Other Should I Become a Mathematician?

[Intervenient]

I just feel like I don't have the confidence for math, statistics in particular. I'm easily intimidated.

 

[mathwonk]

did you see lonesome dove? remeber the scene where the woman with the horse farm hires the ex sherrif? she says: "so you never been nowhere but arkansas and you never handled horses. but you ain't stupid and you ain't nailed down are you?"

get the point? you are as good a man (or woman if that is the case, but i doubt it) as anyone else. believe that.

 

[Bourbaki1123]

my personal history is probably not relevant but may be instructive anyway.

i began as a star high school math student in tennessee who got a merit scholarship to harvard. as an undergrad at harvard i could not easily adjust to the need to study everyday and flunked out.\\i retiurned amnd worked hard at studying and attending class and made A's by memorizing proofs in advanced calculus and real analysis and got into brandeis.

I knew almost nothing of algebra commutative or otherwise, but hung in for a while on talent and tenacity until I was asked to leave brandeis too.

then i went to teach for four years and studied differential topology and advanced calculus and then returned to grad school at utah. there i studied several variable complex analysis for one year and returned to riemann surfaces the second year.

then i wrote a thesis in riemann surfaces and moduli and took a job at UGA. Then I worked hard at learning as much algebraic geometry s possible. i still knew relatively little commutative algebra (and still do).

i made a living off my grasp of several complex variables, differential topology, algebraic topology, homological algebra, and category theory and sheaves.

after my third year I went to harvard again as a postdoc and devoted myself to every word dropping from the lips of mumford, griffiths, and hironaka.

those two years gave me a tremendous boost. then i returned to UGA and benefited enormously from collaboration withf my brilliant colleague Robert Varley.

I still hope to master commutative algebra.

Interesting. In your experience do most algebraic geometers come from a commutative algebra background? I had always gotten the impression that this was standard but I'm generalizing from a limited pool of examples.

Also, do you know if it's reasonably common for students coming into U Georgia who want to do algebraic geometry to have already gotten through something like Eisenbud's Commutative Algebra? I ask because I'm on the third chapter now, and I plan to be reading/doing problems in Hartshorne (other than just the first few segments of the first chapter, which is where I am now) by the time I enter grad school so I want to know if this would put me in good stead.

Lastly, I would be interested in hearing your advice on the following issue of mine:

Unfortunately (or perhaps fortunately?) I have a many areas of interest;
proof theory and constructive categorical logic/ stuff in cartesian closed categories, lambda calculus stuff etc and Model theory (to a lesser extent, for sure) on top of algebraic geometry, but to further complicate this, I also am immensely interested in the philosophy and history of mathematics, evolutionary psychology, machine learning (especially reinforcement learning, also I've been reading about the application of TD reinforcement learning to hebbian learning in dopaminergic neurons), decision theory as it applied to AI, rational choice theory, foundations of statistics (I'm a Bayesian ;p), social impact of future technology a la the work of Nick Bostrom (and Oxford's FHI more broadly), neuroeconomics, metaethics, computational neuroscience (spike train statistics and neural codes seem very interesting), the cognitive science of mathematics (I'm looking for something vaguely like Rafael Nunez's work with Lakoff, but more rigorous); the list goes on and on really.

I am become the inverse of the one-dimensional math nerd, destroyer of... hurdles? More like focus/opportunity, but it doesn't fit as well in the allusion. Needless to say, I did not focus solely on math for the duration of my undergraduate career. I've got quite a bit of anxiety about having to choose what to focus in on, and I've even toyed with the idea of taking the gamble of getting a philosophy PhD for the super slim chance that I find the right connections to get a professorship somewhere that will to some extent let me learn and publish papers about the ideas that I want to learn and publish papers about. However, I've come back to reality, and know that this will almost certainly not happen.

So, I don't know, is there any sort of advice you could offer upon hearing my spiel? Will I at least still have some time to continue to study areas other than my particular focus when I'm in grad school?

 

[Number Nine]

also I've been reading about the application of TD reinforcement learning to hebbian learning in dopaminergic neurons), decision theory as it applied to AI, rational choice theory, foundations of statistics (I'm a Bayesian ;p)

We have much to discuss then. I'm rather knowledgeable about the midbrain dopamine/basal ganglia circuitry and its involvement in reinforcement learning, so feel free to send me a PM if you have any questions.

ps -- I too am a bayesian. One day we will topple the hegemony of the null hypothesis significance test.

 

[mathwonk]

bourbaki, i think you know more than the average entering student.

 

[simplicity123]

Might as well ask about Analytical number theory since got good advice about AT and AG.

But, what branches of Maths should I learn if I wanted to work on the Riemann Hypothesis?

As I know should have down, complex analysis, algebraic geometry, non commutative geometry and ofcourse number theory. But, I was reading a book and it was saying stuff like you needed to know quantum mechanics and quantum chaos. I should know basic chaos theory and I could probably get a lecturer to teach me quantum mechanics or help me with it. But, I don't want to learn Physics because Marcus Du Sautoy was saying that it could solve RH.

I read that statistical physics was being used in P versus NP.

 

[mathwonk]

the probability that you, or anyone else, like andrew wiles, will solve the riemann hypothesis, is very low. so it makes no sense to base your whole life or career on that.

just prepare for a career in number theory and hope for the best.

 

[simplicity123]

the probability that you, or anyone else, like andrew wiles, will solve the riemann hypothesis, is very low. so it makes no sense to base your whole life or career on that.

just prepare for a career in number theory and hope for the best.

I don't believe in probability. I will either prove it or not. I doubt it be luck that proves it.

Surely I should be going into analysis? Like harmonic analysis or something like that. According to a book I read the best approach to RH is from Connes and non commutative geometry. So confused as hell on what to study.

 

[weld]

And also, when researching in theoretical mathematics, since you don't have a lab, do you still have duties such as administration, grant writing, etc? Do you end up spending more time on teaching due to the absence of lab? I really would like to know this.

Also, anyone got an opinion on working as semi-perma postdoc and staff scientists? I wonder if they're worth it or not. Again I would like to know if such positions exist in theoretical mathematics. Any information on how it is to be working as a theoretical, or heck, even applied mathematician would be great. I really need to find facts on it to decide for myself if I really want to commit to it or not. I also appreciate if you can estimate how much time (In %, if possible) is spent on miscellaneous and boring things like doing paperwork and other forms of busywork. I would love to avoid that to the greatest possible degree. Does theoretical computer science really differ a lot from theoretical mathematics in these regards? What about theoretical physics?

Finally, where can I find information on becoming a logician? Is it even a field to do research in? I'm also curious as to how much time is spent on busywork and the like.

 

[mathwonk]

Van den Eynden has a nice intro to number theory.

 

[Robert1986]

So I've been reading several threads on this board with the common theme that it is almost impossible to get into academia as a Physicist. Is the outlook for mathematicians as dismal? I am graduating in May, and obviously I am looking toward my future career. From what I gather, I have three options:

1) Get a Ph.D., and attempt to get a job as a prof, somewhere, anywhere (assuming that it is as difficult to get a job for a mathematician) or do something in the private sector.

2) Get a Master's Degree and plan on teaching high school (or doing something else, but I think I could get a job teaching high school). If I do this, I think I can find some private schools that would hire me to teach while I worked toward my master's. (In my state, I could, in theory, get a job at a government school, as well.) If I do this, I think that I could have a reasonably fulfilling career. Other than time, there is really nothing that would keep me from doing research, anyway. Additionally, I could try to teach part-time at a community college.

3) I am applying to some programs that pay students to get Specialized master's degrees while teaching in a public school. If I could get into such a program the benefits are nice, and I would get about 18 hours of actual graduate-level math credit (the other being "learning to teach" classes). This would allow me to teach high school and possibly part time at a community college. The upside is that I would be allowed to teach in any government or private school and my pay would be pretty good (for a teacher.) The downside is that I would miss a lot of the graduate level math classes. So, if I get a Ph.D., what are my chances of getting a job as a prof? Is it as dismal as it is for physicists? Do you more experienced guys have any advice? What about you younger guys, you are probably facing something similar with similar alternatives, have you thought of anything else?

 

[Bourbaki1123]

I don't believe in probability. I will either prove it or not. I doubt it be luck that proves it.

Read this: http://omega.albany.edu:8008/JaynesBook.html"

It isn't good to ignore the fact that probability theory is a necessary ingredient of highly rational thought.

 

[Bourbaki1123]

So I've been reading several threads on this board with the common theme that it is almost impossible to get into academia as a Physicist. Is the outlook for mathematicians as dismal? I am graduating in May, and obviously I am looking toward my future career. From what I gather, I have three options:

1) Get a Ph.D., and attempt to get a job as a prof, somewhere, anywhere (assuming that it is as difficult to get a job for a mathematician) or do something in the private sector.

2) Get a Master's Degree and plan on teaching high school (or doing something else, but I think I could get a job teaching high school). If I do this, I think I can find some private schools that would hire me to teach while I worked toward my master's. (In my state, I could, in theory, get a job at a government school, as well.) If I do this, I think that I could have a reasonably fulfilling career. Other than time, there is really nothing that would keep me from doing research, anyway. Additionally, I could try to teach part-time at a community college.

3) I am applying to some programs that pay students to get Specialized master's degrees while teaching in a public school. If I could get into such a program the benefits are nice, and I would get about 18 hours of actual graduate-level math credit (the other being "learning to teach" classes). This would allow me to teach high school and possibly part time at a community college. The upside is that I would be allowed to teach in any government or private school and my pay would be pretty good (for a teacher.) The downside is that I would miss a lot of the graduate level math classes.


So, if I get a Ph.D., what are my chances of getting a job as a prof? Is it as dismal as it is for physicists? Do you more experienced guys have any advice? What about you younger guys, you are probably facing something similar with similar alternatives, have you thought of anything else?

A friend of mine worked for the EPA for a while and mentioned that being a statistician at the EPA is a pretty cushy job and it isn't too impossible to find an opening if you've got your PhD.

I was under the impression that I would have to sacrifice quite a bit to find a job opening in academia and that even at that it's far from a sure thing, even at more of a teaching university. That said, since I'm still young I'm convinced that I would be perfectly happy getting paid dirt so long as I can get away with doing what I love.

 

[simplicity123]

A friend of mine worked for the EPA for a while and mentioned that being a statistician at the EPA is a pretty cushy job and it isn't too impossible to find an opening if you've got your PhD.

I was under the impression that I would have to sacrifice quite a bit to find a job opening in academia and that even at that it's far from a sure thing, even at more of a teaching university. That said, since I'm still young I'm convinced that I would be perfectly happy getting paid dirt so long as I can get away with doing what I love.

Stats is different. http://gowers.wordpress.com/2011/07/26/a-message-from-our-sponsors/
If you read this you will see that funding for stats is going to increase(even through it has the biggest slice of funding already) and yet everything else is waiting to see if funding is going to increase or decrease. Postdoc funding is only going to stats. Pretty depressing read.

I think that's good. Everyone who has amazing grades will likely go into banking or finance as academics is crappy pay with no job security. Plus you need to more every two years for a long time.

 

[Bourbaki1123]

Pretty depressing read.

Unless you like stats and have an interest in artificial intelligence and rational choice theory and computational neuroscience.

ETA: Or if you don't live in the UK (I'm in the USA) then it has relatively little impact, all of it being indirect.

 

[simplicity123]

Unless you like stats and have an interest in artificial intelligence and rational choice theory and computational neuroscience.

ETA: Or if you don't live in the UK (I'm in the USA) then it has relatively little impact, all of it being indirect.

Well, logic is the least funded Maths in England, which I think will be the same in the US. Plus you are talking about computer science which isn't Maths.

I'm thinking of doing a PhD in US because I read it's easier to get funding as they need a lot of people to teach calculus and linear algebra.

I don't know through. My grades will probably be a first this year, however I read that in the US it is much better. That there is more funding and better university overall because of high fees.

 

[Bourbaki1123]

Well, logic is the least funded Maths in England, which I think will be the same in the US.

Logic is not terribly well funded, yes. It is one of the areas I would like to go into, so that is a bit unfortunate. That said, I'm also interested in cognitive science and algebraic geometry, though the latter probably doesn't bring in the most funding either (the former, I would expect to bring in much more).

Plus you are talking about computer science which isn't Maths.

It depends on what exactly you're doing.

 

[mathwonk]

since some people here solicit and take my advice i wanted to advertise my credentials.

but the bit limit seems to prohibit my displaying my 10th grade second place geometry trophy. you can take my word for it.

 

[Bourbaki1123]

since some people her solicit and take my advice i wanted to advertise my credentials.

but the bit limit seems to prohibit my displaying my 10th grade second place geometry trophy. you can take my word for it.

I feel like some sort of "Hu won first" gag should ensue but, alas, this is the wrong format.

 

[weld]

I'm firing off new questions whether you like it or not. What I really want to know is what you hear from your peers regarding employment opportunities, mathwonk. Which math subfields generally have more postdoc and tenure positions? Which generally have more applicants, that is competition for such positions? Which subfields are hard to make advances in, which have lots of low hanging fruits? Which have harder competition for gettings grants? Are there any particular subfield which are very susceptible for short-term flunctuations, resulting in a lack of job opportunities, or is this something which affects math as whole (I have the impression that it's more slow moving and stable though)? Are there any particular subfields which are harder to switch over to other subfields from? Which subfields are considered aesthetically satisfying and which are considered aesthetical unsatisfying, according to most mathematicians?

Based on criterias such as the ones I just listed, what are the overall best math subfields to work in would you say?

Also, do you know of any private industry that actually conducts high level pure math research? In academia one doesn't spend all one's time researching, one must lecture, teach and apply for grant as well. Well, how much % of an average mathematician's (On tenure track) time at a research university would you say is spent researching? Like 90%? Would you say it differs once one gets tenure?

http://en.wikipedia.org/wiki/Category:Research_institutes_in_the_United_States

That link contains a huge list of private research institutes. I don't expect anyone to read through all that of course. But I wonder, are places like "American Institute of Mathematics" and similar worth working at? Are they hard to get permanent jobs at?

Facts and figures aren't necessary if you have no such thing, but anecdotes, what you experience yourself, what you hear from peers and conventional wisdom among mathematicians are all greatly appreciated. After all it would kinda suck finding out too late that there's no jobs in one's selected subfield, now wouldn't it?

 

[Bourbaki1123]

I'm firing off new questions whether you like it or not.

lol wut?

I'd mention again that mathematical statistics people seem to be getting a lot of funding.

Which subfields are considered aesthetically satisfying and which are considered aesthetical unsatisfying, according to most mathematicians?

I would like to see a statistical breakdown of this, that said http://en.wikipedia.org/wiki/Mathematical_beauty#Beauty_and_mathematical_information_theory" could indicate that subjective beauty would depend largely on what sort of maths you've already learned. A very deep result that unifies your knowledge into a simple framework is what you will find to be the most beautiful.

Based on criterias such as the ones I just listed, what are the overall best math subfields to work in would you say?

You should probably realize that that is a non-trivial question, and you probably need to do some actual heavy duty data collection to get a decent answer. If you actually could get a solid, statistically well supported answer, you could probably publish your result!

Yes, you can gather anecdotes, but I think if you've actually got some time before grad school you could spend a fraction of your time gathering relevant data.

 

[weld]

A very interesting link you provided there Bourbaki. Thanks. I'll definitely look deeper into the pyschology underpinning math. If you have any other good sources regarding math and psychology I would be happy to see them.

Anyways, yes, I'll probably search around the web to find those much desired statistics. And I've got the time to do it as well. Part of the reason I posted here was that I hoped someone knew at least something regarding working in subfields or that someone had at least some semi-relevant and interesting knowledge at hand.

 

[mathwonk]

I don't have much of that kind of data, partly because it never interested me and partly because I am retired and do not belong to hiring committees anymore.

I just did math because I loved it more than any other subject and wanted to learn as much as possible. Then I chose algebraic geometry over my first love, algebraic and differential topology, because it was more difficult and hence more fascinating. Once I almost resigned the one permanent job I did have in favor of a temporary position at harvard because i thought it was a more mathematically exciting place to be.

I do not advise choosing a field solely for any of those practical reasons you give, because math is so hard and so competitive in every subfield that I doubt one can survive mentally unless one has a strong enjoyment of the stuff one thinks about.

You also have to enjoy teaching because the percentage of time you have in academia to think about research is MUCH less than 90%. Teaching, tutoring, advising, grading, writing notes, serving on committees, hiring, voting, writing dossiers for other people to receive awards or promotions, interviewing, preparing prelims and tests, helping students prepare for them, writing or reviewing grant proposals, revising and writing up largely finished results, ...these activities consume most of your time, especially teaching and grading.

I used to try to set aside 3-5 hours one day a week to discuss research and it frequently got cut into by other duties. Back when our teaching loads at UGA were the highest of any research university in the nation, I often noticed that research work on my computer was only updated during holidays, thanksgiving week, christmas week, spring break, summer...

My son majored in math with emphasis in numerical methods I believe and he has a good job that pays well in silicon valley. But he is very smart and very hard working and his field too is extremely competitive. He is on call essentially 24 hours a day, 7 days a week, even when on vacation, to "put out fires" at his company. And lots of his friends in the same industry have lost their jobs over the past several years.

Some people I know seem to enjoy their work at NSA, if you do not mind working for the government, say breaking codes, or making them.

 

[weld]

Thanks for the helpful reply mathwonk! :D

You also have to enjoy teaching because the percentage of time you have in academia to think about research is MUCH less than 90%. Teaching, tutoring, advising, grading, writing notes, serving on committees, hiring, voting, writing dossiers for other people to receive awards or promotions, interviewing, preparing prelims and tests, helping students prepare for them, writing or reviewing grant proposals, revising and writing up largely finished results, ...these activities consume most of your time, especially teaching and grading.

I used to try to set aside 3-5 hours one day a week to discuss research and it frequently got cut into by other duties. Back when our teaching loads at UGA were the highest of any research university in the nation, I often noticed that research work on my computer was only updated during holidays, thanksgiving week, christmas week, spring break, summer...

What? I've heard elsewhere that in math there's almost no such busywork. That you get like 89% of your time for research as a tenured prof, and 79% when on tenure track. I really would like to believe one gets away from teaching duties and other forms of busywork when in math but if reality says, otherwise, then I can't deny. You sure having way less than 90% of your time for math research is normal in most universities? Cause you said your uni at one point had the biggest teaching loads in the nation, so you sure it's not unique to UGA?

My son majored in math with emphasis in numerical methods I believe and he has a good job that pays well in silicon valley. But he is very smart and very hard working and his field too is extremely competitive. He is on call essentially 24 hours a day, 7 days a week, even when on vacation, to "put out fires" at his company. And lots of his friends in the same industry have lost their jobs over the past several years.

Interesting. How many hours/week would you say Silicon valley people put in, like 70-80/week average? Also, say I got an education in CS and got a job at some well known tech company, would the research done be as interesting as that which is done in academia or mediocre in comparison?

Some people I know seem to enjoy their work at NSA, if you do not mind working for the government, say breaking codes, or making them.

By doing this, are you doing something essentially new like when doing research? Discovering anything new? For working within the same old limited paradigms gets old quick. :(

 

[Bourbaki1123]

By doing this, are you doing something essentially new as you are when doing research? For working within the same old limited paradigms gets old quick. :(

Not only would you being doing stuff that is new, you'll have access to top secret bleeding edge math, algorithms, technology etc. The NSA actually makes you sign a legally binding contract to not work on what you had been doing there (I think it "only" binds you for a decade though) if you decide to leave.

 

[weld]

That's interesting Bourbaki. Would you say a NSA employee is essentially a researcher without busywork (teaching, applying for grants, sitting in committees etc)? Also, do you think they research things other than cryptography there? Also, what are the cances of gaining employment at a place like NSA? What do you imagine thw orkweek and job sceurity would be like? Bad job security and like 80h/week?

 

[mathwonk]

bourbaki, i guess first place probably went to jimmy fidelholtz. at least my teacher used to say we should not expect to beat him, as he had worked his way through a calculus book all by himself.

 

[Bourbaki1123]

bourbaki, i guess first place probably went to jimmy fidelholtz. at least my teacher used to say we should not expect to beat him, as he had worked his way through a calculus book all by himself.

I'm not sure if I should, but I find that to be pretty humorous. It evokes the image of an elderly schoolmarm peering down at you through her spectacles, "You ought not expect to outdo young Mr. Fidelholtz as he has worked through a calculus text all by himself, isn't that right jimmy?" :panning shot to Jimmy with a sh**-eating grin on his face:

Any idea what has become of him?

 

[mathwonk]

i googled him and he seems to be a linguist living in mexico.

 

[Bourbaki1123]

That's interesting Bourbaki. Would you say a NSA employee is essentially a researcher without busywork (teaching, applying for grants, sitting in committees etc)?

Sure, but you have to add academic freedom to the list; I doubt they'll let you research anything you want to. It has to be stuff that is critical to national security, or at least could be critical down the road. Mostly cryptology and computer security stuff as far as I know; of course I could see some game theory and computational complexity stuff as well.

Also, what are the cances of gaining employment at a place like NSA? What do you imagine thw orkweek and job sceurity would be like? Bad job security and like 80h/week?

These sorts of things I can't really give you any solid answer since I would like to know myself.