Math PhD career track

@wis75 Good advice. I don’t see him moving away from wrestling, but who knows. He is definitely looking at schools that are about more than just the wrestling.

He has a college coach that he has worked with in the off season for a couple years that he would love to wrestle in college for, and who I have been told through a back channel would give him a full scholarship, even though they usually only do partials. And I honestly think he could make him a national champion, the program has produced several of them. But the school does nothing for him. It’s probably his final resort back-up plan, which the coach is aware of. But his first priority is the school, not the wrestling program.

@KSMom1518 he should think strategically about who he will ask to write his letters. He could even ask them what he should do to help them write the best letter they can, which courses to take etc. Many people struggle with not knowing 3 faculty well enough.

When calculating the cost of a PhD, don’t forget the net present value of any missed retirement contributions. Likely colossal.

This is generally true for most technical jobs in the computing industry.

Most technical employees in the computing industry with master’s or doctoral degrees are internationals on work visas or started their US careers as such, since getting a work visa is less difficult with an advanced degree. Among those who had US citizenship or permanent residency before starting their careers, bachelor’s degree is the most common educational attainment.

@chzbrgr

Another financial variable, both long-term & for an interim period of time, if one works first before starting graduate school, is the decease in income when switching from full-time employment to living on a PhD stipend. Not only will that affect one’s retirement savings, but one’s quality of life.

One’s gross full-time income, if doing some form of computational work, like coding, could easily be at least 3x that of a graduate student stipend. Plus, possibly losing employer contribution to a 401k or 403b plan.

OTOH, if one works in industry first and saves $$, that can supplement the measly grad stipend!

It’s not so measly. Besides, material comfort is only a part of what makes life interesting at this age. The stipend pays basics. If the rent is reasonable, they can even splurge from time to time. They get to interact with great people and enjoy campus culture that money can’t buy. My D is at a top math grad program. Stressful at times but overall she is having a great time. My impression is that reseach experience is the most important part of application to grad school. Participating in REUs are highly recommended. Students can learn how they do in research and if it’s a career they would like. Research isn’t for everyone. They can also see how they compare with others pursuing an academic career. i am guessing kids from the most competitive REUs end up at selective programs. Of course, if they would like to make money during summer, REUs are not for them. REUs pay far less than industry internships mirroring what’s to come. Comparing my D’s REU pay to her friend’s internship pay, I’d say about 4 times less.

About taking grad courses, most kids run out undergrad courses to take in their junior or senior year. At universities they can take grad courses. Most LACs offer a few graduate courses to remedy that. National Research Council ranks grad programs every 5 or 10 years. USNews really doesn’t work for graduate programs.

I run a quantitative research group in the investment management industry and am in the process of trying to hire a junior quant. The current leading contender is in the process of finishing up his math PhD at a major flagship state school, Curiously, he was a pure math (number theory) guy until a couple of years ago, then made the switch to applied math and then discovered finance. We have put him through the paces, including a serious homework exercise, and he keeps on impressing us, If all works out (next week), he will probably start with something close to a $200k package. What makes him special? Good communication skills, demonstrated interest in the field of application, and an ability to solve problems often associated with engineers.

The bigger problem with the PhD stipends is the uncertainty at places like UCB. The public schools are broke while the top private schools have secure funding and can pay much larger amounts over 30k.

If you are concerned about PhD stipend amounts, there seem to be this survey web site:
http://www.phdstipends.com/results

When my D got offers, the amounts offered were within one ot two thousands. I am sure there was room for negotiation but money wasn’t different enough to play a role in deciding where to go. Reputation of the program was far more important. Cornell math program is not that highly ranked. I know it’s not in top 10, maybe in top 20. Berkeley math program is stellar. Cost of living is a factor except it’s usually more interesting to live where the cost is high.

I wouldn’t really know except I would think some of that is spelled out in the offer, often three years guaranteed funding, etc. It’s not like they can cut TAs. They need them to teach. Once you start doing research hopefully well before three years are up, funding should come from your advisor’s grant not from the university. Soft money on the other hand will depend on the university budget. Stellar programs have well funded faculty.

There is a crisis in funding at University of CA and many public programs for PhD students. My daughter was offered a spot at UCB and was told to avoid it if she was able to find a spot at a comparable private university. The top privates have huge endowments which allow for stable funding and higher stipends. This is going to end poorly for the programs at the public schools.

^Inspite of that, many top 10 programs are public. The key word here would be “comparable”. Not many programs are “comparable” to Berkeley math program. If it were me, I would look at fit and strength of your specific field, where their new PhDs go to do Post Doc and beyond if you are on an academic track well before whether it’s public or private. I don’t know much about UCs but I can’t imagine the state would allow UCs disintegrate to ruins. It’s not like the state is starving.

Excellence in math and other theoretical STEM research is very unpredictable and it’s naive to consider it as a career track without first having aced several years of the most rigorous college courses (even then, taking courses =/= research and many people get the most prestigious degrees only to flame out in research). To be stereotypical, it’s not the path of an athletic recruit.

Igloo, I was saying “measly” compared to what folks in industry make before heading off for a PhD (esp. if one takes the math degree and goes to SV)…my older S lives on not much more than a PhD stipend and he’s banking the rest. He has never been one for spending a lot of money, and could not care less about more than basic comforts. He knows a couple of HS classmates who took the same path he did in college and work and then went back for a PhD. What they saved from their industry jobs usually went to a down payment on a condo or small house.

His best buddy from HS just finished his PhD and was able to live nicely in a lower-cost state on his stipend. He always had apartment mates, but more because he didn’t want to live alone than because of economics.

A problem with doing a PhD after working for a few years is that in pure math at least, people’s ability to make serious new contributions to the field seems to decline rapidly with age. Even 25 is getting on a little, and by 35 pure mathematicians are over the hill.

chzbrgr, that’s what they say about early accomplishments in mathematics, but I don’t think that career studies bear that out.

Look at Andrew Wiles’ age when he proved Fermat’s theorem: 42, when the unflawed proof was published
Terence Tao is 42 now and still publishing
Manjul Bhargava is 43 now. At 41, he and a co-author proved the Birch and Swinnerton-Dyer conjecture “for a positive proportion of elliptic curves,” according to Wikipedia. A proof of the Birch and Swinnerton-Dyer conjecture that covers all cases is worth $1,000,000 from the Clay Mathematics Institute, as one of its seven millennium prize problems (https://en.wikipedia.org/wiki/Birch_and_Swinnerton-Dyer_conjecture).

This is not to say that mathematicians are “over the hill” when they hit their 50’s either. I can’t locate it now, but I remember an article in Science about a Purdue professor of mathematics who proved a notable theorem when he was in his 50’s, and it was the peak of his accomplishment up to that time.

I think the stereotype that mathematicians only contribute significantly when young may come from a few effects: First, a young person may have a truly novel way of looking at things, and he/she “picks off” the problems that are most susceptible to proof in that way. After a while, the problems get harder and deeper. A young (or youngish) person proves something major, and thereafter is only interested in even more challenging problems, that may or may not yield (Einstein perhaps exemplifies this). I have my own conjecture: Andrew Wiles is currently working on the Riemann conjecture. Then, there is the importance of unfettered concentration, in mathematics. This is easier (in my view) before one has a family, mortgage, etc., to say nothing of graduate students to direct, classes to teach, grant proposals to write, university committees . . .

Here’s a suggestion: Go over to the local university’s math department, look for faculty members over 35, and ask them if they are doing any worthwhile mathematics now. (No, wait, don’t do that.)

I think I’ll hold off on sending those emails. In a way, your examples help the point. Andrew Wiles was noteworthy for proving something so major at such a ‘late’ age, and Terence Tao has been producing brilliant research since his teens. And Wiles had already had a pretty stellar career in his 20s.

I can’t comment on Bhargava. As much as I wish it weren’t true (I’m 53!) I suspect that at least part of it is raw intellectual power which does fade.

Oh, I was suggesting going in person to the math departments! :slight_smile:
I think it is the case that exceptional mathematical talent does tend to emerge early.
But I also think it is sustainable.
If you are on this forum, chzbrgr, perhaps you have children in high school, or just recently in college?
If–like me–you are not getting much sleep during your children’s high school years, wait until you can catch up on your sleep. You will find that you get a remarkable increase in intellectual clarity.

@chzbrgr " A problem with doing a PhD after working for a few years is that in pure math at least, people’s ability to make serious new contributions to the field seems to decline rapidly with age. Even 25 is getting on a little, and by 35 pure mathematicians are over the hill. "

I have no idea where people get this foolishness. Literally nobody in my field did their best work before age 30, and the vast majority have done their best work after age 40. That includes two Fields medalists.

For every Terry Tao (who, incidentally, is as brilliant as ever and will surely continue to do outstanding work in his 60s), there are dozens of working mathematicians making “serious new contributions” and doing their best work well into their 40s and 50s.

Even if this were not the case, I find it irresponsible to give advice based on the few incredibly anomalous mathematicians you know anything about because they were famous enough to show up in the newspaper.

The idea that one’s “creativity” mysteriously disappears in one’s late 20’s, so that one can’t do research in pure math any longer is an inane hollywood fantasy. I have no idea why it continues to be perpetuated, but I suppose comfortable untruths die hard.

I feel no need to hunt for data on this but the explanations @QuantMech gives for this phenomenon, such as it is, seem far more plausible than the glamorous one.