16 ms·

2018 Fields Medal and Nevanlinna Prize Winners

111 points by heinrichf 8y ago

heinrichf 8y ago
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.
beambot 8y ago
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.)
- drharby 8y ago
  Echo your concerns. Systemic ageism discriminates against diverse life paths
- sykhic 8y ago
  There’s a commonly held belief (myth?) that mathematics is a young person's pursuit in the sense of great discoveries. If you look at Erdös you see most of his great contributions occurring when he was younger and he was prolific throughout his life. I think the downvotes come from your sentence about significant developments going under reported. I don’t think this happens at all. If someone discovers something great or profound in math no one cares about the age of the discoverer. Wiles was given a special prize because he was past the age of 40 when he proved Fermat's Last Theorem.
  - sanxiyn 8y ago
    Another example is Yitang Zhang and prime gap. He was over 50, so no Fields Medal, but he won many other prizes.
  - Nokinside 8y ago
    It's possible that things are changing over time. When the mathematical knowledge increases, does the general character of the mathematical problems stay the same in the terms of required work and time? It's possible the problem set that young people can solve before they turn 40 will decrease after some time.
- hackernewsacct 8y ago
  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 8y ago
    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 8y ago
      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.
- Kalium 8y ago
  You're right. It does seem ageist, when seen in isolation from the outside. It seems to suggest that the field of mathematics only and solely cares about the work of young mathematicians. Yet, is it perhaps possible that this position may signify a person possessed of a wonderful opportunity to become more educated? The Fields Medal is not intended to be the capstone recognition of a mathematcian's career any more than the Clark Medal is in economics. It's intended to award outstanding achievement for a younger contributor in a field that infamously tends to worship the more senior. The IMU awards other medals as well, including one for lifetime achievement. In short, you're completely right to be bummed out! But perhaps you could take this glorious opportunity to learn more.
  - beambot 8y ago
    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.
    - Kalium 8y ago
      You're right! Perhaps you might start here: https://en.wikipedia.org/wiki/International_Mathematical_Union#Prizes 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 8y ago
        [deleted]
      - dang 8y ago
        Please don't be personally rude on HN. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
- nefreat 8y ago
  Abel Prize is pretty popular and has esteemed winners. The only requirement is that the person being nominated be alive. https://en.wikipedia.org/wiki/Abel_Prize https://en.wikipedia.org/wiki/Abel_Prize
- thraway180306 8y ago
  It is in fact age limited precisely to combat ageism of the early 20th century. Otherwise only elders would get it (would they outlive the queue of their masters), when it's irrelevant to their career development (but beneficial to the prize's prestige). It was intentionally set up with this reasoning - not to be about lifetime contribution (which really compounds linearly in mathematics, there is no age dropoff "in the data" if you will) but making career easier for a very few young upstarts. Otherwise it would be old people game.
- paulpauper 8y ago
  if the accomplishment is worthy it will get recognition regardless of age
- zhonwang 8y ago
  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.
- zhonwang 8y ago
  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.
LeanderK 8y ago
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 8y ago
  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.
angrygoat 8y ago
Australian media coverage of Akshay Venkatesh's Fields medal: http://www.abc.net.au/news/2018-08-02/fields-medal-aussie-genius-akshay-venkatesh-wins-prize/10062218 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.
- deleted 8y ago
  [deleted]
- qmalzp 8y ago
  Him, Tao, Emerton, Kisin, Coates, Calegari Bros... all Australian. Must be something in the water.
  - deleted 8y ago
    [deleted]
mlthrowaway1953 8y ago
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
- throwaway080383 8y ago
  If you're wondering why you're being down voted, it's because very few people believe mathematical discoveries and proofs are going to be automated any time soon. FCT was exceptional in that the theorists were able to reduce the theoretical proof to a brute force check that no human wanted to do. To be honest, making these claims, especially with such certainty, comes off as rather crank-y.
- pathsjs 8y ago
  As a mathematician turned to deep learning, I would say you overstimate the promises of deep learning a bit :-)
- cycrutchfield 8y ago
  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.
- thalesmello 8y ago
  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.
cs702 8y ago
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
- aw1621107 8y ago
  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 8y ago
    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 8y ago
      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?
norepicycle 8y ago
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/perfectoid.pdf https://www.math.columbia.edu/~harris/otherarticles_files/pe...
- posterboy 8y ago
  https://www.math.columbia.edu/~harris/otherarticles_files/perfectoid.pdf https://www.math.columbia.edu/~harris/otherarticles_files/pe... there was an extra > appended
ddoran 8y ago
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-pioneering-mathematical-legacy https://www.newyorker.com/tech/elements/maryam-mirzakhanis-p... [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
Carioca 8y ago
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/iraniano-tem-medalha-fields-roubada-apos-recebe-la-no-rio.ghtml https://g1.globo.com/rj/rio-de-janeiro/noticia/2018/08/01/ir...
- adenadel 8y ago
  Here's an article in English https://www.scmp.com/news/world/americas/article/2157887/moments-after-winning-prestigious-fields-math-award-rio-kurdish https://www.scmp.com/news/world/americas/article/2157887/mom...
deleted 8y ago
[deleted]

111 points by heinrichf 8y ago

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.

beambot 8y ago

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.)

drharby 8y ago
Echo your concerns. Systemic ageism discriminates against diverse life paths
sykhic 8y ago
There’s a commonly held belief (myth?) that mathematics is a young person's pursuit in the sense of great discoveries. If you look at Erdös you see most of his great contributions occurring when he was younger and he was prolific throughout his life. I think the downvotes come from your sentence about significant developments going under reported. I don’t think this happens at all. If someone discovers something great or profound in math no one cares about the age of the discoverer. Wiles was given a special prize because he was past the age of 40 when he proved Fermat's Last Theorem.
- sanxiyn 8y ago
  Another example is Yitang Zhang and prime gap. He was over 50, so no Fields Medal, but he won many other prizes.
- Nokinside 8y ago
  It's possible that things are changing over time. When the mathematical knowledge increases, does the general character of the mathematical problems stay the same in the terms of required work and time? It's possible the problem set that young people can solve before they turn 40 will decrease after some time.
hackernewsacct 8y ago
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 8y ago
  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 8y ago
    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.
Kalium 8y ago
You're right. It does seem ageist, when seen in isolation from the outside. It seems to suggest that the field of mathematics only and solely cares about the work of young mathematicians. Yet, is it perhaps possible that this position may signify a person possessed of a wonderful opportunity to become more educated? The Fields Medal is not intended to be the capstone recognition of a mathematcian's career any more than the Clark Medal is in economics. It's intended to award outstanding achievement for a younger contributor in a field that infamously tends to worship the more senior. The IMU awards other medals as well, including one for lifetime achievement. In short, you're completely right to be bummed out! But perhaps you could take this glorious opportunity to learn more.
- beambot 8y ago
  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.
  - Kalium 8y ago
    You're right! Perhaps you might start here: https://en.wikipedia.org/wiki/International_Mathematical_Union#Prizes 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 8y ago
      [deleted]
    - dang 8y ago
      Please don't be personally rude on HN. https://news.ycombinator.com/newsguidelines.html https://news.ycombinator.com/newsguidelines.html
nefreat 8y ago
Abel Prize is pretty popular and has esteemed winners. The only requirement is that the person being nominated be alive. https://en.wikipedia.org/wiki/Abel_Prize https://en.wikipedia.org/wiki/Abel_Prize
thraway180306 8y ago
It is in fact age limited precisely to combat ageism of the early 20th century. Otherwise only elders would get it (would they outlive the queue of their masters), when it's irrelevant to their career development (but beneficial to the prize's prestige). It was intentionally set up with this reasoning - not to be about lifetime contribution (which really compounds linearly in mathematics, there is no age dropoff "in the data" if you will) but making career easier for a very few young upstarts. Otherwise it would be old people game.
paulpauper 8y ago
if the accomplishment is worthy it will get recognition regardless of age
zhonwang 8y ago
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.
zhonwang 8y ago
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.

LeanderK 8y ago

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 8y ago
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.

angrygoat 8y ago

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

deleted 8y ago
[deleted]
qmalzp 8y ago
Him, Tao, Emerton, Kisin, Coates, Calegari Bros... all Australian. Must be something in the water.
- deleted 8y ago
  [deleted]

mlthrowaway1953 8y ago

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

throwaway080383 8y ago
If you're wondering why you're being down voted, it's because very few people believe mathematical discoveries and proofs are going to be automated any time soon. FCT was exceptional in that the theorists were able to reduce the theoretical proof to a brute force check that no human wanted to do. To be honest, making these claims, especially with such certainty, comes off as rather crank-y.
pathsjs 8y ago
As a mathematician turned to deep learning, I would say you overstimate the promises of deep learning a bit :-)
cycrutchfield 8y ago
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.
thalesmello 8y ago
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.

cs702 8y ago

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

aw1621107 8y ago
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 8y ago
  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 8y ago
    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?

norepicycle 8y ago

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/perfectoid.pdf https://www.math.columbia.edu/~harris/otherarticles_files/pe...

posterboy 8y ago
https://www.math.columbia.edu/~harris/otherarticles_files/perfectoid.pdf https://www.math.columbia.edu/~harris/otherarticles_files/pe... there was an extra > appended

ddoran 8y ago

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-pioneering-mathematical-legacy https://www.newyorker.com/tech/elements/maryam-mirzakhanis-p... [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

Carioca 8y ago

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

adenadel 8y ago
Here's an article in English https://www.scmp.com/news/world/americas/article/2157887/moments-after-winning-prestigious-fields-math-award-rio-kurdish https://www.scmp.com/news/world/americas/article/2157887/mom...

deleted 8y ago

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