Earlier quoted context omitted.
>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. I am interested in pursuing a PhD in Pure Mathematics. What are the career prospects for it? Based on what I read academic prospects don't seem too thrilling. It appears you may have to do multiple post-docs at low pay, a…
> What are the career prospects for it? I typed in a comment rejected as too long, clicked on the wrong icon, and lost it. My view of the prospects is, in a word, poor. Others have described the prospects for an academic math career. I would add, should include a lot of politics, friends, alliances, etc. Outside of academics, long the main source of jobs in math was in US national security, with some of the major com…
Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
31–40 of 56 posts
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#32Uhlenbeck 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…
Quite a wide career.
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#33"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…
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 th…
This is very odd. How can a physics professor not know undergraduate physics material?
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#34"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…
Where is his name spelled like this?
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#35Earlier quoted context omitted.
Personally I enjoyed my PhD, but I watched others get hurt, so I wanted to add some words of warning. It's a risky choice, unless you're very good. You should go in with your eyes open, knowing that you'll be lucky to get an academic job afterwards, especially if you're in a 'pure' field without many applications. For industrial jobs, you'll probably have to re-train through self-study. After a maths phd, doing so ma…
This is a good addition. Did you do a PhD in Math as well? My idea is to pursue a PhD in CS, but have a very theoretical bent. I was concerned since essentially I am studying pure math, under the CS department I'd have similar prospects as a Math PhD. But my aim is to set myself up for industry skills upon graduation, so I'll ensure I beef up my software and leetcode skills as Kevin recommended.
I'd say TCS and pure math are about equivalent in terms of the career opportunties they offer.
Something I forgot to mention: under no circumstances should you self-fund a PhD. Make sure you have a stipend to keep food on the table. Self-funding magnifies the risks I've described tenfold.
This is a realistic perspective of what grad school is like in the average-to-bad case. I could identify with parts of it:
http://nautil.us/issue/56/perspective/what-does-any-of-this-...
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#36Earlier quoted context omitted.
Personally I enjoyed my PhD, but I watched others get hurt, so I wanted to add some words of warning. It's a risky choice, unless you're very good. You should go in with your eyes open, knowing that you'll be lucky to get an academic job afterwards, especially if you're in a 'pure' field without many applications. For industrial jobs, you'll probably have to re-train through self-study. After a maths phd, doing so ma…
This is a good addition. Did you do a PhD in Math as well? My idea is to pursue a PhD in CS, but have a very theoretical bent. I was concerned since essentially I am studying pure math, under the CS department I'd have similar prospects as a Math PhD. But my aim is to set myself up for industry skills upon graduation, so I'll ensure I beef up my software and leetcode skills as Kevin recommended.
Myself I'm not particularly worried about maximising income or whatever. I like what I'm studying and researching, and I'm paid enough to live a comfortable life at least for now. I could honestly do this for the rest of my life (which is what an academia career is, I suppose), but if I ever get fed up with it I also know I have loads of doors open everywhere, which is certainly a comforting thought.
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#37Earlier quoted context omitted.
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…
> 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 d…
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#38Earlier quoted context omitted.
This is a good addition. Did you do a PhD in Math as well? My idea is to pursue a PhD in CS, but have a very theoretical bent. I was concerned since essentially I am studying pure math, under the CS department I'd have similar prospects as a Math PhD. But my aim is to set myself up for industry skills upon graduation, so I'll ensure I beef up my software and leetcode skills as Kevin recommended.
I am a maths PhD researcher in a CS department, just like you describe. In a few short words, my recommendation would be that you do the PhD for its own sake , not as a tool to get a higher-paying job or to learn for an industry job. If you want the latter, you're better off elsewhere, plus you will probably be miserable in a PhD. Be sure that you get into it for the sake of doing research in a field you like (even t…
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#39Earlier quoted context omitted.
Two quick notes on this: > 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. It's the other way around. The faculty are paid to do research from grants they bring in, they are evaluated based on their research, and the university requires them to teach on the side. > E.g., I never had a math or physics prof…
Then the tuition should be much lower than it is. Net, student tuition and state taxes at state universities are paying for a lot of research.
Re: Karen Uhlenbeck, Uniter of Geometry and Analysis, Wins Abel Prize
#40Earlier quoted context omitted.
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 th…
>None of my undergrad physics profs knew either general relativity or quantum mechanics at all well. This is very odd. How can a physics professor not know undergraduate physics material?