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2018 Fields Medal and Nevanlinna Prize Winners

quantamagazine.org

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Re: 2018 Fields Medal and Nevanlinna Prize Winners

#31

Post by cs702 »

aw1621107 wrote: post #30
cs702 wrote: post #20

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…

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".

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.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#32

Post by [deleted] »

Kalium wrote: post #13
beambot wrote: post #11

Earlier quoted context omitted.

Hence my ask in the edit: which specific prize / award / recognition can I follow as an amateur math afficionado that doesn't suffer from age bias? You didn't mention one, beyond saying that it exists or that it's given in special circumstances... Which is the challenge re:Fields being the most prestigious.

You're right! Perhaps you might start here: https://en.wikipedia.org/wiki/International_Mathematical_Uni... I was attempting to encourage you to engage in the wonders of self-education through research, rather than spoon-feed you particular answers. Please accept my apologies for mistaking your desires.

[deleted]

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#33

Post by cycrutchfield »

mlthrowaway1953 wrote: post #19

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…

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.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#34

Post by robotresearcher »

hackernewsacct wrote: post #6
beambot wrote: post #3

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: kudo…

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 g…

“We tend to celebrate talent from the elite class, not the poor.”

We tend to celebrate achievement, not talent.

This may correlate well with elites since they have more opportunities.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#35

Post by mygo »

cs702 wrote: post #31
aw1621107 wrote: post #30

Earlier quoted context omitted.

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".

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 "…

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?

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#36

Post by cosmic_ape »

LeanderK wrote: post #9

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.

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.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#37

Post by zhonwang »

beambot wrote: post #3

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: kudo…

This seems better to me than the Nobel Prize where it may take Decades for your work to be recognized and is kind of a nice retirement gift for old academics. The Fields though can forever change your career trajectory when you win it.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#39

Post by qmalzp »

angrygoat wrote: post #14

Australian media coverage of Akshay Venkatesh's Fields medal: http://www.abc.net.au/news/2018-08-02/fields-medal-aussie-ge... He graduated from the University of Western Australia at 16 with honours in Pure Mathematics.

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

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#40

Post by zhonwang »

beambot wrote: post #3

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: kudo…

This is a strange attitude to have. The prize was specifically designed to highlight the work of promising young Mathematicians so why is this an issue? It would be like complaining that the Little League World Series is ageist because it doesn't allow older competitors. Besides there is also the Abel Prize which is equally if not more prestigious, is open to any living Mathematician and has a far more substantial monetary prize attached.
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