
2018 Fields Medal and Nevanlinna Prize Winners - heinrichf
https://www.quantamagazine.org/tag/2018-fields-medal-and-nevanlinna-prize-winners/
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cs702
For those who don't know, Constantinos Daskalakis, one of the winners
profiled, proved that finding a Nash equilibrium (for example, in an economy)
is a PPAD-complete problem: if anyone discovers an efficient algorithm for
finding Nash equilibria, such an algorithm could be used for efficiently
solving all other problems in the PPAD complexity class. PPAD problems are
widely considered to be intractable. No algorithm is known for solving them
with running time bounded by a polynomial function of input/problem size. The
implications in many fields, starting with economics, are clearly significant.
Daskalakis's prize is well-deserved.

There is a fantastic introductory MIT video lecture on this work by Daskalakis
himself available on YouTube.[a] His enthusiasm and passion in that video
lecture are contagious -- matched only by his ability to explain his work in
an intuitive manner. Highly recommended for those HNers who have computer-
science or economics backgrounds and are interested in computational
complexity but are not yet familiar with Daskalakis's work.

[a]
[https://www.youtube.com/watch?v=TUbfCY_8Dzs](https://www.youtube.com/watch?v=TUbfCY_8Dzs)

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aw1621107
How do PPAD-complete problems relate to P=NP/NP-complete problems/etc., if
they do at all? Your description of PPAD-complete problems reminds me a lot of
descriptions I've read of NP-related problems, but this is the first time I've
heard of the term "PPAD".

~~~
cs702
Very -- very! -- informally: in PPAD-complete problems, a solution is known to
exist (e.g., there is always a Nash equilibrium), but no one knows of an
efficient algorithm for finding the solution. In other complexity classes
widely believed to be intractable, such as NP-complete, the problems are
decision problems that ask a yes/no question, and no one knows of an efficient
algorithm for answering the question. By "efficient algorithm," I again mean
an algorithm whose running time is bounded by a polynomial function of input
or problem size.

~~~
mygo
so I guess, one way to put it, is to look at the Traveling Salesman Problem?

The decision problem asks “given a set of cities is there a tour shorter than
length n?”. This is NP-Complete.

However the pop culture version of the problem is “given a set of cities, what
is a tour of the shortest possible length?”. This would be the PPAD-complete
version of the problem, since that solution does exist, it’s just unknown and
not known to be tractable within polynomial time?

Can the Nash Equilibrium problem have a decision version whose answer is
either true or false?

~~~
sometimesijust
TSP is NP-hard for optimisation version and NP-complete for decision version.
Consider how you would test that a minimal solution is minimal vs testing
whether a given solution has less than a given cost. PPAD is less complete
than these two classes.

The decision problem for Nash Equilibria might be, does a second equilibrium
exist?

~~~
mygo
Aah gotcha. So you’re saying it’s easier to verify the solution to a Nash
equilibrium problem than it is to verify the solution to the TSP optimization
problem?

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beambot
It bums me out that the fields medal is largely considered the top prize in
mathematics, yet it has age restrictions. To people outside the field, this
means that significant developments may go underreported.

Edit: Let me address the down votes / polarization on this comment: Ageism in
the most esteemed prize of a particular field seems obviously wrong to me. Is
there a better alternative available? (That said: kudos to the winners! Truly
great achievements all around.)

~~~
hackernewsacct
I agree. If you look at what a mathematician does they sit around and think.
You don't have that sort of luxury if you are from a poor family and have to
worry about basic survival. In many cases (not all) the people that complete
major accomplishment X at young age Y is from an upper middle class to upper
class family with lots of life advantages. Not everyone have these advantages
early in life and may eventually get to those positions due to their talents,
but it may take them longer given their life situations. There are poor but
extremely talented underrepresented people out there the world may never know.
We tend to celebrate talent from the elite class, not the poor. The elite are
given resources they need to succeed, the poor are often overlooked. This can
cause a major talent drain from truly exceptional but unknown folks in the
world.

~~~
simion314
Is this a problem only in countries where you have to pay a lot to study? I
did not had to pay for my higher education and the people that had a high
talent and potentials achieved good results, there was no need to work to make
money for studying and if you are good you got positions at University or get
jobs at high paying companies.

~~~
hackernewsacct
In countries like the US it starts at birth. Families in rich areas will send
their children to elite, selective high schools that cost upward $30,000+.
Some of these schools have strong math and science curriculum and are
considered direct feeders to elite universities, such as the ivies. These
poorer kids could be high IQ'd just like the richer ones, but with less access
to resources, may be very behind their richer peers. These richer kids will
get into the elite schools, while the poor kids may go to lower end ones or
not go to colleges at all. Rich parents can hire their children SAT tutors,
ensure their children go to good STEM schools, have various college prep
resources for their children, while the poor parents don't know anything about
college, sent their children to lesser high schools, and have children that
may be just as bright, but essentially ones that have no chance to be admitted
to the places they otherwise might have gotten into. College admissions at
elite colleges favor children from the elite that had the resources to prepare
their children for such pedigree. There are exceptions to the rule, but many
poor families face deep struggle. This is regardless of however high IQ'd
their children may be.

~~~
throwaway080383
I agree with all of this, but don't see what it has to do with age. The best
50-year-old mathematicians also heavily tend to come from privileged
backgrounds. Privileged upbringing is simply one required component of what it
takes to be among the best mathematicians of your generation.

~~~
sulam
[https://en.wikipedia.org/wiki/Srinivasa_Ramanujan](https://en.wikipedia.org/wiki/Srinivasa_Ramanujan)

~~~
umanwizard
The exception that proves the rule.

~~~
sulam

      https://en.wikipedia.org/wiki/Albert_Einstein
      https://en.wikipedia.org/wiki/René_Descartes
      https://en.wikipedia.org/wiki/John_Forbes_Nash_Jr.
      https://en.wikipedia.org/wiki/Alan_Turing
      https://en.wikipedia.org/wiki/David_Hilbert
    

I think this rule is just wrong. Some mathematicians come from privilege, some
do not. Even for the ones who do, it's rare that they come from _great_
privilege for the time. They are the children of mayors, not kings --
professors and engineers, not the financial aristocracy.

~~~
throwaway080383
Now it seems you're moving the goalposts on what counts as privilege. Do you
have any quantitatively backed reason to believe Fields medallists are more
likely to come from the financial aristocracy than say Abel prize winners?

~~~
sulam
I don’t have access to a biography of all the Field’s medalists. I am simply
pointing out that there is a wide distribution of financial privilege in a
list of famous mathematicians that I did not choose. I would argue this is
unexceptional, but I point it out because I have trouble with the hypothesis
that one must come from privilege to get anywhere in math. If anything I
should be asking for the quantitative proof of the hypothesis.

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ddoran
As all winners are once again male, it brings Maryam Mirzakhani's achievements
[1, 2], and tragic passing to mind once again [3].

I'm not suggesting that these winners are not deserving, nor suggesting there
is bias. I am looking forward to the day a second woman wins the prize.

[1] [https://www.newyorker.com/tech/elements/maryam-
mirzakhanis-p...](https://www.newyorker.com/tech/elements/maryam-mirzakhanis-
pioneering-mathematical-legacy) [2]
[https://news.ycombinator.com/item?id=14793217](https://news.ycombinator.com/item?id=14793217)
[3]
[https://news.ycombinator.com/item?id=14776357](https://news.ycombinator.com/item?id=14776357)

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heinrichf
Funny bit in Venkatesh's interview:

> Accustomed to meeting the highest of standards, he saw his dissertation as
> mediocre. Quietly, Venkatesh started eyeing the exit ramps, even taking a
> job at his uncle’s machine learning startup one summer to make sure he had a
> fallback option.

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Carioca
As a side note, Caucher Birkar's medal was stolen less than half an hour after
the award[1] (link in Portuguese)

1: [https://g1.globo.com/rj/rio-de-
janeiro/noticia/2018/08/01/ir...](https://g1.globo.com/rj/rio-de-
janeiro/noticia/2018/08/01/iraniano-tem-medalha-fields-roubada-apos-recebe-la-
no-rio.ghtml)

~~~
adenadel
Here's an article in English

[https://www.scmp.com/news/world/americas/article/2157887/mom...](https://www.scmp.com/news/world/americas/article/2157887/moments-
after-winning-prestigious-fields-math-award-rio-kurdish)

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angrygoat
Australian media coverage of Akshay Venkatesh's Fields medal:
[http://www.abc.net.au/news/2018-08-02/fields-medal-aussie-
ge...](http://www.abc.net.au/news/2018-08-02/fields-medal-aussie-genius-
akshay-venkatesh-wins-prize/10062218)

He graduated from the University of Western Australia at 16 with honours in
Pure Mathematics.

~~~
qmalzp
Him, Tao, Emerton, Kisin, Coates, Calegari Bros... all Australian. Must be
something in the water.

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LeanderK
I find it always a bit sad that I have to accept it that whatever I'll do, I
can't reach the genious of their work.

Especially Scholze seems like a very nice guy. I hope he continous his very
productive (and hopefully fun!) journy through mathmatics.

~~~
cosmic_ape
But keep in mind this, as another comment here mentions:

> Accustomed to meeting the highest of standards, he saw his dissertation as
> mediocre. Quietly, Venkatesh started eyeing the exit ramps, even taking a
> job at his uncle’s machine learning startup one summer to make sure he had a
> fallback option.

------
norepicycle
Scholze's win has been predicted for quite a while now, as it turns out. He's
a number theorist of stunning originality primarily known for developing a new
kind of geometry, that of _perfectoid spaces_ , for arithmetic purposes.

Here's an interview with him that will be accessible to nonspecialists:

[https://www.youtube.com/watch?v=J0QdTYZIfIM](https://www.youtube.com/watch?v=J0QdTYZIfIM)

At a higher level, here's an appraisal of his work by a professional in a
closely related area:

    
    
      It's not often that contemporary mathematics provides such a clear-cut example
      of concept formation as the one I am about to present:  Peter Scholze's
      introduction of the new notion of perfectoid space. The 23-year old Scholze
      first unveiled the concept in the spring of 2011 in a conference talk at the
      Institute for Advanced Study in Princeton.  I know because I was there.  This
      was soon followed by an extended visit to the Institut des Hautes Études
      Scientifiques (IHES) at Bûres- sur-Yvette, outside Paris — I was there too.
      Scholze's six-lecture series culminated with a spectacular application of the
      new method, already announced in Princeton, to an outstanding problem left over
      from the days when the IHES was the destination of pilgrims come to hear
      Alexander Grothendieck, and later Pierre Deligne, report on the creation of the
      new geometries of their day.  Scholze's exceptionally clear lecture notes were
      read in mathematics departments around the world within days of his lecture —
      not passed hand-to-hand as in Grothendieck's day — and the videos of his talks
      were immediately made available on the IHES website.  Meanwhile, more killer
      apps followed in rapid succession in a series of papers written by Scholze,
      sometimes in collaboration with other mathematicians under 30 (or just slightly
      older), often alone.  By the time he reached the age of 24, high-level
      conference invitations to talk about the uses of perfectoid spaces (I was at a
      number of those too) had enshrined Scholze as one of the youngest elder
      statesmen ever of arithmetic geometry, the branch of mathematics where number
      theory meets algebraic geometry.)  Two years later, a week-long meeting in 2014
      on Perfectoid Spaces and Their Applications at the Mathematical Sciences
      Research Institute in Berkeley broke all attendance records for "Hot Topics"
      conferences.
    

\- Michael Harris, "The Perfectoid Concept: Test Case for an Absent Theory"

[https://www.math.columbia.edu/~harris/otherarticles_files/pe...](https://www.math.columbia.edu/~harris/otherarticles_files/perfectoid.pdf)

~~~
posterboy
[https://www.math.columbia.edu/~harris/otherarticles_files/pe...](https://www.math.columbia.edu/~harris/otherarticles_files/perfectoid.pdf)

there was an extra > appended

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mlthrowaway1953
Is the Fields Medal going to still be relevant in 10 years, when most of the
the major mathematical discoveries are made by deep learning and deep
reinforcement learning systems? Already systems are learning to reason about
concepts [1] and of course there is classical work on proof checkers [2]. It's
very likely that the 2028 Fields medal will be awarded to a programmer, not
some mathematical super-genius (assuming that the committee is fair, and not
biased against machines).

[1] [https://arxiv.org/abs/1806.01261](https://arxiv.org/abs/1806.01261) [2]
[https://en.wikipedia.org/wiki/Four_color_theorem](https://en.wikipedia.org/wiki/Four_color_theorem)

~~~
cycrutchfield
It's shit like this that tells me we deserve another AI Winter. Just at the
very least to drive out the dilettantes and charlatans.

