Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
quantamagazine.org
Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
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Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#2"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
[2] https://www.quantamagazine.org/titans-of-mathematics-clash-o...
[3] https://www.cnet.com/news/yitang-zhang-a-prime-number-proof-...
[4] https://terrytao.wordpress.com/career-advice/does-one-have-t...
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#3"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 de…
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.
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#4"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 de…
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."
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#5[deleted]
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#6Uhlenbeck 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) 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.”
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#7"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 de…
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
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#8They say she was a voracious reader as a child.
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#9"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 de…
Erdos is renowned precisely because he was so out of the ordinary.
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#10"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 de…
Turns out she is the daughter-in-law of the Ornetein-Uhlenbeck Uhlenbeck. I bet their family reunions were interesting.