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2014 Fields Medals announced (mathunion.org)
308 points by johnb556677 on Aug 12, 2014 | hide | past | web | favorite | 74 comments

Quanta Magazine, published by the Simons Fonundation, has an article on each of the four Fields Medallists and the Nevanlinna Prize winner, Subhash Khot.

Artur Avila - A Brazilian Wunderkind Who Calms Chaos http://www.simonsfoundation.org/quanta/20140812-a-brazilian-...

Manjul Bhargava - The Musical, Magical Number Theorist http://www.simonsfoundation.org/quanta/20140812-the-musical-...

Martin Hairer - In Noisy Equations, One Who Heard Music http://www.simonsfoundation.org/quanta/20140808-in-mathemati...

Maryam Mirzakhani - A Tenacious Explorer of Abstract Surfaces http://www.simonsfoundation.org/quanta/20140812-a-tenacious-...

Subhash Khot - A Grand Vision for the Impossible http://www.simonsfoundation.org/quanta/20140812-a-grand-visi...

Oh, this is great: I'd only seen the one for Dr Mirzahani. Truly inspirational. I wish I'd had these role model stories as a high schooler!

I was in the same Harvard class as Manjul Bhargava, one of this year's Fields Medal winners. I remember having lunch with him as a freshman and being amazed that he was already taking Math 134 (topology). I slowly realized he'd effectively taken a full undergraduate math curriculum in high school.

I had a friend who was Manjul's TA for a probability class our senior year. I still remember him exclaiming, "There's no way that series telescoped!" [1] when Manjul solved one problem in a particularly clever way.

The strange thing is that it was hard to tell at first if Manjul was particularly smart. Two of our other mathematically accomplished classmates, Lenny Ng and Kiran Kedlaya (both of whom I knew much better than Manjul), were obviously brilliant, but with Manjul it took a lot longer to figure out he was a genius.

I think now the secret is out.

[1]: http://en.wikipedia.org/wiki/Telescoping_series

> I had a friend who was Manjul's TA for a probability class our senior year. I still remember him exclaiming, "There's no way that series telescoped!" [1] when Manjul solved one problem in a particularly clever way.

By any chance, can you remember that problem? I have no way to understand Manjul Bhargava's work that got him the Nobel prize, but I could probably understand how he solved that problem, which would enable me to perceive a slight bit of his genius.

Alas, I don't remember the details of the particular sum.

I'm a current Duke student and took multivariable calculus taught by none other than Lenny Ng a year ago. I had no idea who he really was until about halfway through, though we all knew he was brilliant. One of the nicest professors I've ever had, exceptional at explaining concepts too. He also draws pictures like a god, something that's obviously really beneficial in that sort of class. He used to say his drawings were a bit off while we would just sit there astonished. Such an amazing guy.

Lenny was one of my lab partners in Physics 15c. It was especially cool since I'd read about him in Newsweek the year before. Really smart, super nice guy.

Notably, Maryam Mirzakhani is the first woman to win a Fields medal.


Also notably,

1. Mirzakhani is the first Iranian 2. Bhargava is the first Canadian 3. Hairer is the first Austrian 4. Avila is the first Brazilian

Since there are still ~200 countries without a Fields Medal, this isn't mathematically remarkable in comparison to the parent point.

So, I understand instead that you're identifying this as notable for the following reason:

There are 100 times more women in the world than Canadians, yet women and Canadians have the same number of Fields Medals.

First of all, there's not enough data to be statistically significant in any of my ramblings, so it's all kind of hand-wavy and I apologize for that.

But my general feeling is that there used to be a few "powerhouse" countries and institutions that dominated, but that has been changing for many years. There's a lot more diversity these days. So I think kiyoto's point speaks to the changes there.

In 1950, it would have been pretty inconceivable that a woman from Iran would have had the access and opportunities to contribute to mathematics in a way that would have earned a Fields medal; in 2014, it's a first-time feat; hopefully, in the future, it quickly becomes mundane.

"not enough data to be statistically significant"

^suspect this is incorrect.

Mirzakhani is the first woman to ever win, which is even more notable than being the first Iranian.

True. But now she takes her rightful place in a line reaching back to Omar Khayyam and earlier. Congratulations to Maryam Mirzakhani.

Well, as an undergrad, she went to one of the best universities in the world.


We don't hear about it much, but Iran has one of the best universities in the world.

It's important to note that successful Iranians generally become successful _despite_ the country they grow up in, not because of it. In my opinion, and having first-hand experience with that environment, the credit for this incredible achievement belongs to her and herself only.

I don't know of the details of the Math World, but probably this isn't true. Till now, a country as big as Brazil, one of the biggest economies of the world, never had won none of the most important scientific prizes. Argentina, our neighbor, has 3: http://en.wikipedia.org/wiki/List_of_Nobel_laureates_by_coun...

The medal is not just Artur brilliance and hard work, but also due to the IMPA: http://www.impa.br/ A sixty years old institution that gathered Brazil best mathematicians and gave Artur the resources to become a great researcher. Brazil had to cultivate and invest in this institution for decades.

Iran has great universities: http://www.newsweek.com/surprising-success-irans-universitie... The Medal is is probably just crowning their hard work.

I am well aware of the quality of the schools in Iran and can directly compare it US schools, having gone to school in both countries. That Newsweek article is not surprising to me, but in some areas it is inaccurate in my opinion. You do see high quality individuals graduating from Sharif university, which is highlighted in the article, but concluding the school itself is "successful" or competitive is incorrect. The fact of the matter is that there is a nationwide exam to enter college level education for all schools and you basically choose your school (and major) based on your rank in that exam. In that society, engineering majors, specifically Electrical Engineering majors, tend to have high status, so if you do well, you end up going to study EE at Sharif University, probably not because you are a fan of EE or you think Sharif is any good: it just has to be better than other schools.

The outcome of this is simple: you'll have selected top N individuals from an exam of half a million people and put them in a single school. Of course you're going to see those people shine. That says _nothing_ about the absolute quality of what that school gives you, just how good it is relative to its peers in the country, and I define quality as "output - input". The "input" is high quality, but the delta is merely meh in my opinion. Also, the students are high quality--the faculty are generally not (unlike what's mentioned in the article), but they do end up taking some credit.

In terms of the contribution of the country, I can just say that she is a survivor of an accident years ago, where seven talented math students died, whom had similar achievements to hers at the time. Overall, the contribution of the country to its mathematicians has been negative, specifically so to the female ones.

I want to second the sentiment that national investment supports achievement like this. IMPA has been very important for Brazilian mathematics, bringing people from across the world to Brazil to do high-level research. This means that some Brazilians who don't have have the opportunity or desire to move to Germany or California or Korea can work with and learn from amazing mathematicians who come to them, in Brazil.

Since 1990, at least one Fields Medal winner has worked in France -- until this year. France has a culture of supporting mathematics and mathematicians. It has its quirks and difficulties, but national support for research has played an important role.

I have to correct a misstatement :( Turns out Artur Avila is now a Brazilian-French dual citizen and spends 6 months a year as a research director of CNRS. So... France wins again!

> It's important to note that successful Iranians generally become successful _despite_ the country they grow up in

What you say doesn't make sense as she went to a very good Iranian school..

Successful people in Individually dominated professions become successful due to their own efforts. That's not just the case with Iranians, but with people every where around the world.

If some one is good enough to win Fields medal every one and every thing around works more like friction to their overall direction. And that's true for every country in the world.

So she just appeared in her current form out of nowhere with no causes and conditions?

I think Iran has a culture that respects mathematics and engineering and values accomplishments in those areas. Anecdotally/in my experience, there are many very good female Iranian mathematicians. (I guess I personally haven't met male Iranian mathematicians, only engineers; anecdote, as I said.)

Hehe, I imagine Muḥammad ibn Mūsā al-Khwārizmī [0] would be very proud of her. :)


Thank you for pointing that out. I hadn't actually noticed after glancing at the pictures that a woman was among the winners.

EDIT - I'm not trying to be funny, her hairstyle makes her look like she has a receding hairline so I thought she was a man.

Wow! I seem to have touched a nerve.

Remarking that a woman looks like a man (or vice versa) is often seen as insulting, even if the intent is not to insult.

Amazing group of people. Manjul is my wife's cousin so I have heard of a few examples of his brilliance (like the time he corrected his mom, a Math prof, during one of her lectures - he was a middle-schooler at the time).

Here's a nice piece NPR did on him: http://www.npr.org/templates/story/story.php?storyId=4111253

The more I read HN, the more I am impressed by the diversity of its readers. Now we have the cousin of a field medalist, nothing less!

You should see one of my all-time favorite Hacker news threads:


I'm finally beginning to appreciate how my embarrassing behavior ends up trotted out regularly.

Tell me about it...

But aren't you glad to be in a place where that incident could even happen?

Man, this guy is impressive as well.

He went on to found Tarsnap about a year after that exchange.

The whole thread is really incredible. Just a bit further down[1] you see someone criticize him and his startup (Tarsnap) for having a "phenomenal misunderstanding of what it takes to create a successful software startup."

And then Drew Houston of Dropbox chimes in to say that he's building a similar backup solution.

He went on to found Tarsnap about a year after that exchange.

Your chronology is a bit off -- I started writing code about a year before that thread. I had my first alpha testers at the time, and opened Tarsnap to the general public a few months later.

I just saw that. That's like history being made. Incredible.

Even more impressive is Drew houston chiming in. cperciva would've been a billionaire (not that he cares :))!

cperciva would've been a billionaire

Doubtful. First, Forbes says that dhouston has a net worth of $1.2B; and even if I had been an extra cofounder, splitting the cofounder shares more ways would have brought it below $1B.

Second, I really doubt I could have stuck it out at Dropbox for the necessary time. I like to do things in ways which are technically right rather than necessarily financially right; Dropbox is a phenomenally successful business, but it's not a product which I like.

2nd point is key. From collectong comic books to running companies, there are many people who had the requisite starting potential to be a success, but attrition peels off almost all of them for so many small and often unrelated reasons.

Make the post of your own path, and play to your strengths.

The Nevanlinna Prize was also awarded. This is the award mathematicians give to theoretical computer scientists. This year the winner is Subhash Khot from NYU. His main result is the Unique Games Conjecture (UGC) and how it can be used to obtain hardness of approximation results for algorithmic problems. For example, it is used to show that MaxCut cannot be approximated better than a factor of 0.878.. unless UGC does not hold. Remarkably this exact approximation factor is achievable by the breakthrough SDP algorithm of Goemans and Williamson. It is not currently clear if UGC is true and the opinions of theoreticians are split.

Martin Hairer is a OS X developer and the author of the fantastic Amadeus multi-track audio editor.


I'm sorry, what? A Fields medalist AND a OS X dev. I...

I suppose that when you're working on Field medal awarding problems, building software seems like a way to relax your mind.

That's a technique i tried when i was bulding my latest "complex" algorithm (graph diffing with the graph stored in a sql db): Whenever i felt stuck, i went and took an online lesson in quantum mechanics ( susskin ones, the best).

All of the sudden, all my problems seemed really easy, and i was able to move forward almost right away.

'Manjul Bhargava completed all of his high school math and computer courses by age 14.[..] Princeton hired him at the rank of tenured full professor within only two years of finishing graduate school, which is considered a record in the Ivy League.'

Fascinating. http://en.wikipedia.org/wiki/Manjul_Bhargava

Most of the undergraduate math majors finished high school math by age 14. Manjul was a cut above even them in mathematical talent and experience.

In-depth profiles and videos about all 4 Fields medalists here: http://www.simonsfoundation.org/quanta/20140812-a-brazilian-...

A pity only very few people in the world can fully understand the beauty of the mathematical proofs these geniuses created

It is weird. Doing great mathematics is like writing great poetry in a language only a few hundred people can read. And yet, every once in a while a mathematical poem changes the world.

Yes, and it's often the case that, faced with such a "poem", the world changes without ever understanding the mechanism of the change, as with both relativity and quantum theories.

Cedric Villani (Fields Medal 2010) wrote a book about his work [1] where he tries to give the reader a hint of what it looks like to be a mathematician on a day to day basis. It's quite interesting, even though he does not try to explain his theory.

[1] http://www.amazon.fr/Théorème-vivant-Cédric-Villani/dp/22467...

Strange to see this precisely today.

I can't help seeing this and remember once more Robin Williams (RIP) in 'Good Will Hunting', where I first knew about the Field Medal and the magic of Maths was a recurring theme in that fantastic movie.

"... Former winners include Nobel laureates, Field's medal winners, renowned astrophysicists and lowly M.I.T. Professors"

R.I.P. Robin Williams

Is it just me, or are the winners not listed anywhere on this site? It says "The Prize Committees for ICM 2014 have begun their work." And "last updated: 2014-07-30" at the bottom. Was the page reverted to an older version for some reason?

The winners were listed yesterday, then I noticed they removed the list, but now it's back.

They accidentally released the names early, then pulled them. I heard @JSEllenberg tweeted the results right away, but they were supposed to be released after the ceremony.

Those are beautiful stories of truth exploration!

>>created an abstract theory of regularity structures for stochastic partial differential equations

Fairly obvious but whatever.


Why the down vote, not funny at all? Hey I would be in support of them all getting the same money as Nobel or Abel laureates :).

Sorry WhitneyLand. In case you haven't noticed, the one thing Hacker News is most afraid of is becoming anything like Reddit.

Genuinely funny and on-topic humor is appreciated (see edw519's comment history for examples.) If the comment had been a subtle pun based on something from stochastic PDEs, it probably would have been upvoted.

We're not particularly interested in average jokes.

Ah, thank you for pointing that out. I would agree with the anti-snark stance I just didn't perceive it quick enough in my own comment.

I do not understand why should HN be afraid to give reasonable reason for down voting. Looking at picture I also thought that Maryam Mirzakhani is man. I understood my mistake only by reading down-voted comments. Someone is spoiling valuable comments and it happens too often. Sad.

> I do not understand why should HN be afraid to give reasonable reason for down voting

It's not about being afraid, it's about not lowering the signal/noise ratio any further.

You should post a comment when, and only when, you have something substantive to say. There are many more downvotes than there are substantive things to say, which is why subthreads about downvotes invariably degenerate.

> it's about not lowering the signal/noise ratio any further.

idea: you can track an explanation why something was downvoted without showing it as a comment. It can be shown only if a user clicks on some type of "why this was downvoted" link.

This would not lower the signal/noise ratio on the main thread. People can continue having a discussion that degenerates to low signal/ratio about the downvoting into this other link. If anything positive comes out of it, and enough people upvote it out of the downvoted status, then you can start commenting on it again.

This would also be aligned with the policy of posting a comment when, and only when, you have something substantive to say.

Because unless the comment was restored back to a positive score, you wouldn't be able to post a comment on the main thread (as a reply to that comment; not the whole thread). The policy would be enforced, and you dang wouldn't have to be telling people to not comment about downvoting.

A long discussion of why something was downvoted (like this one) degrades the quality of the thread, and it's usually obvious why the comment might have been downvoted, especially after reading the guidelines.[1]

W/ respect to your specific "sad" example, the topmost comment on that thread gives the relevant information and has not been downvoted (as I'm reading it). The downvoted comment below it doesn't seem to add anything useful (but I didn't downvote it).

Plus, if you think something's been downvoted inappropriately, vote it up. People make mistakes sometimes.

[1] https://news.ycombinator.com/newsguidelines.html

Some of this stuff is pretty abstruse. Can someone rephrase the winners' research programs in the form of Harry Potter fanfic?

Haha, "But Khot’s Unique Games Conjecture has already amply proven its value, even should it ultimately be disproven. It has cast a bright light on previously dim areas of computational complexity and provided critical insight — and, yes, Khot has also used it to prove major results, ones that stand regardless of its truth."

weak people conjecture and then get results "if my conjecture stands". This guy is a black belt, he makes a conjecture, gets a field medal for it, and then removes it from his proof ("just joking, it works wether it's true or not").

Still gets the medal for the now useless conjecture and not for the ultimate proof.

My world got a little smaller. Khot's advisor -- Sanjeev Arora -- was the guy who cemented my decision of where to go to school.

Nice humblebrag, bro

"It is better to keep your mouth closed and let people think you are a fool than to open it and remove all doubt."

Strange that you feel the need to comment on a topic that you appear to know absolutely nothing about.

Whereas a personal attack is a demonstration of knowledge and wisdom.

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