Home > math > I love math and I hate the Fields Medal

I love math and I hate the Fields Medal

August 15, 2014

I’ve loved math since I can remember. When I was 5 I played with spirographs and learned about periodicity, which made me understand prime numbers as colorful patterns on a page. I always thought 5-fold symmetry was the most beautiful.

spirograph

 

In high school I was incredibly lucky to attend HCSSiM and learn about the wonders of solving the Rubik’s cube with group theory.

rubiks-cube

Then I got to college at UC Berkeley and in my second semester was privileged to learn algebra (and later, Galois Theory!) from Ken Ribet, who became my very good friend. He brought me to have dinner with all sorts of amazing mathematicians, like Serge Lang and J.P. Serre and Barry Mazur and John Tate and of course his Berkeley colleagues Hendrik Lenstra and Robert Coleman and many others. Many of the main characters behind the story of solving Fermat’s Last Theorem were people I had met at dinner parties at Ken’s house, including of course Ken himself. Math was discussed in between slices of Cheese Board Pizza and fresh salad mixes from the Berkeley Bowl.

How lucky was I?!?

And I knew it, at least partially. Really the best thing about these generous and wonderful people was how joyful they were about the serious business of doing math. It was a pleasure to them, and it made them smile and even appear wistful if I’d mention my difficulties with tensor products, say.

They were incredibly inviting to me, and honestly I was spoiled. I had been invited into this society because I loved math and because I was devoting myself to it, and that was enough for them. Math is, after all, not an individual act, it is a community effort, and progress is to be celebrated and adored. And it wasn’t just any community, it was a really really nice group of guys who loved what they did for a living and wanted other cool and smart people to join.

I mention all this because I want to clarify how fucking cool it can be to be a mathematician, and what kind of group involvement and effort it can feel like, even though many of the final touches on the proofs are made inside closed offices. Being part of such a community, where math is so revered and celebrated, it is its own reward to be able to prove a theorem and tell your friends about it.

Hey, guess what? This is true too! We always suspected it but now we can use it! How cool is that?

Now that I’ve explained how much I love math (and I still love math very much), let me explain why I hate the Fields Medal. Namely, because that group effort is utterly lost and is replaced with a synthetic and false myth of the individual genius working in isolation.

Here’s the thing, and I can say this now pretty confidently, journalism has rules about writing stories that don’t really work for math. When journalists are told to “put a face on the story,” they end up with all face and no story.

How else is a journalist going to write about progress in some esoteric field? The mathematics itself is naturally not within arms reach: mathematics is by nature deep and uses multiple layers of metaphor and notation which even trained mathematicians grapple with, never mind a new result on the very far edge of what is known. So it makes sense that the story becomes about the mathematician himself or herself.

It’s not just journalists, though. Certain mathematicians do their best to represent research mathematics, and sometimes it’s awesome, sometimes it kind of works, and sometimes it ends up being laughably or even embarrassingly simplistic. That’s the thing about math, it’s deep. It’s hard to boil down to a nut graf.

So here’s the thing, the Fields Medal is easy to understand (“it’s the Nobel Prize for math!”) but it’s incredibly and dangerously misleading. It gives the impression that we have these superstars who “have it” and then we have a bunch of wandering nerds who “don’t really have it.” That stereotype is a bad advertisement for mathematics and for mathematicians, who are actually much more generous and community-spirited than that.

Plus, now that I’m in full rant mode, can I just mention that the 40-year-old age limit for the award is just terrible and obviously works against certain people, especially women or men who take parenting seriously. I am not even going to explain that because it’s so freaking clear, and as a 42-year-old woman myself, may I say I’m just getting started. And yes, the fact that a woman has won the Fields Medal is a good things, but it’s a silver lining on an otherwise big old rain cloud which I do my best to personally blow away.

And, lest I seem somehow mean to the Fields Medal winners, of course they are great mathematicians! Yes, yes they are! They’re all great, and there are many great mathematicians who never get awards, and doing great math and making progress is its own reward, and those mathematicians who do great work tend to be the ones who already have lots of resources and don’t need more, but I’m not saying they shouldn’t be celebrated, because they’re awesome, no question about it.

Here’s what I’d like to see: serious outward-facing science journalism centered around, or at least instructive towards, the incredible collaborative effort that is modern mathematics.

Categories: math
  1. August 15, 2014 at 7:29 am

    There are awards in mathematics that can go to collaborations, e.g., the AMS “medal” prizes (Cole Prize, Veblen Prize).

  2. August 15, 2014 at 7:54 am

    I don’t agree that math is a group thing, I grew up a nerd and alone… no friends, and no one to play with, I played with my spirograph and too learned patterns, my Dad also quizzed me at multiplication tables but that was as close to a group that I ever got. Math for me was individual challenges, when I answered something correctly it gave me a good feeling, you know the ones other kids were getting from playing games with other kids…. Math IMO doesn’t need an award for those of us that live, eat and breathe logic and math, it is our lives… we are not used to being patted on the back for it or anything else (they beat kids like me up in school, memories, giggle) and usually. unless you are part of the math club or the chess club…. you are alone… Fast forward 20 years… I work in an office with my head down and still pretty much alone, even my co-workers think I talk over their heads and most of them can’t keep up in a conversation. Fast forward another 20 years, I find that working with most co-workers is not something I care to do anymore. I opened my own business, so now I go to the client, work my magic – explain exactly what I have done (a liaison between IT and C-Suite) and leave to go back to my office, where I am alone. So for me, math is NOT a group thing! Congrats to Maryam Mirzakhani on winning – 1st women to win the Fields Metal!

  3. August 15, 2014 at 8:22 am

    With Robin Williams now gone, I could not help but think of:

    Good Will Hunting (1997)
    Lambeau: You’re angry at me for doing what you could have done; but ask yourself, Sean. Ask yourself if you want Will to feel that way, if you want him to feel like a failure.
    Sean: Oh, you arrogant shit! That’s why I don’t come to the goddamned reunions, ’cause I can’t stand that look in your eye. Ya know, that condescending, embarrassed look. You think I’m a failure. I know who I am, and I’m proud of what I do. I was a conscientious choice, I didn’t fuck up! And you and your cronies think I’m some sort of pity case. You and your kiss-ass chorus following you around going, “The Fields Medal! The Fields Medal!” Why are you still so fuckin’ afraid of failure?

    • Allen Knutson
      August 16, 2014 at 10:13 am

      Please, please, never bring up Good Will Hunting in the context of what mathematicians are actually like. Note that Will Hunting was originally intended to be a physicist, but when the story idea was run by physicist Shelly Glashow, he wisely told the filmmakers to instead make mathematicians look like assholes. (I am inferring his motivations.)

      • August 16, 2014 at 1:14 pm

        Good Will Hunting is to mathematicians as House or Grey’s Anatomy is to doctors. Great entertainment, but not meant as a documentary. Nevertheless, I remembered that quote (and others) from the movie. I’ve met plenty of mathematicians at the hedge fund where Cathy and I, albeit at different times, had worked. Several of them were from Haavaad. Also I had the pleasure of meeting some Haavaad and MIT math geniuses at the now defunct Salomon Brothers. My own math background is in Engineering math, which I know is nothing like what “real” mathematicians do.

  4. mrgeocool
    August 15, 2014 at 8:50 am

    I seldom see anyone complain that baseball’s MVP award is bad for baseball. It’s understood that you’re measuring an individual contribution to a team sport, and you’ll see arguments galore about what the criteria should be and how different factors should be weighted and who might be more or less deserving. But you don’t see people saying that those who have never won an MVP award are wandering jocks who “don’t really have it.” No one says that winning baseball games isn’t a collaborative effort.

    • August 15, 2014 at 8:54 am

      Baseball is entertainment and totally transparent. Except for the steroid abuse of course. In other words, a very different situation.

      Having said that, let me step up to the plate (har har) and mention that, as a hard-core baseball fan myself, I really hate the obsessive focus on the Hall of Fame, for many of the same reasons.

      • August 15, 2014 at 12:50 pm

        I know nothing about the Fields prize but in general, the creation of celebrities and the year-round “awards culture” by its nature tends to reduce and misrepresent what any field or endeavor is about.

        The “committee” is often a false authority, usually an establishment promoting itself: the most commercial and conservative elements of Hollywood call themselves an “Academy,” five retired Norwegian parliamentarians chosen by party leaders play realpolitik on behalf of “peace,” the Bank of Sweden sets up a bogus “Nobel Prize” to legitimate capitalist economics as though it were a science.

        Awards help establish star systems, shrinking and consolidating who and what is taken seriously and favoring the idea of lone “genius” individuals from whom all wonderful things emerge. This is amplified in societies driven by media cycles. (Awards chosen by popular vote are usually worse, of course.)

        “Baseball” here means the MLB, math is an open-ended endeavor of inquiry about a million different questions, so no comparison. The baseball MVP award usually prompts a controversy among the writers choosing it and debates between romantics and statisticians about the meaning of MVP and how it distorts understanding of the game. But the real awards in organized sports are championships, a season is reduced to its winner and let’s not pretend, they are often determined by how a ball bounced in Game 7. The structure is an elimination contest, only one can survive. This reinforces a society living by the motto, “if you’re not a winner you are a loser.”

      • August 16, 2014 at 1:21 pm

        But who do we remember from our baseball teams of old, if not the Hall of Famers (or those who deserved to be)? If you asked me who played for the SF Giants, I would mention Willie Mays, Willie McCovey, Juan Marichal and Gaylord Perry. I don’t remember the other players. Yet, it’s ironic that they never were World Champs, and the lesser known players of the 2012 team won the World Series. A team effort.

        • bruno marr
          August 16, 2014 at 4:54 pm

          Willie Mays won the World Series in 1954. Many consider him the greatest all-round player, ever. (Mike Trout could change that, but I doubt it (pitching is too dominant)>

        • August 17, 2014 at 1:14 pm

          You are absolutely right. That was the NY Giants and before I knew what a baseball is. But I did refer specifically to the SF Giants, because by the time I started watching baseball they had moved to Baghdad by the Bay and it was a team of stars who just couldn’t make it the ultimate magic happen. But Joe Montana and Jerry Rice (SF 49ers) made up for that on the football field especially in the Super Bowl.

  5. August 15, 2014 at 10:04 am

    To the extent that I know about this (I am not a mathematician, but I am a scientist), this seems right to me, but it also seems like it’s part of a more general phenomenon in the sciences, to wit, to boil down complex ideas, and the complex of interactions which breed those ideas into a few publicly digestible points attributed to a few people. One example that I have some personal familiarity with is the Nobel awarded in Physics for the Higgs. There, not just journalists, but governments, and (some) of the physics community itself expended an inordinate amount energy (pun partially intended) lobbying for who really deserved the prize when 6 individuals really contributed (and all of whom were awarded the 2010 Sakurai Prize).

    The prize situation seems also to be concomitant with ‘talking head syndrome’ in popularized science journalism. That is, the tendency to get much of a field’s publicly disseminated information from a select few talking heads, generally – but not exclusively – from Harvard, MIT, and Stanford. It promotes a star system in the sciences and is perniciously unhealthy.

  6. August 15, 2014 at 10:25 am

    So, I mostly agree, but that doesn’t seem exciting, so here are the points where I disagree:
    (1) The Quanta write-ups did a good job of flagging how extensively the winners have collaborated with other mathematicians. I agree it could have been emphasized more, but seemed to be the unstated theme behind the profiles. Maybe that’s only in the context of how math already has so much of a lone hero myth.

    (2) I also think Quanta did a pretty good job of providing a sense of the work. This is particularly true for Manjul, maybe because that is part of the beauty of the work he does?

    (3) The prize culture is going to change with the explosion of the number of top prizes and the introduction of large money prizes. Not to say all these will be good changes, but it seems like it will be hard for the Fields Medal to maintain a prestige advantage against prizes of $1mm, $3mm, etc, but also hard for these new prizes to develop a similar level of prestige to where the Fields Medal is now.

    The thing I think the winners’ profiles emphasized, far more than lone mathematical genius working in isolation, was the impression that they are all natural mathematical geniuses. Maybe this is true, but it doesn’t make for an inspirational biography that I can show to enthusiastic kids to encourage them.

  7. Matthew Ando
    August 15, 2014 at 10:30 am

    I love the blog, and I love this essay about the community of mathematicians and the problem with our prizes. And, thanks for making an excellent point about yet another problem with the age restriction of the Fields Medal.

  8. mathematrucker
    August 15, 2014 at 10:42 am

    It’s a mix of collaboration and alone time. I think the isolated loner is to be celebrated at least as much as the collaboration if not more. Nothing about the story of Andrew Wiles made me more delighted than that he worked in isolation (initially, at least) for many years. I totally disagreed with Erdős’s harsh critique at the time and still do. The other major contributors who paved the way were guaranteed to receive their due, and they did, both before and after FLT got proved.

    However I do still agree that the general public should somehow gain a better understanding of just how collaborative mathematics is. I got to meet and have a private conversation with John Tate once myself, in his office at UT-Austin in 1991. Somehow we ended up discussing this same topic. When I said mathematics is “a social activity,” Tate countered by claiming it was much more something that gets produced by individuals working alone. His comment didn’t make me drop my “social activity” viewpoint entirely, but it did help to shape my current opinion on the subject.

    • August 15, 2014 at 10:45 am

      But even Wiles needed Richard Taylor to get it right.

      • patrick_g
        August 16, 2014 at 1:36 pm

        >>>But even Wiles needed Richard Taylor to get it right.

        So take Laurent Lafforgue. Six years of work in complete isolation and, at the end, the Fields medal for his proof of the Langlands conjectures in function field case.

  9. August 15, 2014 at 12:14 pm

    I’m not fond of the very same elements of the Fields you’re not fond of, but on the other hand anything that highlights mathematics to the public these days, bringing widespread attention, I think is largely a good thing! And collaboration, after-all is probably part of most all science now-a-days… in fact, part of almost any prize — an Oscar-winning actor/actress likely had a great acting coach, great script, great director/editor/cameramen etc….

  10. NY
    August 15, 2014 at 12:18 pm

    Cathy, how cliquey is it in academia, especially along racial/cultural lines? In grad school, I’ve always noticed this stark divide – the Eastern Europeans would hang out by themselves, as well as the Asians, and the Americans/Western Europeans. I have managed to get into some of these house parties you mention, but only after REALLY going out of my way to get to befriend individuals who were a bit standoffish at first.

  11. Joesefina
    August 15, 2014 at 1:03 pm

    >It gives the impression that we have these superstars who “have it” and then we have a bunch of wandering nerds who “don’t really have it.” That stereotype is a bad advertisement for mathematics and for mathematicians, who are actually much more generous and community-spirited than that.

    First sentence: why does the Fields medal give this impression?
    Why does giving an award imply that only “superstars” “have it”?
    In the Olympics, we give medals to the three people who run 100m the fastest; that doesn’t imply that the others are not fast or don’t “have it”. It is common knowledge that there is little difference between their times and that of the #4 person.

    True, mathematicians may be generous or community-spirited. But can you deny that, in many cases, Fields medal mathematicians produced extremely high quality _single-author_ work? Note, this doesn’t contradict the possibility that they are, as human beings, generous, etc.

  12. Amy
    August 15, 2014 at 1:05 pm

    Cathy , are u going to the ICM 2014 or are u there ? Who do u know who is attending ? Is it usual to attend the conference for a working mathematician ?

  13. DF
    August 15, 2014 at 1:52 pm

    I’ve noticed the explosion of big-money science prizes in recent years, established by various very rich people. These are purportedly motivated by altruistic reasons, to give scientist the “recognition they deserve”, etc. I wonder though if, deeper down, there is something less altruistic at work, with these people attempting to graft the winner take all culture which benefited them in the business world, onto academia. Perhaps they find it psychologically comforting in some way, to see academia reformed as a stunted version of their own world.

  14. August 15, 2014 at 2:40 pm

    “All face and no story.” This is a great general purpose line that can be applied,to more than just science and mathematics reporting. It’s not uncommon for experts to read journalist versions of their work and wonder if the reporter had really met them.

  15. Ethan
    August 15, 2014 at 3:23 pm

    The most clear example of why the 40 year old limit is nonsense has a name: Andrew Wiles.

    In 1998, when the IMU was faced with the problem that it had to reward a mathematician who had finished an amazing body of work at the age of 41 and a half (without the fix he developed in September 1994, his work would had not meant much), it said: we will stick with the nonsensical rule even though Andrew Wiles’ case shows why the Fields Medal rewards the wrong type of mathematical work.

    In fact the work of Gregori Perelman followed a similar path: a mathematician obsessed with a very hard problem who worked several years in obscurity. Instead, the Fields Medal as of late seems to reward very good mathematicians who have solved one or more “tough enough” problems in collaboration with others.

    I am not going as far as saying that the Fields Medal should be abolished but it should certainly change its rules if attracting people of all walks of life into mathematics is its objective. The incentives the Fields Medal creates under its current form do not serve mathematics at large well.

  16. Ethan
    August 15, 2014 at 4:02 pm

    DF,

    I am not sure about that. Certainly somebody like Mark Zuckerberg is well aware that it takes a large team to create something like Facebook. And while he got billions in the process, the compensation structure of Facebook and companies like that, especially at the very beginning, is such that many people get “millions”, including ordinary employees.

    If anything, I think that the world of academic prizes has a lot to learn from Silicon Valley companies and the way they reward teamwork: the guy at the top gets a lot, but those who made his/her success possible also get their share, enough as to be proud of having been part of the success. The winner take all is more a “traditional corporate America” thing than a Silicon Valley way of doing things.

  17. August 15, 2014 at 6:22 pm

    Cathy, did you read the articles in Quanta Magazine? I thought the one on Subhash Khot winning the Nevanlinna prize gave a pretty good idea of the collaborative effort. Specifically, he came up with this conjecture, but it was only through the massive collaboration of many researchers to realize how universally relevant it was. He got the prize for spearheading the charge, but I got the clear impression from the article that it was a group effort.

  18. Richard Séguin
    August 16, 2014 at 12:10 am

    I’m one who is annoyed by the 40-year-old age limit. I really don’t see the point, and it’s insulting to older people.

    This particular Fields Medal has done something positive though. I heard mention of Maryam Mirzakhani on TV (I think it was CBS News), and have twice heard her on public radio. I’m sure that this was a positive thing for the many young females who probably also heard the same things.

    Public debate about the value of prizes like this usually gets nowhere because the discussion usually does not recognize that there are actually two separate issues that need to be addressed: what is the public good that we desire the prize to accomplish, and does the prize actually typically accomplish this? Both questions must be answered, with the second, of course, dependent on the answer to the first.

  19. August 16, 2014 at 1:11 am

    prizes have a celebratory effect and yes admittedly also a distorting effect. prizes/ contests are surely as old as humanity. its a form of social darwinism. they will be with humans as long as there are humans. math is both collaborative and independent. there are true lone geniuses! math is one of the best subjects to find them in. there is truly something for everyone. its great to see it cross a major egalitarian milestone with the 1st female winner! see also fields medals/ nevanlinna prize :D 8-) :star:

  20. Keenan
    August 16, 2014 at 9:27 am

    Cathy:

    Richard Feynman was also eloquent in his critique of the business of the Nobel Prize & other such honors:

  21. mathematrucker
    August 16, 2014 at 11:40 am

    For those who like irreverent award acceptance speeches, the backhandedly gracious “blah” one by Alex Lifeson of Rush accepting induction into the Rock and Roll Hall of Fame in 2013 and the nonchalant one by Eddie Vedder of Pearl Jam accepting a Grammy in 1996 are sure to please:

  22. Linda Hoff
    August 17, 2014 at 9:21 am

    I agree, on behalf of my math-queen daughter, that the age 40 limit should not exist. (When she turned 41, she sighed and lamented, “Now I can’t win the Fields Medal.” It was a sad little moment.)

  23. August 17, 2014 at 8:18 pm

    Seems like this piece should be headed something like ‘Why I hate most science journalism’ more than ‘why I hate the Fields medal.’

    Many of your problems with the Fields Medal itself, I submit, would at least be lessened if, apart from the journalistic problems of forcing stories to be about individuals regardless of whether that’s appropriate, journalists were able to give their attention to more than one prize for top-level mathematics, and, of course as you say could find inspiring mathematicians without the assistance of awards committees.

    The answer to the last seems to be to encourage mathematicians to be their own journalists, as who else can recognise outstanding mathematicians?

    Gotta say, it also seems like GH Hardy and ET Bell have to take at least some of the blame for the cult of the young male genius working alone. Perhaps it is time for someone to provide some counter-iconography.

    • August 18, 2014 at 7:48 pm

      Can;t blame Bell for ageism. He romanticized everything, including Euler’s productivity at an advanced age.

      • August 18, 2014 at 8:25 pm

        You’re right, but I think that a major cause of what’s frustrating Cathy is the romanticised view versus reality. And the romance isn’t always bad- many people have been inspired by the romance at various stages of their mathematical careers. The problem is that journalists and other outsiders can see nothing but the romance, and they don’t want to see anything non-romantic. So you’ve got to create romantic myths about the other aspects you want to highlight. In some ways I would have thought it wouldn’t be too hard to mythologise about some collaborations – Bourbaki seems like the basis for a semi-successful independent movie, maybe starring Matthew McConaughey.

        • Wooderson
          August 18, 2014 at 10:40 pm

          “That’s what I love about these Fields medalists, man. I get older, they stay the same age. Yes they do.”

  24. August 18, 2014 at 12:30 am

    I have to agree with travellingactuary, we need compelling stories to counteract Hardy and the current science journalism.

    I recently read Kahneman’s Thinking, Fast and Slow and one of the things that truly moved me about it was the authentic respect and love and sense of camaraderie that he had with his long-term collaborator Amos Tversky. I don’t remember feeling any of that from Hardy toward Littlewood, or even toward Ramanujan. In other words, even the thing Hardy called “the one romantic incident in my life” was lost in his writing.

    The only famous math culture work that I can think of that even starts to come close to sharing the sense of community with a wider audience is The Man Who Loved Only Numbers (Hoffman’s biography or Erdos). Of course, that work is still not community centered enough due to being a biography; the details of Erdos’ many collaborators are washed away by his personality.

    I would love to read a biography of a community or school of mathematicians. I am sure some exist (and I would appreciate recommendations; does one exist for Bourbaki?), but more need to be written.

    Cathy, I would encourage you to write in more detail about your experiences of community. Especially in venues read more widely outside math circles. I think you have a personal story that would do a great service of sharing the math community with the general public.

  25. August 18, 2014 at 7:38 am

    I would like to come out in support of the 40 year age limit.

    At first I was dismayed that the age limit was there, becasue after all, what happens if one proves the Riemann hypothesis at age 41? But when we look at other major prizes without an age limit, both inside and outside mathematics, there is a tendancy to give these prizes to older people on the basis of work they did often many years ago.

    On the other hand, the age restriction in the Fields medal necessarily forces the prize to be awarded for work completed in the recent past, and this focus on top quality work of a contemporary nature is something I appreciate about the Fields medal.

    (I hope that my change of mind about the age limit is not a selfish function of realising that I am not on track to prove the Riemann hypothesis at age 41)

    • Ethan
      August 18, 2014 at 3:47 pm

      The problem with the “age limit” as much as with the “publish or perish” is that it puts in place the wrong set of incentives.

      You can fund mathematics at large, as it happens with other scientific fields, so that enough people make a decent living out of it without putting in place something that necessarily rewards the wrong type of work.

      Take the two most famous -both in terms of public impact as well as impact to mathematics itself- results proved in the last 20 years: Fermat’s Last Theorem and the Poincare Conjecture. Both were proved by people who worked in isolation for many years without publishing much while they were working on the respective problems. Andrew Wiles was refused the Fields Medal because of the nonsensical age limit. Grigori Perelman himself refused the Fields Medal because of the politics surrounding the award.

      Don’t take me wrong. I think that there is room for rewarding both kinds of activities: the activities of those who publish regularly important new stuff which is not Millennium Award grade and the activities of those who dedicate themselves to tackling extremely hard problems. The main issue with the age limit (and other politics surrounding the Fields Medal) is that it disproportionally rewards the first type of mathematics which is the least likely to produce the most significant results that will have long lasting impact in mathematics.

      To be sure, this is not something exclusive to mathematics, but it is sad that it happens. And because the people who make the cut are of the first kind, they surely favor that type of work over the other, riskier one.

      • August 20, 2014 at 1:19 pm

        I agree. It makes no sense to me what age has to do with spectacular mathematical achievement. Genius lives throughout the spectrum of human existence, it should be judged for its product, not its surroundings. Gender, age, politics, religion–do any of these things disprove a beautiful theorem once proven? If the answer is no, then they cannot be used to measure its innate or relative value, either. Why must science always plod forward at the pace of egos and fear?

        The timing of discovery is unimportant. The fact of it is all that matters.

        • August 21, 2014 at 6:35 pm

          Your point is not responsive to Peter McNamara’s argument. If there is no age limit then the tendency is to create a “lifetime achievement” award given for an entire career rather than an award aimed at specific recent work. Those are two different kinds of awards that serve different purposes and the Fields wants to emphasize the latter. The obvious flaw is that people over 40 can do a single, great new thing and then be ineligible, as in the case of Wiles. But it seems to me that the range of prizes–the Abel, the Fields, the Millennium Challenges, and probably many others I haven’t heard of–adequately incentivize and publicize a wide range of extraordinary achievement in math.

          Now, if what you object to is recognizing and rewarding extraordinary achievement at the expense of collective, workaday, incremental progress, that’s a deeper dispute. Math is not alone in having a multitude of unsung workers–think of how much we all depend on unknown package-delivery drivers, IT specialists, physicians, building contractors, etc. Most of those fields don’t have publicly recognized prizes of any kind.

        • August 21, 2014 at 7:17 pm

          Whoosh! Heat that? That was the sound of my point going right over your head. Mazel tov.

        • August 22, 2014 at 7:12 am

          IMHO the main problem with the 40 year age limit is that it discriminates against women who decide to have children. See Mary Ann Mason’s “Do Babies Matter?” Unfortunately the PDF version at:

          http://grad.berkeley.edu/deans/mason/Babies%20Matter1.pdf

          gives a 404 error as she is no longer at Cal.

          (I’ll search for it later.)

          But the book is available.

          http://rutgerspress.rutgers.edu/product/Do-Babies-Matter,4767.aspx

      • Ethan
        August 23, 2014 at 2:47 am

        stevepostrel,

        I am not against rewarding individual people. Quite the contrary, I do think that while mathematics and other areas of science and technology are the result of a lot of people working together, it takes very talented people to take things to the next level. As somebody said, almost anybody can do calculus, but it takes a genius like Newton or Leibniz to invent it.

        My point is that the Fields Medal, as long as it keeps its status as the most prestigious award in Mathematics, puts in place the wrong set of incentives -publish a lot and young- that spread to mathematics at large, even among those who are not competing for the award. In addition, the Andrew Wiles matter falsifies another point that allegedly justifies that 40 year limit. For all their wisdom, the committee that decided the 1994 medals was unable to “predict” that Andrew Wiles would fix his proof just one month after the closure of the 1994 ICM. So much the medal allegedly “predicting” future work.

        So given that people, even those who do the type of mathematical contributions that is groundbreaking, can do outstanding mathematical work well after the age of 40, what’s the point of keeping an age limit that implies that people older than 40 are past their prime?

        It is very ironic that of all people, those in charge of the IMU fail to understand that Andrew Wiles’ work provides a counterexample to the “40 year old conjecture”!

  26. August 18, 2014 at 12:32 pm

    Being neither scientist nor mathematician, but part of an extremely nerdish community, I wonder: Isn’t that kind of narrow journalism and vain efforts to explain the unexplainable just par for the course regarding any high-level theoretical and/or practical endeavour in all fields? The blog’s surely reasonable complaints would be just as relevant for all sufficiently advanced technology, which will be presented as some kind of individual magic.

  27. August 18, 2014 at 5:23 pm

    I would agree to every single word of this article. But still, I think it’s unfortunate that you’ve written this just after a woman, who is originally from Iran, wins the Fields Medal for the first time.

  28. JohnC
    August 18, 2014 at 5:48 pm

    Unless you’re really a contender, it’s all academic. I liken it to a marathon race. There’s maybe 5 runners that have a chance of winning. The rest are just running for themselves.

    Now if you really are a contender for such accolades, there’s the Abel.

  29. August 19, 2014 at 5:32 pm

    Could you clarify something for me? How much of your dislike is of the Fields Medal itself, and how much is it the way that journalists in turn write about it? Something that seems important to me is that the Fields Medal is given to mathematicians by other mathematicians; presumably we should get to work putting our house in order if the problem is the awards we give out ourselves.

    I was also impressed, like commenters above, by the coverage of the Fields Medalists by Quanta. It seemed that their coverage was put together in close collaboration with the IMU. That feels like a good move in helping to get more accurate and fuller pictures of the activity of—and the personalities behind—the doing of mathematics.

    Thanks for sharing your math backstory in this post. It was lots of fun to read. And I do agree that more public celebration of mathematics as a “team sport” would be wonderful.

  30. Otter
    August 19, 2014 at 5:35 pm

    If you want to inspire people to enter the guild, you need to reward those who inspire people to enter the guild. Teachers. Bloggers. Reporters. Maybe also you fund the creation and publication of fascinating problems, games, puzzles, at all levels.

  31. August 20, 2014 at 2:08 pm

    If you’re a math nut then maybe you should take it too the next level and study physics. Math and science tend to go hand in hand perfectly.

  32. August 20, 2014 at 8:01 pm

    I enjoyed the read, although I far from the world of mathematics. But this problem transcends math. It glosses over non-traditional mathematicians, i.e. mathematicians who are not privileged white males, which seems to happen in most fields.

  33. August 20, 2014 at 9:32 pm

    hey love your blog

  34. August 20, 2014 at 11:17 pm

    Reblogged this on Apps Lotus's Blog.

  35. August 21, 2014 at 6:11 am

    Loved the post!!

  36. August 21, 2014 at 3:30 pm

    I am in the field of biology, not math but some of what you write about is universal in academia. there are challenges to advancing in an academic career, especially for women, especially for parents!

  37. August 25, 2014 at 6:54 am

    I agree, this kind of Fields Medal and other glorifying of some one persons as geniuses is very misleading in a way. Saw you loved the Spirograph when you were younger, I think you would like http://GeoKone.NET then, it’s like a spirograph on steroids running in your browser :)

  38. Joeli Bacsi
    August 28, 2014 at 6:09 pm

    I don’t buy this math babe. Look, math has enormous problems with publicity. Here is something that does get publicity. Sure, the journalist isn’t going to explain Differential Geometry — but thats the case anyway. And I don’t buy your screed about math being a group activity. It is both group and individual but prizes, generally, are given to individuals. Should the Best Actor/Actress Oscar’s be removed because it takes a whole cast (and lots more) to make a movie. I hope not! And as for it being for those under 40 — yeah, thats the way it is. There are plenty of other prizes, most notably the Abel Prize (and Wolf and
    Kyoto …) that have different criteria.
    I LOVE math prizes — they are certainly good for the winners but much much more they stimulate work by lots and lots and lots of very good (often, equally good) people.
    Indeed, even from your perspective, one very good thing about Fields is that so FEW
    people get it. (Unlike, say, 3 or so Nobels a year in Physics.) That way, if someone doesn/t get it — they still can be felt to be really great.
    Love your blog, but you are way off the mark on this one.

    p.s.: Hurray for Aise!

    • August 28, 2014 at 6:25 pm

      Agree to disagree! Except for the Aise part.

      On Thu, Aug 28, 2014 at 6:09 PM, mathbabe wrote:

      >

  1. August 15, 2014 at 11:44 am
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