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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

#41
post #13
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.

Please don't be personally rude on HN.

https://news.ycombinator.com/newsguidelines.html

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#43
post #38

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...

Here's an article in English

https://www.scmp.com/news/world/americas/article/2157887/mom...

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#44
post #35
post #31

Earlier quoted context omitted.

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 an…

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?

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#45
post #35

Earlier quoted context omitted.

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 an…

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?

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?

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#46
post #41
post #13

Earlier quoted context omitted.

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.

Please don't be personally rude on HN. https://news.ycombinator.com/newsguidelines.html

Sorry.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#47

Earlier quoted context omitted.

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.

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 riche…

Arguing for fixing education seems a better goal then fixing the limitation for some prizes

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#48
post #39

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.

[deleted]

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#49
post #29

Earlier quoted context omitted.

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.

https://en.wikipedia.org/wiki/Srinivasa_Ramanujan

The exception that proves the rule.

Re: 2018 Fields Medal and Nevanlinna Prize Winners

#50

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…

Mathematics require the exact type of abstract thinking machines suck at. Machines can execute things fast, learn things fast (provided we have well stablished rules), but than can't (at our current moment in time) come up with useful abstractions to help solve new problems.

So I think it's going to stay relevant.

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