley in 1986, and that year I don’t remember much speculation earlier about the prize, just because the results of Donaldson, Faltings and Freedman were so dramatic it seemed pretty obvious who the prize winners would be (I also suspect there was much less effort to keep the news secret). To some extent this was also true in 1990 (with that year an interesting controversy about giving the prize to Witten, a non-mathematician).

    From 1994 on though, my impression is that a few of the choices have been obvious, but while the rest go to very good people, they are choices that could easily have been different and no one would have been surprised. Instead of two-four people with results dramatically more significant than everyone else’s, there may be just one such person. For example, this year I think people would have been surprised if Bhargava didn’t get a prize, but not surprised if the other three winners had been, for example, Lurie, Ben Green, and Sophie Morel. Similarly, last time Ngo was a clear choice, but the other three names could easily have been different.

    So, these days I see Fields medalists as getting a lot more attention from outside mathematics than in the old days. From within the community, the emphasis on academic stars mean they get more attention, while the second trend means they get less, since there’s an awareness that there are equally good people in the same cohort without the prize.

  11. Michael Nielsen commented on Terry Tao’s post


    that the announcement on the official site was removed, then reinstated. Seems like it could have been a mistake.

  12. Ethan says:


    Thank you for the detailed explanations.

    I have always loved mathematics. Although I got my PhD in engineering, my adviser was a mathematician and my thesis work involved applied mathematics, so I tend to follow the discipline closer than other people in my field.

    I have not been around professionally for that long but it is definitely true that when I was in graduate school both trends you mention were in full force.

    While I see it as a welcome development that society at large gives due recognition to scientific work, mathematics in particular, I find the “celebrity driven culture” a bit troublesome, both in academia and society at large, but particularly in academia where the pursuit of knowledge for its own sake should trump other issues.

    Thanks for this interesting blog.

  13. John McAllison says:

    Iran, of all places in the world, manages to produce the first female Field’s Medalist in Maryam Mirzakhani?

    No script writer would have the imagination to think this story line up.

  14. Ethan says:


    Up until I went to graduate school at Stanford, I was also ignorant about Iran’s very strong tradition of cultivating intellectual elites both male and female.

    It is perhaps Iran’s best kept secret, although if you look at the winners of scientific Olympiads for high schoolers, you see Iranians at the top every year. Some of the good friends I made in graduate school went also to Sharif University, including several brilliant females.

    The real tragedy for Iran is that it educates all these bright people only to expel them from Iran, “intellectually speaking”, that is.

  15. John McAllison says:


    My understanding of Iran is that women’s rights were severely eroded after the 1979 Islamic revolution, and only started to recover significantly around the start of the 90s. Even today, Iran still comes across as generally being very backward when it comes to gender equality compared to more secular Islamic majority nations like Turkey.

    It’ll be interesting to see how the Islamic Republic of Iran Broadcasting reports this, given that the Quran claims a man’s testimony is worth twice that of a woman’s in an Islamic court of law.

  16. Boon says:

    Any idea as to why Lurie didn’t win?

  17. Ethan says:

    My experience with Iranian scholars contradicts the general perception :). In fact, there are many Iranian women educated after 1979 who hold faculty positions in America’s top universities. As I said, knowing my share of Iranian Americans, or Iranians who have settled in America, the news of an Iranian woman settled in the US receiving the Fields Medal wasn’t that surprising.

    I think that many here in the West confuse giving females opportunities to become brilliant scholars with embracing Western feminism. I do not know personally Maryam Mirzakhani but I know people who know her. Most Iranians that I know -in fact I would say the overwhelming majority of them-, both male and female, hold what would be considered “socially conservative values” in the US when it comes to sex outside marriage, gay marriage, abortion, etc.

  18. Bill says:

    Boon, see Peter’s comment above for possible answers. Or let’s wait and see who was on the committee. If you watch Quanta videos, Hairer’s main insight came from the theory of wavelets (Daubechies was the President of the IMU and the chair of the committee, also the first female chair). Avila and Mirzakhani’s main work is on dynamical systems (billiards), so I wouldn’t be surprised to see people from that area on the committee. All four were great choices, but clearly Jacob Lurie would also be a great choice.

  19. Als says:

    “Up until I went to graduate school at Stanford, I was also ignorant about Iran’s very strong tradition of cultivating intellectual elites both male and female.”

    Exactly. People forget that Iran is a very old and great civilisation, with many great mathematicians (actually most of so-called “arab” mathematicians were actually Persians).

    “Any idea as to why Lurie didn’t win?”

    There’s no way to know, but it’s easy to guess: he didn’t prove any big theorem, all the four recipients did.

  20. Ethan says:

    Another quick question, is there a streaming link so we can watch the plenary sessions live? I haven’t found any in the main page http://www.icm2014.org/

  21. Ethan says:

    OK, here it comes,


    The pop up blocker was preventing me from seeing it :).

  22. A.J. says:

    Regarding Lurie: He’s done some very notable work — his proof of the cobordism hypothesis is indeed a big theorem, likewise his geometric construction of tmf — but much of it hasn’t gone through traditional peer review channels. I’d guess the selection commitee is waiting to see something more formal in print.

  23. Bourbaki says:

    “Any idea as to why Lurie didn’t win?”

    There’s no way to know, but it’s easy to guess: he didn’t prove any big theorem, all the four recipients did.”

    Jacob Lurie proved the Baez-Dolan Cobordism hypothesis. Along with Denis Gaitsgory, he proved Seigel-Mass formula for function fields. Saying that Jacob Lurie didn’t prove any “big” theorem is like saying Grothendeick never proved any “big” theorem.

    “Any idea as to why Lurie didn’t win?”

    Fields Medal these days is a function of whose is in the Prize committee.
    Even then omission of Jacob Lurie in the list was quite surprising.

  24. Andy says:

    Bourbaki – A correction: he has *claimed* proofs of those results. However, he still has not managed to produce papers containing said proofs. Moreover, it’s not clear to me that either of them is particularly central to mathematics (maybe the mass formula is, but the cobordism hypothesis is pretty technical and marginal).

    Also, Grothendieck had plenty of deep results to his name early in his career (e.g. Grothendieck-Riemann-Roch).

  25. Als says:

    “Also, Grothendieck had plenty of deep results to his name early in his career (e.g. Grothendieck-Riemann-Roch).”

    And don’t forget his work in analysis, where there are some beautiful results.

  26. Saying that Jacob Lurie did not prove any big theorem is like lamenting the lack of a rock when faced with a mountain.

  27. Bourbaki says:


    Jacob Lurie has already published a detailed sketch of the proof.

    Also, Grothendieck never published his Reimann-Roch theorem, as he was never satisfied with the proof. And the reason why Grothendeick is Grothendeick is not because of his results in functional analysis.

  28. Andy says:

    Bourbaki – A detailed sketch is not the same thing as a proof. I don’t care how smart Jacob is, he is not exempt from the ordinary rules of mathematical practice. Until a detailed proof appears (written by him or someone else), the theorems are not yet proved. Period.

    And Grothendieck did publish a proof of GRR in SGA6 (which I guess was not peer-reviewed in the usual sense, but it’s all there). Moreover, Borel-Serre published a detailed account of GRR in 1958, long before Grothendieck’s Fields medal

  29. Bourbaki says:

    Most mathematicians working in Lurie’s area actually believe the proof is complete and correct as well. And that’s what matters.

    As far Grothendeick is concerned, his important works were never went through the traditional peer-review process (for the the obvious reasons.)

    And yes, Edward Witten got the Fields medal with ever proving any theorem.

  30. Als says:

    “Most mathematicians working in Lurie’s area actually believe the proof is complete and correct as well. And that’s what matters.”

    I agree that there are precedents (Witten, Perelman, Thurston), so I don’t think it’s the reason the committee didn’t chose him.

  31. AJ says:

    Technically Lurie will be qualified for 2018 since he will just be 40.

  32. mkf says:

    Regarding, that the names were already in wikipedia on Monday, they accidentally put the names on the official ICM 2014 page on Monday morning (Middle European time) where I also saw them (and also the other prize winners, it seemed that they wrote the entries at that time since they appeared one after the other).

  33. Bill says:

    Lurie will turn 40 a few weeks before January 1, 2018, so this was his last chance.

  34. jjj says:

    Avila is the only one I happen to know, and whose work I know something of. He certainly deserves it. Everyone has known this for a long time, and he is just 35. It has been both scary and exciting to work in this general area in recent years
    (interval exchange transformations, Teichmueller flow) where much deep and fascinating work had been done by many people (to avoid offending anyone I will just mention the first greats: Keane, Veech and Masur) when Zorich appeared with lucid explanations, an exciting conjecture and his wonderful approach to math (generous, kind) and all of a sudden many superstars were involved: Yoccoz, Kontsevich, McMullen. I stop there mentioning only the Fields medalists, since it is unfair to mention one other name without a long historical discourse and many many names, explaining all the deep and wonderful contributions. You will note I didn’t even mention Thurston, though I should have.

    Avila has not worked in isolation; much the opposite, he has in a very egoless way
    benefited and learned from everyone else and given back to them. Basically, he just loves math, and this is what is such an inspiration. But this shows the paradox of one
    amazing person being singled out for a prize, when it is the whole community they represent who should (and will) celebrate; we know we are part of it. “We” doesn’t just mean dynamicists, it means mathematicians, or beyond that anyone who draws inspiration from the wonders of nature, and of its interaction with the human mind.

    My one real talk with Artur was after an amazing lecture of his; at lunch I asked for further explanation of some point, and he talked (rapidly and clearly) for 5 or 10 minutes. I felt like the ideas were pouring into my head, which was on the verge of exploding.

    Well, that’s Artur. It is so great that there have been places and opportunities like
    IMPA and the CNRS where someone like this has had the conditions to work and grow and to inspire, and let’s hope that the powers can be can see that these working conditions need to be made more generally available; freedom and inspiration is how you get good math done, the opposite of the bureaucratic and business-style models that are forced over every part of human existence, more and more. To think, really to think and to create, and to encourage that in others, is the revolutionary antidote, revolutionary in that it turns the apparent world right on its head and says, “really?”, and laughs.

    So, congratulations to all of us, and let’s use the inspiration to prove some theorems!

  35. Als says:


    I completely agree concerning Avila and I think Peter is wrong when he says it could have been anyone along with Bhargava. Many people were expecting him to get it for quite some time.

  36. Ethan says:

    Now that most media have covered the news, the emphasis seems to be on,

    – First woman to ever win a Fields Medal (less emphasis on her being Iranian).

    – First Brazilian/South American to ever win a Fields Medal.

    This, I think, is linked to Peter’s observation that we are increasingly a star driven culture, which tends to favor shallow superficial things instead of content. You can also see this reflected in the number, and content, of the comments in the respective Quanta entries.

    I think that this emphasis on matters not related to the research for which they (and the other two) received the medal is bad for Mathematics. It is also bad for the winners themselves because there will always be doubts whether somebody else could have been named winner, like the aforementioned Jacob Lurie, had it not been because of the “firsts”. Gowers said http://gowers.wordpress.com/2014/08/13/icm2014-opening-ceremony/#more-5567

    “I think that this time round there were an unusually large number of people who could easily have got medals, including other women. (This last point is important — one should think of Mirzakhani’s medal as the new normal rather than as some freak event.) I have two words to say about them: Mikhail Gromov.”

  37. JG says:

    Congratulations to all the winners. Iran’s strong tradition in the Mathematics Olympiad is impressive, they usually have performed better than Israel, France, UK, Germany for example. It is sad that this is not matched with a strong publication record. I assume this is due to emigration, as in Mirzakhani’s case, though she has said that there was a big emphasis on problem solving rather than theory, and she had to learn a lot of basic undergraduate mathematics when she went to Harvard – which makes her subsequent publication record all the more impressive.

    For a humbling experience, see if you can match Mirzakhani’s perfect score from the 1995 olympiad (problems) . Preferably within two days 🙂

  38. egan says:

    Question : is it possible for a mathematician to win two Fields medals? For instance one at the beginning of his career and a second one just before turning 40 after having proved a big theorem?
    Os is it explicitly forbidden by the rules of the Fields committee?

  39. Ethan says:


    Unclear. The IMU’s nominating rules say,


    “No winner of one of these Medals/Prizes is eligible for one of the others. ”

    Which clearly excludes a winner of one of the prizes/medals from being considered for the others -something that I find odd, particularly with respect to the Chern Medal- but I don’t think it necessarily follows that somebody cannot win two Fields Medals.

  40. Yatima says:

    @John McAllison

    It’ll be interesting to see how the Islamic Republic of Iran Broadcasting reports this, given that the Quran claims a man’s testimony is worth twice that of a woman’s in an Islamic court of law.

    Well … what do you expect? Iran ≠ ISIS.

    IRIB world service: Iranian woman wins Nobel Prize of mathematics

  41. Peter Woit says:

    Enough about the Iranian government here, thanks.

  42. Mathematician says:

    I was surprised at this, here
    “Hairer learned that he had won the Fields Medal during a visit to Columbia University in February.”
    I didn’t realise they were informed so far in advance. That’s a long time to have to keep a secret.

  43. Bourbaki says:

    “The second though is that something has changed in math research, with a lot more research mathematicians working on more and more specialized problems. ”

    I would be interested in knowing what caused this change. It seems mathematicians are now focused more specialized and more accessible problems than going for the big problems (of course, there are exceptions to this rule).

  44. Frederick says:

    “This, I think, is linked to Peter’s observation that we are increasingly a star driven culture, which tends to favor shallow superficial things instead of content. You can also see this reflected in the number, and content, of the comments in the respective Quanta entries.”

    In fairness, I believe the Quanta entries were aimed at a lay audience. Very few people outside of the profession, no matter how smart, are going to have more than a cutaneous understanding of the work produced by Fields Medalists. I’m not sure what kind of analysis you were expecting. Even Terence Tao admitted that much of Bhargava’s work is beyond his ken.

    Personally, I’d rather see scientists, mathematicians, novelists, and other intellectuals turned into celebrities than actors and athletes. In many Asian cultures, the results of Science Olympiads are followed with the same enthusiasm that Europeans show for soccer.

  45. Ethan says:


    Please don’t take me wrong.

    I am not talking about the question of which type of celebrities I rather have, in which case, I agree with you, I rather see scientists and mathematicians celebrities than professional athletes, actors or, my absolute worse, people like Paris Hilton or Kim Kardashian .

    What I am saying, and I think that this is what Peter was saying too, is that I do not see the fact that increasingly academia, or my field of engineering, are becoming star/celebrity driven as a good thing for either.

    Here in Silicon Valley this star/fame driven culture caused a crash of gigantic proportions in the late 1990s that had reverberations in the larger economy. Some say that it is about to cause another one in the next 1-2 years. To a certain degree, the financial crash of 2007/2008 was driven by similar forces.

    Some take, in my opinion, the wrong view that increasing the celebrity status of people working in these fields will attract more high quality interested students to them but in fact I contend that those who are more prone to make significant contributions to either field (academia, engineering) are going to be attracted to it no matter what (they have always been throughout history). What “celebrity” attracts is, well, those who are attracted to “celebrity/star status” to the detriment of everybody else. In a way, we have seen the same phenomenon happening in undergraduate admissions. For many years “reputation conscious” applicants have targeted universities based on reputations/ranking alone not which school is better for them. As a result, you get a lot of burnout with many seniors graduating from top schools picking “good paying”, but uninteresting, careers instead of going to graduate school to apply their talents to scholarship.

    Now, this is not to say that those working on science or engineering should resign themselves to be poor. On the contrary, I am a big advocate of paying scholars well so the choice is not between poor and middle class but between upper middle class and rich, which will cause a lot of people, the ones that matter anyway, to pick the “upper middle class” over wealth and continue to work as scholars or engineers.

    The problem with star/celebrity driven academia is that the stars get a disproportionate share of resources. Just as the skyrocketing of the ratio CEO salary to average salary has only managed to alienate the workforce http://blogs.wsj.com/atwork/2013/06/11/the-state-of-the-american-workplace-is-meh/ , the same is likely to occur in academia long term. Star driven cultures, by definition, concentrate resources on a few stars (otherwise they would not be stars) causing the non stars to get the message that while they are necessary to maintain the discipline, there will be no reward for them.

    In Silicon Valley, smart companies have a philosophy of sharing rewards among the rank and file as well, not only the executives. Those companies who focus the rewards on those at the top, do not end up doing very well in the long run although their executives all get wonderful golden parachutes.

  46. Ethan says:


    “Those companies who focus the rewards on those at the top”

    should say

    “Those companies WHICH focus the rewards on those at the top”

  47. @Ethan:

    Or “Those companies THAT focus the rewards at that top” 🙂

  48. Ethan says:

    Forgot to comment (there is no edit button),

    “In many Asian cultures, the results of Science Olympiads are followed with the same enthusiasm that Europeans show for soccer.”

    But then these countries do not produce top notch scientific results, precisely because the top people these countries produce are more interested in continuing being “stars” than in contributing to science at large.

    What sets American higher education apart from what I hear from Asian countries (China and India in particular) is the emphasis on ingenuity and original contributions combined, and this is important, with being very open regardless of people’s background and age.

    In the US it is not unusual to hear people who did badly in high school, started in a community college and went on to become leaders of their respected fields (to the surprise of the “academic stars”). The more academia becomes “star driven”, the more its doors will be closed to those with unusual backgrounds.

    Touching on the topic that gives this blog its name, I think that a very convincing case can be made that certain academic “stars” who shall not be named are probably responsible for the stagnation of physics nowadays. There are too many “stars” interested in keeping string theory alive to the detriment of alternative ways to get to a theory of everything.

  49. Ethan says:


    Oh well, the point remains, THAT I have elaborated in my other comment 🙂 .

  50. Harry says:

    Hi Peter,
    the link to T. Tao’s blog post is broken,

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