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

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!

>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, and still not be able to be hired at a good school. What is the path to becoming a professor and making a livable salary?

If that is the case what are the industry prospects? Would whatever software company want to hire you, if your pure math specialization isn't directly applicable to what they're focused on? In turn, it seems better to learn how to code. But will your pure math specialization (as in not applicable to anything anyone is doing) + coding abilities set you apart?

I would rather study mathematics, pure mathematics and not be unemployable. But I don't really know what the job prospects are like. Could you speak to that, say, from a realistic perspective?

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 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.

How odd. I went to a state university, and I'd say that pretty much all my physics professors had a good grasp of all of this besides general relativity, and several understood all of this at a really deep level and used it in applications.

I did a PhD in pure math and now work for a big tech company. Having the PhD will get your foot in the door basically anywhere, so you'll at least make it to the screen, but ultimately you have to pass the same interview as anyone else. That means doing LeetCode and reading Yegge's stuff etc.

If your goal is to maximize lifetime earnings, a PhD is maybe not the right choice, but if you want to spend years studying something you love while financially breaking even then go for it. I definitely don't regret it, even though I would be worth a lot more if I had gone into tech straight out of college.

Btw, finance is also a common destination for pure math PhD's looking to leave academia.

>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.

Not true for most departments outside of engineering and some of the sciences, and not true for most math departments. Most faculty members in other departments get little to no grant funding. Math departments always have a small number of faculty members chasing grants, but the rest of them do not. Yet they still are evaluated based on research.

In my experience, the level of back stabbing in math departments is a lot lower precisely because of the lack of pressure to acquire grant money.