7 ms·

Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize

309 points by digital55 8y ago

otoburb 8y ago
"Mathematics research had another feature that appealed to her at the time: It is something you can work on in solitude, if you wish. In her early life, she said in 1997, “I regarded anything to do with people as being sort of a horrible profession.”" This sentence struck me as slightly odd if only because Erdõs was renowned for his social approach to mathematics[1], and my layperson's understanding of mathematics departments being somewhat collaborative within their sub-fields. I know there are some notable examples of other solo breakthrough endeavours, such as Shinichi Mochizuki[2] or Yitang Zhang[3], and but those examples seemed to be exceptions to the rule. Perhaps I'm channeling too much Terence Tao[4], or maybe the lone wolf researcher only applies to literal geniuses who work exclusively in academia. Is mathematics research still a primarily solitary activity? [1] https://en.wikipedia.org/wiki/Paul_Erd%C5%91s https://en.wikipedia.org/wiki/Paul_Erd%C5%91s [2] https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/ https://www.quantamagazine.org/titans-of-mathematics-clash-o... [3] https://www.cnet.com/news/yitang-zhang-a-prime-number-proof-and-a-world-of-persistence/ https://www.cnet.com/news/yitang-zhang-a-prime-number-proof-... [4] https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ https://terrytao.wordpress.com/career-advice/does-one-have-t...
- natestemen 8y ago
  mathematics research is typically very social. if you look at the mathematics research community as a whole you will find a very small percentage working completely in isolation. also i would add Grigori Perelman to your list of mathematicians working primarily by themselves.
- heinrichf 8y ago
  Later, she also says: "All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more."
- kevinventullo 8y ago
  In my experience with pure math, it was mostly solitary. There is some collaboration, but it's often between people at different universities, so that collaboration may mean emailing back and forth every few days and visiting a few times a year (exceptions being grad students/postdocs working with their advisor/sponsor). Other solo works include Wiles's proof of Fermat (which admittedly later had to be fixed with the help of his student Richard Taylor), Perelman's proof of Poincare, and much of Scholze's foundational work on perfectoid spaces. Besides Poincare, three of the other millennium problems were posed by a single author (Riemann, Hodge, and Cook). If you look at the recent arxiv listings for differential geometry say, there are many solo authored papers: https://arxiv.org/list/math.DG/recent https://arxiv.org/list/math.DG/recent
  - throwawaymath 8y ago
    > In my experience with pure math, it was mostly solitary. I disagree, but it might be because I interpret the spirit of the question differently. I would not call an activity involving some collaboration between people at different universities (including email), "solitary." It may not be very socially engaging, but it's categorically not a solitary endeavor. People are working together. To speak to your examples directly: as you're aware, they're extreme outliers. They're not just extreme because of the level of achievement; they're also nearly heroic in scope for a single person to work on without collaboration. It just doesn't happen much at that level of sophistication and complexity. More to the point, if you peel back those examples you see quite a lot of non-solitary work. For example, Perelman refused the Fields medal with a declaration that the substantial prior work was just as important for the solution as his own work. He's a pretty big champion of the important of the community aspect of mathematics. Likewise Wiles actually needed collaboration to fix a critical flaw in his original proof of Fermat's Last Theorem. And that really captures the heart of what I'm getting at, which is what mathematics is "about" by practice and intention. Most mathematicians engage with the research community by attending conferences and collaborating with their peers, even if that collaboration is largely asynchronous. They keep their fingers on the pulse of the academic landscape by talking with other people. In the cases where someone produces noteworthy research on their own, it still exists in a social framework. A mathematical proof is intrinsically a social endeavor. To prove a theorem is to convince someone else that it must follow from a series of axioms, definitions and other theorems. Sometimes you can do the work on your own, but it won't matter if it's disconnected from the research community, and the easiest way to stay connected to the research community is through collaboration. If no one else in the world agrees with your proof, your proof is meaningless (as an example, see the controversy around Mochizuki's Inter-universal Teichmüller theory). This is what peer review is for. Moreover if you construct a new mathematical theory, it's only meaningful insofar as it builds upon existing work developed by other researchers. The choice of axioms and definitions must be interesting and significant within the context of an existing body of work. This is one of the reasons you so rarely see nontrivial research produced by isolation. It's (approximately) a myth, and instances of it happening receive outsized attention precisely because they're extraordinarily rare and unconventional. In reality, it's usually not a good sign for a researcher to work on something in solitude. In most cases it coincides with the stagnation of a mathematician's career, not the glorious unveiling of a solution to a decades-old open problem or a grand new theory. I can see why the idea that mathematics is a solitary endeavor (or suited to solitary work) is an attractive one, because the most visible parts of it (writing papers, solving problems) can be done alone. But it's usually very inadvisable to go it alone in learning or practicing mathematics.
- hyperbovine 8y ago
  Erdos is renowned precisely because he was so out of the ordinary.
  - throwawaymath 8y ago
    Erdos wasn't out of the ordinary because he published with (read: collaborated with) so many coauthors. He was out of the ordinary because he published so many papers, period. His sociability was more of a difference of degree within mathematics, not category.
    - hyperbovine 8y ago
      I beg to differ. Anecdotes of Erdos' itinerant lifestyle are legendary in the field: > Dr. Erdos traveled from meeting to meeting, carrying a half-empty suitcase and staying with mathematicians wherever he went. His colleagues took care of him, lending him money, feeding him, buying him clothes and even doing his taxes. In return, he showered them with ideas and challenges -- with problems to be solved and brilliant ways of attacking them. (https://www.nytimes.com/1996/09/24/us/paul-erdos-83-a-wayfarer-in-math-s-vanguard-is-dead.html https://www.nytimes.com/1996/09/24/us/paul-erdos-83-a-wayfar...) Even in the rarefied club of oddball math personalities, he stood out.
      - throwawaymath 8y ago
        Ah, by sociability I just meant the number of collaborators he worked with. What I'm getting at is that he's abnormal because he published so much, not because he published with so many coauthors. Many mathematicians would have similar looking publication records if they maintained the same level of collaboration and simply published...more. But he was an oddball too, for sure.
- hyperbovine 8y ago
  Turns out she is the daughter-in-law of the Ornetein-Uhlenbeck Uhlenbeck. I bet their family reunions were interesting.
  - lordnacho 8y ago
    Aha, I quickly scanned her Wikipedia because I was wondering if it was either her or a relative that had done Ornstein-Uhlenbeck, missed that part. I thought OU was invented as a physics thing in the 1930s though. Indeed a very interesting mathematical family. It will be hard for future members not to revert to the mean :)
- graycat 8y ago
  It is interesting to read what she saw in math, why she liked it. For me, I just thought it would be useful, especially for physics which I thought was even more useful! No one ever explained to me how a career in academic math research would work: I never suspected that just digging into questions that were fun and curious and maybe someday somewhat useful, making discoveries, and writing papers could be a career that could support a family. In particular, I still don't understand why the US has so much respect for research universities: My guess was that college was for teaching the students. But in a research university, nearly all the effort by the professors is their research, and the teaching is a sideline. E.g., might have a really good researcher in far out topics in analysis teaching junior level linear algebra. So, the money to the university, for people directly paying full tuition often a LOT of money, is only a little for that teaching but much more for the research. An analogy for restaurants would be that each hamburger had to come from some three star Michelin place and cost $200. E.g., when I was a B-school prof, I was really discouraged to see that what the B-school was teaching had next to nothing to do with business. Instead, the school was interested in research, e.g., the question P vs NP. If medicine were taught that way, then no one would go to a hospital no matter how badly they hurt. B-school tried to be academic research, not professional training. Besides, for me as a college student, I had to conclude that after junior year level material, the profs really needed to understand what they were teaching much better than they did. For that, they just needed to do a much better job learning and presenting what was already in the library and without more research. E.g., I never had a math or physics prof who had a good grasp of the theory and applications of Stokes theorem, classic potential theory, multipole coordinates, or both the theory AND applications of Fourier theory. None of my undergrad physics profs knew either general relativity or quantum mechanics at all well. I wanted to learn that stuff, not for research but for applications. Math research solitary? It always has been for me. For learning the standard stuff, sure, can have people to talk to. But if they are in the same course and it is competitive, then maybe they don't want to talk? The reason my math research was solitary is mostly just because the new work I was doing was so focused that no one else around knew much about it or had much interest in it. For a lot of math research, being focused is close to necessary and, then, the solitary aspect gets to be close to automatic. Moreover it appears that there can be an effect from outside: Some people are more socially skilled, polished, talented, interested, motivated, etc. than others. In some fields, such social skills are important for success. But in math, if you can learn it, mostly on your own, then you can teach it -- good social skills can help but can get by with not much. This is even more the case for math research: Pick a problem, do some research, get some results, type in a paper, send it to an appropriate journal, maybe all with essentially no contact from anyone else. So, since in math can get by with less than the best social skills, people without great social skills can find math, be successful, and stay, and, then, the result is that comparatively math is not a very social field. But, a lot of people can learn to be social: Gee, a lot of grade school girls (sorry to bring gender into this) have just astounding social skills: E.g., it seems clear enough that long ago Hollywood discovered that among child actors the girls were much better -- they paid attention what was going on socially, reacted to others, had lots of facial expressions on tap, were good at glancing, averting, head tossing, pose striking, cases of body language, expressiveness in their voices, etc. Well, what a grade school girl commonly knows others can pick up, too! Okay performance in the lessons is not seriously difficult. Reading some of what Uhlenbeck said about herself, she was doing well in the E. Fromm recommended social activity "Giving knowledge of oneself" and that can help a person be social because they are letting others know who they are. Or little so interests people as other people; if some other person communicates no better than a stone wall, then there's not much for others to be interested in; Fromm's giving knowledge can help with that. For a nutshell description, my view of mathematicians is that they are less manipulative than most other people. Well, in some activities, can seem to get progress by manipulation, but in math, can't prove a theorem by a fake, manipulative proof!
- nikofeyn 8y ago
  i suspect erdos' socialization of mathematics had as much to do with mathematics as it did about having a place to eat and sleep. his vagabond lifestyle sort of necessitated he frequently socialize his mathematics so as to not wear out his welcome in any one particular place.
- msla 8y ago
  > Erdõs Where is his name spelled like this?
  - klyrs 8y ago
    Umm... everywhere? It often gets anglicized to "Erdos" but the correct spelling is Erdős.
    - bhk 8y ago
      ő ≠ õ
      - klyrs 8y ago
        oh neat, those look different on my laptop but not my phone
deleted 8y ago
[deleted]
kaitai 8y ago
Uhlenbeck is delightful, and one of her big ideas discussed in this article -- bubbling -- truly has changed both her field and algebraic geometry. It's a cool idea. In a previous thread here (How I learned to love algebraic geometry, https://news.ycombinator.com/item?id=19397957 https://news.ycombinator.com/item?id=19397957) there was some discussion of singularities. Algebraic geometers like polynomials, while symplectic geometers like Riemann surfaces. These coincide at times but Riemann surfaces include lots of non-polynomial examples. Anyhow, as an algebraic geometer, the place I learned about Uhlenbeck's work was in compactification of moduli of curves. Basically, say I want to look at all the polynomial curves that can live in a certain 'environment'. (One 'application' is string theory -- what particle interactions can occur given a certain set of energy constraints? The particle interactions are curves traced out over time by particles/Riemann surfaces traced out over time by the little loops that represent closed strings in string theory; the energy constraints constrain the shapes the particle interaction can take.) If you want to look at limits of families of these interactions, you're looking at some odd behavior. An example is the equation xy = t^2 -- this gives you nice hyperbolas for values of t not equal to zero, but as t -> 0, you get something singular, two crossed lines. Or x^2 - y^2 - z^2 = t^2: you have a nice smooth hyperboloid when t neq 0, and a double cone when t=0. However, these examples are just showing you the idea of how singularities appear in families of smooth polynomials. Uhlenbeck's older work really worked with the system of constraints that I mentioned -- figuring out what can appear under those constraints is a considerably more complicated problem! This is a very imprecise discussion above and I'm totally blurring together Uhlenbeck's bubbling and compactness theorems from gauge theory -- but I never followed her work in a systematic way but instead was plunged into seeing its aftereffects from another related field that the work affected. Last quote really resonates: “Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”
- Cobord 8y ago
  Meanwhile as a mathematical physicist, I learned about her through instantons. Quite a wide career.
swayvil 8y ago
They say she was a voracious reader as a child.
dquarks 8y ago
Enjoyed her IAS lecture on Emmy Noether's laws. She's incredibly fun to watch. Well deserved. Congratulations, Karen.
marai2 8y ago
The closest I will every get to something like an Erdõs number is that I can now claim the one and only female Abel prize winner was my Differential Equations teacher at college! I missed taking a class with Steven Weinberg when I got to UT because he semi-retired the year before.
- selimthegrim 8y ago
  There is a story around UT that Weinberg heckled her during a lecture of his when she asked about the convergence of a series and promptly got a talking-to by the department chair. I hear he’s been much better behaved since.
- volkadav 8y ago
  I felt very lucky to have had her for an experimental mathematical modeling course (M375) back around 2000. She was simply delightful as a professor, even for a mathematical lummox like myself. :) Encouraging, informative, brilliant ... we should all be so lucky as to have teachers and influences like her in our lives.

309 points by digital55 8y ago

"Mathematics research had another feature that appealed to her at the time: It is something you can work on in solitude, if you wish. In her early life, she said in 1997, “I regarded anything to do with people as being sort of a horrible profession.”" This sentence struck me as slightly odd if only because Erdõs was renowned for his social approach to mathematics[1], and my layperson's understanding of mathematics departments being somewhat collaborative within their sub-fields. I know there are some notable examples of other solo breakthrough endeavours, such as Shinichi Mochizuki[2] or Yitang Zhang[3], and but those examples seemed to be exceptions to the rule. Perhaps I'm channeling too much Terence Tao[4], or maybe the lone wolf researcher only applies to literal geniuses who work exclusively in academia. Is mathematics research still a primarily solitary activity? [1] https://en.wikipedia.org/wiki/Paul_Erd%C5%91s https://en.wikipedia.org/wiki/Paul_Erd%C5%91s [2] https://www.quantamagazine.org/titans-of-mathematics-clash-over-epic-proof-of-abc-conjecture-20180920/ https://www.quantamagazine.org/titans-of-mathematics-clash-o... [3] https://www.cnet.com/news/yitang-zhang-a-prime-number-proof-and-a-world-of-persistence/ https://www.cnet.com/news/yitang-zhang-a-prime-number-proof-... [4] https://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/ https://terrytao.wordpress.com/career-advice/does-one-have-t...

natestemen 8y ago
mathematics research is typically very social. if you look at the mathematics research community as a whole you will find a very small percentage working completely in isolation. also i would add Grigori Perelman to your list of mathematicians working primarily by themselves.
heinrichf 8y ago
Later, she also says: "All in all, I have found great delight and pleasure in the pursuit of mathematics. Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more."
kevinventullo 8y ago
In my experience with pure math, it was mostly solitary. There is some collaboration, but it's often between people at different universities, so that collaboration may mean emailing back and forth every few days and visiting a few times a year (exceptions being grad students/postdocs working with their advisor/sponsor). Other solo works include Wiles's proof of Fermat (which admittedly later had to be fixed with the help of his student Richard Taylor), Perelman's proof of Poincare, and much of Scholze's foundational work on perfectoid spaces. Besides Poincare, three of the other millennium problems were posed by a single author (Riemann, Hodge, and Cook). If you look at the recent arxiv listings for differential geometry say, there are many solo authored papers: https://arxiv.org/list/math.DG/recent https://arxiv.org/list/math.DG/recent
- throwawaymath 8y ago
  > In my experience with pure math, it was mostly solitary. I disagree, but it might be because I interpret the spirit of the question differently. I would not call an activity involving some collaboration between people at different universities (including email), "solitary." It may not be very socially engaging, but it's categorically not a solitary endeavor. People are working together. To speak to your examples directly: as you're aware, they're extreme outliers. They're not just extreme because of the level of achievement; they're also nearly heroic in scope for a single person to work on without collaboration. It just doesn't happen much at that level of sophistication and complexity. More to the point, if you peel back those examples you see quite a lot of non-solitary work. For example, Perelman refused the Fields medal with a declaration that the substantial prior work was just as important for the solution as his own work. He's a pretty big champion of the important of the community aspect of mathematics. Likewise Wiles actually needed collaboration to fix a critical flaw in his original proof of Fermat's Last Theorem. And that really captures the heart of what I'm getting at, which is what mathematics is "about" by practice and intention. Most mathematicians engage with the research community by attending conferences and collaborating with their peers, even if that collaboration is largely asynchronous. They keep their fingers on the pulse of the academic landscape by talking with other people. In the cases where someone produces noteworthy research on their own, it still exists in a social framework. A mathematical proof is intrinsically a social endeavor. To prove a theorem is to convince someone else that it must follow from a series of axioms, definitions and other theorems. Sometimes you can do the work on your own, but it won't matter if it's disconnected from the research community, and the easiest way to stay connected to the research community is through collaboration. If no one else in the world agrees with your proof, your proof is meaningless (as an example, see the controversy around Mochizuki's Inter-universal Teichmüller theory). This is what peer review is for. Moreover if you construct a new mathematical theory, it's only meaningful insofar as it builds upon existing work developed by other researchers. The choice of axioms and definitions must be interesting and significant within the context of an existing body of work. This is one of the reasons you so rarely see nontrivial research produced by isolation. It's (approximately) a myth, and instances of it happening receive outsized attention precisely because they're extraordinarily rare and unconventional. In reality, it's usually not a good sign for a researcher to work on something in solitude. In most cases it coincides with the stagnation of a mathematician's career, not the glorious unveiling of a solution to a decades-old open problem or a grand new theory. I can see why the idea that mathematics is a solitary endeavor (or suited to solitary work) is an attractive one, because the most visible parts of it (writing papers, solving problems) can be done alone. But it's usually very inadvisable to go it alone in learning or practicing mathematics.
hyperbovine 8y ago
Erdos is renowned precisely because he was so out of the ordinary.
- throwawaymath 8y ago
  Erdos wasn't out of the ordinary because he published with (read: collaborated with) so many coauthors. He was out of the ordinary because he published so many papers, period. His sociability was more of a difference of degree within mathematics, not category.
  - hyperbovine 8y ago
    I beg to differ. Anecdotes of Erdos' itinerant lifestyle are legendary in the field: > Dr. Erdos traveled from meeting to meeting, carrying a half-empty suitcase and staying with mathematicians wherever he went. His colleagues took care of him, lending him money, feeding him, buying him clothes and even doing his taxes. In return, he showered them with ideas and challenges -- with problems to be solved and brilliant ways of attacking them. (https://www.nytimes.com/1996/09/24/us/paul-erdos-83-a-wayfarer-in-math-s-vanguard-is-dead.html https://www.nytimes.com/1996/09/24/us/paul-erdos-83-a-wayfar...) Even in the rarefied club of oddball math personalities, he stood out.
    - throwawaymath 8y ago
      Ah, by sociability I just meant the number of collaborators he worked with. What I'm getting at is that he's abnormal because he published so much, not because he published with so many coauthors. Many mathematicians would have similar looking publication records if they maintained the same level of collaboration and simply published...more. But he was an oddball too, for sure.
hyperbovine 8y ago
Turns out she is the daughter-in-law of the Ornetein-Uhlenbeck Uhlenbeck. I bet their family reunions were interesting.
- lordnacho 8y ago
  Aha, I quickly scanned her Wikipedia because I was wondering if it was either her or a relative that had done Ornstein-Uhlenbeck, missed that part. I thought OU was invented as a physics thing in the 1930s though. Indeed a very interesting mathematical family. It will be hard for future members not to revert to the mean :)
graycat 8y ago
It is interesting to read what she saw in math, why she liked it. For me, I just thought it would be useful, especially for physics which I thought was even more useful! No one ever explained to me how a career in academic math research would work: I never suspected that just digging into questions that were fun and curious and maybe someday somewhat useful, making discoveries, and writing papers could be a career that could support a family. In particular, I still don't understand why the US has so much respect for research universities: My guess was that college was for teaching the students. But in a research university, nearly all the effort by the professors is their research, and the teaching is a sideline. E.g., might have a really good researcher in far out topics in analysis teaching junior level linear algebra. So, the money to the university, for people directly paying full tuition often a LOT of money, is only a little for that teaching but much more for the research. An analogy for restaurants would be that each hamburger had to come from some three star Michelin place and cost $200. E.g., when I was a B-school prof, I was really discouraged to see that what the B-school was teaching had next to nothing to do with business. Instead, the school was interested in research, e.g., the question P vs NP. If medicine were taught that way, then no one would go to a hospital no matter how badly they hurt. B-school tried to be academic research, not professional training. Besides, for me as a college student, I had to conclude that after junior year level material, the profs really needed to understand what they were teaching much better than they did. For that, they just needed to do a much better job learning and presenting what was already in the library and without more research. E.g., I never had a math or physics prof who had a good grasp of the theory and applications of Stokes theorem, classic potential theory, multipole coordinates, or both the theory AND applications of Fourier theory. None of my undergrad physics profs knew either general relativity or quantum mechanics at all well. I wanted to learn that stuff, not for research but for applications. Math research solitary? It always has been for me. For learning the standard stuff, sure, can have people to talk to. But if they are in the same course and it is competitive, then maybe they don't want to talk? The reason my math research was solitary is mostly just because the new work I was doing was so focused that no one else around knew much about it or had much interest in it. For a lot of math research, being focused is close to necessary and, then, the solitary aspect gets to be close to automatic. Moreover it appears that there can be an effect from outside: Some people are more socially skilled, polished, talented, interested, motivated, etc. than others. In some fields, such social skills are important for success. But in math, if you can learn it, mostly on your own, then you can teach it -- good social skills can help but can get by with not much. This is even more the case for math research: Pick a problem, do some research, get some results, type in a paper, send it to an appropriate journal, maybe all with essentially no contact from anyone else. So, since in math can get by with less than the best social skills, people without great social skills can find math, be successful, and stay, and, then, the result is that comparatively math is not a very social field. But, a lot of people can learn to be social: Gee, a lot of grade school girls (sorry to bring gender into this) have just astounding social skills: E.g., it seems clear enough that long ago Hollywood discovered that among child actors the girls were much better -- they paid attention what was going on socially, reacted to others, had lots of facial expressions on tap, were good at glancing, averting, head tossing, pose striking, cases of body language, expressiveness in their voices, etc. Well, what a grade school girl commonly knows others can pick up, too! Okay performance in the lessons is not seriously difficult. Reading some of what Uhlenbeck said about herself, she was doing well in the E. Fromm recommended social activity "Giving knowledge of oneself" and that can help a person be social because they are letting others know who they are. Or little so interests people as other people; if some other person communicates no better than a stone wall, then there's not much for others to be interested in; Fromm's giving knowledge can help with that. For a nutshell description, my view of mathematicians is that they are less manipulative than most other people. Well, in some activities, can seem to get progress by manipulation, but in math, can't prove a theorem by a fake, manipulative proof!
nikofeyn 8y ago
i suspect erdos' socialization of mathematics had as much to do with mathematics as it did about having a place to eat and sleep. his vagabond lifestyle sort of necessitated he frequently socialize his mathematics so as to not wear out his welcome in any one particular place.
msla 8y ago
> Erdõs Where is his name spelled like this?
- klyrs 8y ago
  Umm... everywhere? It often gets anglicized to "Erdos" but the correct spelling is Erdős.
  - bhk 8y ago
    ő ≠ õ
    - klyrs 8y ago
      oh neat, those look different on my laptop but not my phone

deleted 8y ago

[deleted]

kaitai 8y ago

Uhlenbeck is delightful, and one of her big ideas discussed in this article -- bubbling -- truly has changed both her field and algebraic geometry. It's a cool idea. In a previous thread here (How I learned to love algebraic geometry, https://news.ycombinator.com/item?id=19397957 https://news.ycombinator.com/item?id=19397957) there was some discussion of singularities. Algebraic geometers like polynomials, while symplectic geometers like Riemann surfaces. These coincide at times but Riemann surfaces include lots of non-polynomial examples. Anyhow, as an algebraic geometer, the place I learned about Uhlenbeck's work was in compactification of moduli of curves. Basically, say I want to look at all the polynomial curves that can live in a certain 'environment'. (One 'application' is string theory -- what particle interactions can occur given a certain set of energy constraints? The particle interactions are curves traced out over time by particles/Riemann surfaces traced out over time by the little loops that represent closed strings in string theory; the energy constraints constrain the shapes the particle interaction can take.) If you want to look at limits of families of these interactions, you're looking at some odd behavior. An example is the equation xy = t^2 -- this gives you nice hyperbolas for values of t not equal to zero, but as t -> 0, you get something singular, two crossed lines. Or x^2 - y^2 - z^2 = t^2: you have a nice smooth hyperboloid when t neq 0, and a double cone when t=0. However, these examples are just showing you the idea of how singularities appear in families of smooth polynomials. Uhlenbeck's older work really worked with the system of constraints that I mentioned -- figuring out what can appear under those constraints is a considerably more complicated problem! This is a very imprecise discussion above and I'm totally blurring together Uhlenbeck's bubbling and compactness theorems from gauge theory -- but I never followed her work in a systematic way but instead was plunged into seeing its aftereffects from another related field that the work affected. Last quote really resonates: “Along the way I have made great friends and worked with a number of creative and interesting people. I have been saved from boredom, dourness, and self-absorption. One cannot ask for more.”

Cobord 8y ago
Meanwhile as a mathematical physicist, I learned about her through instantons. Quite a wide career.

swayvil 8y ago

They say she was a voracious reader as a child.

dquarks 8y ago

Enjoyed her IAS lecture on Emmy Noether's laws. She's incredibly fun to watch. Well deserved. Congratulations, Karen.

marai2 8y ago

The closest I will every get to something like an Erdõs number is that I can now claim the one and only female Abel prize winner was my Differential Equations teacher at college! I missed taking a class with Steven Weinberg when I got to UT because he semi-retired the year before.

selimthegrim 8y ago
There is a story around UT that Weinberg heckled her during a lecture of his when she asked about the convergence of a series and promptly got a talking-to by the department chair. I hear he’s been much better behaved since.
volkadav 8y ago
I felt very lucky to have had her for an experimental mathematical modeling course (M375) back around 2000. She was simply delightful as a professor, even for a mathematical lummox like myself. :) Encouraging, informative, brilliant ... we should all be so lucky as to have teachers and influences like her in our lives.