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…