Becoming a Mathematician?

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Lemminkainen
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Becoming a Mathematician?

Postby Lemminkainen » Sat Oct 10, 2009 3:05 am UTC

I'm currently a freshman at Rice University, and I originally entered planning to study physics. In high school, I took differential equations at a local university. The instructor for ODE, a mathematics graduate student, encouraged all of us to at least try out more proof-based or abstract math courses, and told me that she thought that I seemed to have an appropriate sort of personality for doing work in pure math. So I listened to her advice and, when signing up for my courses in the fall, decided to take the more theoretically focused, proof-writing-focused versions of multivariable calculus and linear algebra. Now, halfway through my first semester, I'm starting to find myself somewhat disillusioned in physics-- the material in my waves and optics course just hasn't really come alive for me, and I'm finding that I don't really enjoy the requisite lab very much. In the meantime, I've been finding that I'm having a blast in, well, what I guess qualify as my first two real mathematics courses-- I'm finding that writing proofs comes fluidly to me, and that I feel enormously satisfied when, having written up a knockdown argument by contradiction, I can validly write "QED" at the end of my paper. At the moment, I'm feeling more desire to work in this field, and I'm strongly considering a switch away from physics. So I'm wondering-- am I making the right decision for the right reasons? Also, as a math major at Rice, presuming that I did research and maintained relatively high grades, what would my prospects be for applying to graduate schools? And, well, when I finished up, what would be my prospects for getting an interesting research career afterward? Thank you all.

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Re: Becoming a Mathematician?

Postby skeptical scientist » Sat Oct 10, 2009 3:55 am UTC

I did much the same thing; switching from physics to math as I found I was enjoying my math classes more and more, while the physics classes didn't hold my interest nearly as strongly. So I made a similar decision for similar reasons. I'm now doing quite well in grad school at a well-respected university, so it worked out well for me. Of course I can't say whether or not it will work out well for you, but I would encourage you to keep taking math, as long as you keep enjoying it. And of course you don't have to stop taking physics - continuing to take physics will leave your options open in case you decide to go back to physics. In fact, pretty much any math classes you take will help you with physics, and examples from physics motivate a lot of mathematics, so taking both math and physics will likely make you better at both.

Lemminkainen wrote:Also, as a math major at Rice, presuming that I did research and maintained relatively high grades, what would my prospects be for applying to graduate schools? And, well, when I finished up, what would be my prospects for getting an interesting research career afterward?

My guess is your prospects for applying to grad school would be good, especially if you can impress some of your professors (preferably ones with tenure) and get them to write good recommendations for you. As for your post-grad school prospects, that largely depends on what you do in grad school. ;) If you prove interesting theorems and get noticed, you will have good prospects.
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Re: Becoming a Mathematician?

Postby Certhas » Sat Oct 10, 2009 11:02 am UTC

I agree with skeptical. I started in physics and moved to borderline maths/physics because that was the physics that interested me most. Now I'm writing "physics" papers which go Theorem Lemma Lemma QED.

In any case your reasons are definitely the right ones, but don't give up on physics it does get better further down the line.
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Re: Becoming a Mathematician?

Postby Yakk » Sat Oct 10, 2009 9:22 pm UTC

Be aware that grad school is a pyramid scheme. 1 tenured professor teaches 10+ PhD students in their career, and after they retire maybe gets replaced by a single professor (or not). The professor gets research done by their PhD and grad students, the university gets cheap highly educated instructors for their undergrad classes, and the PhD gets a thesis done.

Then ~90% (maybe more) of PhD students don't get a tenured professor job (at least anywhere near the same tier), because there just aren't the jobs out there for them. (It possibly isn't that bad; this relies on tenured professors having this high grad student ratio. But it definitely is true within any given research university tier; the supply of X-tier educated or better PhDs is higher than the demand for X-tier tenured professors).

At the same time, many people I know who went to grad school in mathematics are now in tenure-track jobs at various institutions. But it isn't a high-success-rate career path; it is a competition career path with a low success rate, often against extremely smart (and sometimes hard working) people.

And there are alternatives to tenured professor that involve research, and being at a high-prestige university means you have a better chance of getting a tenure-track job at a low-prestige university than the grad students there, etc. (As an example, much of modern technology relies on some relatively neat mathematics, and firms hire people who have PhDs in related areas to work on improving their technology)

People with degrees in mathematics (even higher degrees) do quite reasonably well financially if you look at it statistically. Getting your dream job as a tenured professor at a top end research institution would require lots of work and sweat and not a little bit of luck; being well off after getting that kind of education isn't an unreasonable expectation, however. The path isn't foolish, but do manage expectations.

To quote one friend of mine (who doesn't have a tenure track job yet, despite being ridiculously smart (he is insufficiently career minded, we suspect!)), go to grad school because you want to research a problem, and wouldn't mind having 2-5 years to do it in. Plus, spending time at a university in a research environment is just invigorating; being able to spend your time talking with ridiculously smart people about ridiculously interesting things. You can make far far far worse choices on how to spend your life, even if it doesn't "pay off" at the end.

Talk to your undergraduate advisor, and to the mathematics undergraduate advisor, at your university. Express how much you want to go to grad school to them, and ask them for advice and what you should do to make it happen.
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Re: Becoming a Mathematician?

Postby skeptical scientist » Sat Oct 10, 2009 11:04 pm UTC

Yakk, that's some very good advice.
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Re: Becoming a Mathematician?

Postby HenryS » Mon Oct 12, 2009 3:13 am UTC

Yakk wrote:Be aware that grad school is a pyramid scheme. 1 tenured professor teaches 10+ PhD students in their career, and after they retire maybe gets replaced by a single professor (or not).
It isn't quite as bad as this, there are lots of undergraduate institutions without graduate programs that need professors.

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Re: Becoming a Mathematician?

Postby stephentyrone » Mon Oct 12, 2009 3:55 pm UTC

Fortunately, lots of people get PhD's and then go work on wall st, the national labs, silicon valley, etc. So it's not nearly as bad as it could be. Just don't think that you'll automatically end up teaching at Harvard/wherever. Getting to the top in academia requires absurd amounts of luck, just like anything else.
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Re: Becoming a Mathematician?

Postby Certhas » Mon Oct 12, 2009 8:46 pm UTC

Actually the stats I hear frequently for all of academia are that 1 in 3 or 1 in 4 people who seriously pursue an academic career end up in a permanent position. It's probably slightly better in Maths as the exit options are sweeter than in, say, critical theory. That still means it's a huge risk and time investment, especially as those numbers are after people self selecting out of the process. That's why honest self evaluation along with a clear sense of why you're here and how many sacrifices you are willing to make is crucial. There is a real danger of a war of attrition, in that each sacrifice by itself seems justifieable given all the ones before but their cumulative effect leaves you in a dire position indeed.

And of course you never see failed academics at universities, they failed to get permanent positions after all...
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Re: Becoming a Mathematician?

Postby Incompetent » Tue Oct 13, 2009 8:33 am UTC

It depends what you mean by 'seriously pursue'. Also, I think the numbers are significantly better for maths. For instance, in the UK, about 200 people start a maths PhD every year, and about 85 lecturers retire; given universities are expanding, there's probably slightly more than 85 permanent lectureships appearing per year. Now of those 200, how many seriously pursue an academic career? Some of them won't even finish the PhD! Now of course, you have to bear in mind international migration and so on, but I don't think the numbers are so terrible. If nothing else, universities around the world (but particularly under the US system) need huge numbers of people to teach maths to undergrads, and not just those undergrads specialising in maths either.

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Re: Becoming a Mathematician?

Postby Bobobo » Tue Oct 13, 2009 9:34 am UTC

"If nothing else, universities around the world (but particularly under the US system) need huge numbers of people to teach maths to undergrads, and not just those undergrads specialising in maths either."

isn't that what phds students and postdocs are for though?

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Re: Becoming a Mathematician?

Postby Incompetent » Tue Oct 13, 2009 2:41 pm UTC

Bobobo wrote:"If nothing else, universities around the world (but particularly under the US system) need huge numbers of people to teach maths to undergrads, and not just those undergrads specialising in maths either."

isn't that what phds students and postdocs are for though?


Postdocs are there for research. PhD students can get roped into teaching, but a) a lot of places (especially in the US) need to teach undergraduates maths but don't have any maths PhD students, and b) a lot of places have restrictions on how much PhD students can actually teach (both in terms of quantity and in terms of the level of tuition - eg they may be allowed to give tutorials but not lectures).

Some general thoughts about becoming a mathematician:

1. Don't do it for the money. Mathematicians are well-paid by the standards of the population as a whole, but they are not well-paid relative to their skill level. Expect to have rather unstable finances early on, and to become only moderately well-off (though with amazing job security) even if you eventually get tenure.

2. You won't know if you are cut out to be a mathematician until you do some serious independent research. Doing exercises and following courses is nothing like original research, and some people are much better at one than the other. The most difficult part of original research is asking the right questions, and you won't get any practice with this before you start a PhD (and in some cases even with the PhD, if the supervisor is the one asking all the questions). If you're not cut out for it, don't try to drag it out, try something else.

3. There's more to starting a career than sheer talent. You need to find a good research area, produce good results, get a good reputation from your results (warning: many good papers in mathematics languish in obscurity!) and get a good network of contacts who will argue your case. There's a lot of luck in all of these, but you have to work on all of them as well, and there are sometimes trade-offs to be made. For instance, when looking for a supervisor, you want someone with lots of contacts, but not so busy that they have no time for you, and you want someone smart, but not so smart that they will solve all the problems that they would otherwise give to you.

4. Don't take on more financial liabilities you have to. In most European countries, it's actually quite possible to earn more than you spend while you are a graduate student, so you come out with more savings/less debt than you started with. This is harder in the US, which really does seem to treat its grad students like dirt, but you still want to try to come out without too much debt. It's hard to tell when you will get a job or what your earnings will be, so be prepared to live frugally, and make money along the way where you can, ideally through grants, but if not then by tutoring and marking (as long as it doesn't interfere with your research).

5. There aren't many jobs where you need a PhD to get you the job - but there are plenty of jobs where the PhD experience will make you better at the job, and not just because it will make you better at dealing with mathematical problems. Writing a PhD in mathematics is analogous in terms of the level of skill and effort required to writing a novel or directing a feature-length film - by which I mean not only the technical aspect, but the creativity, the ability to organise ideas and break things down into smaller tasks, and the insight into the cultural context. You have also shown the ability to learn a great deal of specialised skills of your own accord, and you can easily learn more. Finally, you have developed a precision and clarity of thought that is possessed by only a tiny minority of the population - so far it has been directed at maths, but it can easily be aimed at other things (not least because mathematics is our principal way of thinking clearly and precisely about the world). Many employers will not realise this, not having done PhDs or having much maths background themselves, and you shouldn't be afraid to tell them, unless you're worried that they will be afraid of you.

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Re: Becoming a Mathematician?

Postby achan1058 » Tue Oct 13, 2009 3:12 pm UTC

Incompetent wrote:1. Don't do it for the money. Mathematicians are well-paid by the standards of the population as a whole, but they are not well-paid relative to their skill level. Expect to have rather unstable finances early on, and to become only moderately well-off (though with amazing job security) even if you eventually get tenure.
That only applies to academic mathematicians.
Incompetent wrote:4. Don't take on more financial liabilities you have to. In most European countries, it's actually quite possible to earn more than you spend while you are a graduate student, so you come out with more savings/less debt than you started with. This is harder in the US, which really does seem to treat its grad students like dirt, but you still want to try to come out without too much debt. It's hard to tell when you will get a job or what your earnings will be, so be prepared to live frugally, and make money along the way where you can, ideally through grants, but if not then by tutoring and marking (as long as it doesn't interfere with your research).
Same for many universities in Canada as well, at least in the Math department. I am currently earning more than I spend.

I guess the biggest thing that makes Ph.D. math students different than say Ph.D. Arts students is that if all else fails, you can usually join the dark side (industry) without too much trouble.

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Re: Becoming a Mathematician?

Postby Sir_Elderberry » Wed Oct 14, 2009 4:14 am UTC

How much of this applies to Ph D. Physics?
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Re: Becoming a Mathematician?

Postby Certhas » Thu Oct 15, 2009 2:19 pm UTC

Depends. Theoretical physics? Almost all of it. My PhD is in Maths, but in many other countries I would be doing the very same thing I'm doing now in the physics department. For experimental physics I don't really know.
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Re: Becoming a Mathematician?

Postby Incompetent » Fri Oct 16, 2009 7:54 am UTC

achan1058 wrote:That only applies to academic mathematicians.


The OP seemed to be talking about getting into pure maths, and it's difficult to get paid for that outside academia, almost by definition. On the other hand, if it doesn't work out then it's not that difficult to turn to the dark side afterwards, so it's not like you're condemning yourself to poverty.

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Re: Becoming a Mathematician?

Postby Yakk » Thu Oct 29, 2009 6:39 pm UTC

I am under the impression that this might give you a good idea:
http://www.aip.org/statistics/
there are some tasty stats there. It is physics and not math, but theoretical physics and applied mathematics are relatively adjacent fields.
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Re: Becoming a Mathematician?

Postby andrewxc » Fri Oct 30, 2009 2:28 am UTC

I am in academia... Sort of. If you want to teach and you are any good at it (do more than lecture at your students and watch the words hit them in the face and dribble onto the floor), you can basically write your own ticket anywhere you want. I worked in the public high schools for a year and a half and hated it. I am currently working at a Community College, and love it.

Many of my friends around here work for the government and get very nice salaries ($50-60K+ (depending upon performance) after 3-4 years, with a BS in Math / CS), benefits (including graduate degrees for reciprocated time in the job), and have wonderful job security. Honestly, if I were not planning to have a kid in the next few years, I would apply to the NSA, after finishing my grad degree (in Applied & Computational Math from Johns Hopkins Applied Physics Lab). There was a hiring freeze a couple of years ago, but it should be back almost to normal, now.
You could also try for an internship at the Agency, to see if it's something you would like...

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Re: Becoming a Mathematician?

Postby andrewxc » Fri Oct 30, 2009 2:40 am UTC

Also, after taking a class on Neural Networks and reading as much as I can about Evolutionary Biology, I'm starting to forge my own research path (currently only on my own free time), not just saying "I need a traditional career path," like being an actuary :roll: , and sticking only to that.

You really need to find something that you are interested in - and not just in academics; read some outside books, wiki articles, and research papers on various subjects, even the ones you thought you didn't like in high school - and try to research the mathematics behind it, even if it is not immediately obvious. That will, eventually, lead you down a great and fun road.

I hated Biology in high school. Thanks to Richard Dawkins and Darwin, I really do get it, now, and I'm working on applying non-linear differential equations to Self-Organizing Maps in order to show the population distribution of multiple competing / predator-prey / scavenging species of animals.
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