On August 13, 2014, at the opening ceremony of the [International Congress of Mathematicians]( the Fields Medals, the Nevanlinna Prize and several other prizes were announced.
A full list of awardees with short citations:

Fields medals:
Artur Avila

is awarded a Fields Medal for his profound contributions to dynamical systems theory, which have changed the face of the field, using the powerful idea of renormalization as a unifying principle.

Quanta Magazine on Artur Avila

Manjul Bhargava

is awarded a Fields Medal for developing powerful new methods in the geometry of numbers, which he applied to count rings of small rank and to bound the average rank of elliptic curves.

Quanta Magazine on Manjul Bhargava

Martin Hairer

is awarded a Fields Medal for his outstanding contributions to the theory of stochastic partial differential equations, and in particular for the creation of a theory of regularity structures for such equations.

Quanta Magazine on Martin Hairer

Maryam  Mirzakhani

is awarded the Fields Medal for her outstanding contributions to the dynamics and geometry of Riemann surfaces and their moduli spaces.

Quanta Magazine on Maryam  Mirzakhani

Nevalinna prize:
Subhash Khot

is awarded the Nevanlinna Prize for his prescient definition of the “Unique Games” problem, and leading the effort to understand its complexity and its pivotal role in the study of efficient approximation of optimization problems; his work has led to breakthroughs in algorithmic design and approximation hardness, and to new exciting interactions between computational complexity, analysis and geometry.

Quanta Magazine on Subhash Khot

Gauss Prize:
Stanley Osher

is awarded the Gauss Prize for his influential contributions to several fields in applied mathematics, and for his far-ranging inventions that have changed our conception of physical, perceptual, and mathematical concepts, giving us new tools to apprehend the world.

Chern Medal Award:
Phillip Griffiths

is awarded the 2014 Chern Medal for his groundbreaking and transformative development of transcendental methods in complex geometry, particularly his seminal work in Hodge theory and periods of algebraic varieties.

Leelavati Prize:
Adrián Paenza

is awarded the Leelavati Prize for his decisive contributions to changing the mind of a whole country about the way it perceives mathematics in daily life, and in particular for his books, his TV programs, and his unique gift of enthusiasm and passion in communicating the beauty and joy of mathematics.

In addition to that, Georgia Benkart was announced as the  2014 ICM Emmy Noether lecturer.
It might be interesting to note a curious fact about the new group of Fields medalists:

each of them [is] a notable first for the Fields Medal: the first woman and the first Iranian, Maryam Mirzakhani; the first Canadian, Manjul Bhargava; Artur Avila, the first Brazilian; and Martin Hairer, the first Austrian to win a Fields Medal.

However, this unusual diversity of nationalities does not necessarily translate into a corresponding diversity of institutions, since (according to wikipedia) three out of four winners work in (or at least are affiliated with) universities that have already had awardees in the past.

Some notes on the works by Fields medalists can be found on Terence Tao's blog.

A related discussion on Hacker News.


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17 comments, sorted by Click to highlight new comments since: Today at 4:30 PM

I think Bostrom puts it nicely in his new book "Superintelligence":

A colleague of mine likes to point out that a Fields Medal (the highest honor in mathematics) indicates two things about the recipient: that he was capable of accomplishing something important, and that he didn't.

WTF. That's a fucking ignorant remark.

You know, I'm having a bit of a bad day, so there's more venom in me than there normally is. And I might sometimes hesitate to attack a person for being stupid, since I might have committed an isomorphic stupidity myself.

But today, I am not going to care, I am just going to vent. Right now, I feel contempt for the arrogant ignorance of whoever said that. Lacking context, it's hard to know exactly where they are coming from. Is it some transhumanist, whose definition of "something important" reduces to research on life extension / nanotechnology / artificial intelligence / whatever activities it is whose importance they appreciate? Is it just someone, as one comment suggests, who uses applied math rather than working in pure math?

Could it be a comment, not about math, but about the sort of math that wins the Fields Medal? Possible, but unlikely. Anyway, this will be the core of my rebuttal: progress in math is progress in expanding what's thinkable. There was a time when we didn't have the concept of chaos theory, or sets, or calculus, or... by god the remark is so retarded, it reduces me to tumblr levels of illiterate vituperation.

A longer quote, for context, with the relevant passage highlighted:

Crunch time

We find ourselves in a thicket of strategic complexity, surrounded by a dense mist of uncertainty. Though many considerations have been discerned, their details and interrelationships remain unclear and iffy—and there might be other factors we have not even thought of yet. What are we to do in this predicament?

Philosophy with a deadline

A colleague of mine likes to point out that a Fields Medal (the highest honor in mathematics) indicates two things about the recipient: that he was capable of accomplishing something important, and that he didn’t. Though harsh, the remark hints at a truth.

Think of a “discovery” as an act that moves the arrival of information from a later point in time to an earlier time. The discovery’s value does not equal the value of the information discovered but rather the value of having the information available earlier than it otherwise would have been. A scientist or a mathematician may show great skill by being the first to find a solution that has eluded many others; yet if the problem would soon have been solved anyway, then the work probably has not much benefited the world. There are cases in which having a solution even slightly sooner is immensely valuable, but this is most plausible when the solution is immediately put to use, either being deployed for some practical end or serving as a foundation to further theoretical work. And in the latter case, where a solution is immediately used only in the sense of serving as a building block for further theorizing, there is great value in obtaining a solution slightly sooner only if the further work it enables is itself both important and urgent.1

The question, then, is not whether the result discovered by the Fields Medalist is in itself “important” (whether instrumentally or for knowledge’s own sake). Rather, the question is whether it was important that the medalist enabled the publication of the result to occur at an earlier date. The value of this temporal transport should be compared to the value that a world-class mathematical mind could have generated by working on something else. At least in some cases, the Fields Medal might indicate a life spent solving the wrong problem—for instance, a problem whose allure consisted primarily in being famously difficult to solve.

Similar barbs could be directed at other fields, such as academic philosophy.

I agree that in this case Bostrom is at best misguided.

EDIT: he clarifies later:

We could postpone work on some of the eternal questions for a little while, delegating that task to our hopefully more competent successors—in order to focus our own attention on a more pressing challenge: increasing the chance that we will actually have competent successors. This would be high-impact philosophy and high-impact mathematics.

His error, in my view, is assuming the fungibility of the two.


I completely agree that this was a dumb thing for Bostrom to quote.

Mathematics research generates positive feedback with almost every other branch of science; obviously existential risk is no exception. It's clear that we shouldn't devote all of our resources to merely mathematics, but at the same time saying Fields-level research is flatly not important is going too far.

Yeah. It's quite retarded in the context as well. Bostrom's basically going on and on of how it is crunch time for the philosophy to solve eternal questions of ethics and such, and how this specific philosophy is so much more important.

Let's say someone actually solved those eternal questions.

To be specific, let's say we understood suffering. We can look at a description of a physical system, and then tell how much suffering that system is experiencing.

What does he think such answer would even look like? Picture a piece of paper, it has the answer on it, what do you think it looks like?

(Same as every other hard answer ever encountered by mankind, which wasn't bullshit: Mathematical formulas, with derivations and proofs, in all likelihood involving objects and algebras we didn't even come up with yet. Answer that is literally unthinkable today)

edit: I think it'd be fair to say that answering a difficult question before there's even a language in which an answer could be expressed is probably one of the most counter productive efforts known to mankind.

I'm reminded of my petroleum engineering professor who assured me that a friend would eventually stop wasting his time on physics and come around to what was really important, namely petroleum engineering.

Given the sterility of a lot of physics and sex appeal to nerds, the unpopularity of petroleum engineering, the very low pay for physics grads vs very high pay for petroleum engineering grads, the crucialness of petroleum products to the global economy which pays for all research, and of course the lamentable influence of 'the devil's excrement' & resource curse on regions like Iraq, I could more easily make the case that the professor was right than the student.

I actually agree with you, as evidenced by the fact that I got all my degrees in that area. But I feel like the professor would have said the same thing in the same tone of voice if he were a professor of butterfly taxonomy. I think experts tend to think what they are doing is the most important thing.

I actually agree with you, as evidenced by the fact that I got all my degrees in that area.

Didn't know that.

I think experts tend to think what they are doing is the most important thing.

I think there is a definite tendency that way, for the obvious self-selection reason, but I don't think the tendency is necessarily that bad. A fair number of my professors did do a little spiel justifying the value of their particular field, but I don't remember any of them which were that grossly out of whack in their assessment - eg the cognitive psychology prof argued it was important and interesting, which I don't disagree with, but he didn't say it was 'what was really important'; the philosophy professors generally tried to justify the field, but they were satisfied if you saw some value to philosophy at all and didn't try to claim it was the most important field, etc.

What award does the recipient get if they actually accomplish "something important"?

Not really an answer, but one could say that a scientist should conduct their research with one hungry eye on the Nobel Peace Prize.

(Obviously, this is a quip; cf medical research etc etc. But I think it conveys the spirit pretty well)

conduct their research with one hungry eye on the Nobel Peace Prize.

Specifically the Nobel Peace Prize is pretty much discredited nowadays, it became a rather meaningless political gesture.

Nobel Prizes, especially in physiology/medicine and economics, are probably more indicative of social impact (which is what I think Bostrom's colleague meant when he used the word "important").

He was explicitly talking about mathematicians, in math Fields medal is the equivalent of Nobel. Besides, the same exact criticism Bostrom levels against Fields can be applied to Nobels.

Wow. I'm in theoretical physics and that quote is like a slap in the face. Not saying it is wrong though.

This colleague of his is a philosopher then?

My guess would be physicist or computer scientist, or some other field that uses a lot of complicated applied math.

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