2015 Breakthrough Prizes in Mathematics

The first set of winners of the $3 million Milner/Zuckerberg financed Breakthrough Prizes in mathematics was announced today: it’s Donaldson, Kontsevich, Lurie, Tao and Taylor. There’s a good New York Times story here.

When these prizes were first announced last year, I was concerned that they would share a problem of Milner’s Fundamental Physics Prizes, an emphasis on rewarding one particular narrow area of research. I’m happy to say that I was wrong: the choices made are excellent, including a selection of the absolute best people in the field, working in a wide range of areas of pure mathematics. The prize winners are mathematicians who are currently very active, doing great work. It’s clear that there was an effort to avoid making this a historical prize, i.e. giving this to people purely for great work done in the past (which to some extent the Abel Prize is doing). The recipients are on average in their 40s, at the height of their powers.

One oddity is the award to Kontsevich, who already received $3 million from the Fundamental Physics prize. Given my interests, I suppose I shouldn’t criticize a prize structure where physicists get $3 million, mathematicians $3 million, and mathematical physicists $6 million.

While this prize doesn’t suffer from the basic problem of the Physics prize (that of rewarding a single, narrow, unsuccessful idea about physics), it’s still debatable whether this is a good way to encourage mathematics research. The people chosen are already among the most highly rewarded in the subject, with all of them having very well-paid positions with few responsibilities beyond their research, as well as access to funding of research expenses. The argument for the prize is mainly that these sums of money will help make great mathematicians celebrities, and encourage the young to want to be like them. I can see this argument and why some people find it compelling. Personally though, I think our society in general and academia in particular is already suffering a great deal as it becomes more and more of a winner-take-all, celebrity-obsessed culture, with ever greater disparities in wealth, and this sort of prize just makes that worse. It’s encouraging to see that most of the prize winners have already announced intentions to redirect some of the prize moneys for a wider benefit to others and the rest of the field.

Update: Among the private reactions I’ve heard from prominent mathematicians this morning, one is the desirability of funding a new “sidekick” prize for collaborators of the $3 million winners…

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24 Responses to 2015 Breakthrough Prizes in Mathematics

  1. Als says:


    I think it has the potential to challenge the Fields medal in the long run if the committee chooses wisely the next recipients.

  2. someonesomewhere says:

    Well, the Nobel prize was initially also awarded to people who already were famous, so it’s not a new concept to initially award the prize to already famous people, so that the fame of the past winners shines on the new ones.

  3. Bill says:

    All of them are great mathematicians and deserve the award as much as anyone else, but the selection seems a bit random. Some of them are obviously rewarded for old breakthroughs, not for recent work, and some for work that nobody really understands to call it a breakthrough. What is the main criterion? Starting from next year when only one person gets the award, is it going to turn into another lifetime achievement award or will they reward genuine recent breakthroughs? Why not turn this into a Fields Medal without age restriction – reward for genuine breakthroughs in the last few (4?) years? Actually, the award is big enough to share among possible coauthors (Birkar- Cascini-Hacon-McKernan, Marcus-Spielman-Srivastava, etc).

  4. Bill says:

    Shouldn’t this be “2014 Breakthrough Prizes in Mathematics”?

  5. Peter Woit says:

    These prizes will be awarded in November at a ceremony for the prizes in physics and biology officially called the 2015 prizes. I see the Milner site is naming them not by year, but as “Inaugural”. It seems though that the plan is to award the math ones each year at the same time at the others, and next year’s will be the 2016 ones, so 2015 seems a better choice than 2014…

  6. Bill says:

    From NYT: “The size of the award, I think it’s ridiculous,” he said. “I didn’t feel I was the most qualified for this prize.” But Dr. Tao added: “It’s his money. He can do whatever he wants with it.”

    Not true that he can do whatever he wants with it, you can say no and encourage others to say no, if you believe this is not a good idea. Mathematics community can put Milner’s money to good use, but on their terms.

    Also, any rumors that Wiles refused the prize? Obviously, they didn’t even dare to ask Perelman. By the way, more kids would be inspired to do mathematics if mathematicians acted more like Perelman. This prize is not going to make them into celebrities in that sense.

  7. Als says:

    “Update: Among the private reactions I’ve heard from prominent mathematicians this morning, one is the desirability of funding a new “sidekick” prize for collaborators of the $3 million winners…”

    The problem of the side-kick award is that it could feel like an insult. I would be very uncomfortable telling Taylor he gets the “Wiles’s sidekick award” for instance.

  8. John Doe says:

    New prizes like this tell me more and more how pointless prizes are becoming.

    This post hits the target. What is the purpose of a prize? Why do prizes include money and if they do, how much should it be?

    If the purpose of a prize is to ‘help Mathematics’ (whatever that means) at large, this prize has a big risk, since it puts a lot of power (money is just a measure for power) in the hands of few mathematicians, not lelected for their choices regarding power, but for their solutions to mathematical problems. It is pretty much up to them what they do with it. It is interesting how the piece you link says that Tao tried to reject it but in the end took it because it is up to this guy what he does with his money. He is just going along with the system. If he keeps it, that sounds fake. If he does something else to ‘help Mathematics’ with it, whatever that is, it is as if he had become a jury for the prize, which shows how pointless this prize is.

    I don’t think 3 million dollars are going to help these guys to do better math, and I don’t think it’s going to make any difference other than to their wallets. They’ll keep doing what they do, just a bit richer.

  9. Als says:

    BTW, the Milner website says Taylor proved the “Taniyama-Weil conjecture”. I wonder who wrote the blurb and kept Shimura out….

  10. Peter Woit says:

    I think how insulting this might be would depend strongly on the size of the check. At, say $1 million, I think most mathematicians would overcome any sense of grievance about being a “sidekick”.

    About Taniyama-Weil I also noticed that. If Serge Lang were still alive, it would kill him.

  11. Peter Woit says:


    The people Milner chose are relatively young (all younger than me…), and have major results from within the past few years, which would be one reason Wiles is not on the list, not that he turned it down.

    I don’t want to start a Perelman pro/con discussion, but I disagree with you about Perelman as a role model. I do think though he almost surely would have turned down the money.

  12. Thomas says:

    It would be great if one could read Clozel’s exposition of the recent work by Taylor, Patrikis: http://www.institut.math.jussieu.fr/projets/tn/STN/files/annonce-7-4-14.pdf

  13. M.K. says:

    “it’s still debatable whether this is a good way to encourage mathematics research”

    I disagree on the seemingly obvious conclusion that a high-doted distinction distributed among a small number of already famous mathematicians would lead to less ‘encouragement’ of mathematics research than a distribution among a higher number of lesser known mathematicians. Given such prizes are also in the latter case based on past achievement of people working on established mathematical institutes (thus established mathematical areas) it is very difficult to see how such prizes would lead to something else than to a substitution of public funding by private or corporate funding. Further, it is very difficult to imagine indeed how a non-mathematical jury, or a random jury, could have the expertise to decide if non-mainstream ideas could be fruitful or not, while indeed the present price-winners are with a relatively high probability capable to decide this. So as usual in our society, everything depends on the good-will of individuals in a system that is organized on questionable measures and aims in general.

  14. Ian says:

    If this prize allows these mathematicians to not apply for grants (for some number of years), then it may serve a useful purpose. Not only would it free up time that might be taken applying for grants and allow them to conduct research unconstrained by grant proposals, but it should also allow others to have a better chance of obtaining them (such as NSF grants, which are getting less funded over time).

  15. Peter Woit says:

    That’s an interesting point, but given the way these awards are set up and the positions of the people getting them, they generally won’t replace NSF grants. One could take a look at what happened in physics, where a quick search shows
    Although the IAS physics faculty each got $3 million awards in 2012, the IAS is still applying for and getting NSF grants to pay for postdocs and overhead to the institution.

    The people getting these awards don’t really need research grants to conduct their own research, they typically apply for grants to fund students, postdocs, and their institution. The prize money goes directly to their bank account, not to the institution. If they want to use the money for students, postdocs, their institution they could do this, but would have to set this up themselves, which would likely be every bit as time consuming as the grant application process.

    That said, I’m sure some of the prize money will end up being used by the recipients to support research in ways that a grant might have in the past, and can replace some NSF grants. It’s not at all clear though how much of that is happening for the physics grants, and how much will happen for the math grants.

  16. Peter Woit says:

    Put differently, the explicit goal and structure of these prizes is to make the recipients personally rich and famous, not to support their research. Once they are rich, in principle they can devote their time to philanthropy and support research, but it’s unclear how much of this will happen, will be interesting to see.

  17. Bobito says:

    Why doesn’t Xiuxiong Chen or Yan Soibelman deserve a bit of the cake?

  18. Jess Riedel says:

    Two alternative ideas for structuring the prize:

    (1) Make it more about honor. Give the mathematician a few hundred thousand dollars, but use the bulk of the money to endow a research position in the mathematician’s name. (An MIT professorship is $3M: http://giving.mit.edu/priorities/faculty/)

    (2) Give the money to the awardee, but require them to pledge to not write grant proposals for 5 years. Maybe unfeasible since they need to write grants to support their students, postdocs, and institution, but part of the award could go to cover this.

  19. Peter Woit says:

    Good suggestions. I’ve often wondered why more of this private money isn’t going into the traditional philanthropic path of endowing positions, which would have a big, long-term effect on the health of the field (Simons has the “Math + X” program, but I can’t think of many other examples).

    If each year, instead of giving a $3 million personal check to a string theorist the Breakthrough Prize people endowed a position in string theory, the effect on the subject would be huge (and would do a lot more to encourage young people to go into it).

  20. Bork says:

    I agree that this is a double-edged sword, even for the winners. Now they have to worry about what to do with all that money. If they spend it on themselves, they will be criticized, or are likely to feel so, and if they try to distribute it somehow, in some sort of “fair” way, that could eat up time and cause a headache and ironically take them away from research. And their choices could, again, be criticized.

    Of course the type of mathematician who likes being a big honcho would love that, but my guess is these are not of that sort. They probably would much prefer just to, basically, be left alone. Perlman was only the extreme version of that.

    What a research mathematician really needs is: more free time, plus a modicum of financial stability, plus a good research environment. A good research environment includes: happy colleagues, and good basic education.

    This is why Simons’ donations seem much more creative and better thought out,
    and much more likely to be effective.

    One of the great things about mathematics as a human endeavor and a part of human culture and as a path through life, is the relative equality and openness
    compared to other realms of activity. This sort of prize might end up doing more harm than good to the overall culture and enterprise of mathematical life and mathematical research.

    I say, give a $100,000 prize, and then just give half the remaining $$ to Simons to spend as he sees fit, and give the other half to lobbyists in support of: the NSF funding of basic research, and a bigger NSF budget; and basic school education reform: not Bill Gates style (test, test, iPad, test) but small class sizes, sabbaticals and better salaries for teachers, real books for kids, as well as bringing back instruction in music, cursive writing, PE…oh and math and physics I suppose, why not…

  21. Patrice Ayme says:

    Milner is a celebrity. And a financial manipulator who became immensely wealthy with what Roosevelt and the Bible called contemptuously “money changing”. He profited immensely of a system, plutocracy, that is mostly about oligarchy pushed so far, that even the character of those “leaders” become diabolical.

    It’s diabolical to make us believe that mathematics will progress more by giving more power to those who have more than enough to do good math.

    Overall, science and mathematics do not have enough practitioners. A striking example is antibiotic research where a small effort needs to be done to find new antibiotics. To have a few individuals who are much richer will have no positive effect whatsoever. This is certainly true in math and physics.

    In biology, immense greed has clearly undermined research (individuals have made up to half a billion dollar a year in that field, but one cannot find the modest finance for new antibiotics research). Making a few persons very rich promotes greed.

    So why is Milner doing this? Maybe it’s subconscious. The oligarchic principle is that humanity is unworthy, but for a few celebrities who never get enough. This is what Milner is truly rewarding. His reason for being what he is. Someone obsessed by individual power.

    Want to help science and math? Finance studies on how to persuade governments to finance enough advanced public free instruction in science and math, starting in preschool. Through heavy taxation of the richest celebrities, starting with Milner and his kind.

  22. Bill says:

    Jess Riedel,

    Endowing a research position is the best idea I’ve seen so far. I would add that such a position should not be given permanently to one person until his/her retirement but instead given for a period of, let’s say, 10 year to an active researcher.

  23. NLR says:

    Endowing a research position is a good idea, but the problem with the Milner Prize is similar to a remark made by Norbert Wiener said in his book “Ex-Prodigy,” that, often, people who are already well-known and well-rewarded get more awards, resulting in a “pyramid of awards.” However, the people who could most benefit from such awards are lesser-known researchers who do not have financial stability.

    Also, the idea of making mathematicians celebrities is completely at odds with the reason to do mathematics. The value of math does not come from fame or money, but from the intrinsic interest and value of mathematics. In fact, I would think that many people study math precisely to engage with a part of the world that has nothing to do with things such as money or celebrity.

  24. Anders says:

    In Economics we have something called tournament theory to try and explain the very large CEO remuneration you often see in the US. Basically the idea is that you overpay the CEO to get people further down in the organization to work very hard, to have a shot at the CEO position. Maybe these prizes in science can work the same way, they do not change the productivity of the recipients but maybe of other researchers that have a decent chance of getting a prize later in their career.

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