Should I Become a Mathematician?

[PowerIso]

I don't know why you'll be "ruled out." I don't think a university can punish you for being a good student!

 

[mathwonk]

you'll have to ask if you can get credit for both. the good part is you are learning the material.

dummitt and foote is a good book for use at several levels, from beginning undergrad to beginning graduate.

 

[kaotak]

Ah, okay, thanks.

I was afraid I'd be ruled out because if I were to take the class in a year or two from now, I may have already done a good portion of the problems on the assigned problem sets, giving me a bit of an edge. Though I'm probably being paranoid, since any student can do this, and a lot probably do this during the summer preceding the course.

So I'll just dive into it then in my free time.

 

[JasonJo]

How bad does a 740 on the GRE quant look? I mean the regular GRE exam. Should I even bother retaking the exam if I want to get into a top 10 grad program?

 

[leon1127]

How bad does a 740 on the GRE quant look? I mean the regular GRE exam. Should I even bother retaking the exam if I want to get into a top 10 grad program?

I got 800 on it and i got rejected by top 20 schools.

 

[JasonJo]

I got 800 on it and i got rejected by top 20 schools.

I don't know, first of all I don't have the cash to retake it. I guess I'll have to look at some different schools. Thats the only bad mark on my grad school application. I have a 3.81 GPA, I'm doing an honors thesis in mathematics on an unsolved problem (not that its the buzz of the field, but it is unsolved and definitely publishable is what my professor said), i just finished an REU in math over the summer, I can get 3 really good letters of reccomendations and my undergrad instituion is a top 20 grad school in it's own right. the only other variable left is my GRE math exam. I guess I'm the lots of research experience, good grades, good letters, did not do well on the standardized exams (i'm hoping I can get a good GRE math score to make up for the GRE quant).

 

[leon1127]

I don't know, first of all I don't have the cash to retake it. I guess I'll have to look at some different schools. Thats the only bad mark on my grad school application. I have a 3.81 GPA, I'm doing an honors thesis in mathematics on an unsolved problem (not that its the buzz of the field, but it is unsolved and definitely publishable is what my professor said), i just finished an REU in math over the summer, I can get 3 really good letters of reccomendations and my undergrad instituion is a top 20 grad school in it's own right. the only other variable left is my GRE math exam. I guess I'm the lots of research experience, good grades, good letters, did not do well on the standardized exams (i'm hoping I can get a good GRE math score to make up for the GRE quant).

I wish i have retaken my GRE for the verbal section... I regret now because I didnt not get into any PhD programme.. and it was 1300 dollars of application fee. I think you should pay extra 100 dollars to avoid not getting into a better school (and try to apply again in the next year)

 

[JasonJo]

I wish i have retaken my GRE for the verbal section... I regret now because I didnt not get into any PhD programme.. and it was 1300 dollars of application fee. I think you should pay extra 100 dollars to avoid not getting into a better school (and try to apply again in the next year)

I got a 630 on the verbal, which I think is like an 87% score, which is actually a higher percentile than my math. I'm still gunning for a top 10 school.

 

[mathwonk]

why do you want to get into a school where the criteria for admission are higher than you are able to achieve? do you want to set yourself up to fail? or do you believe the admissions process is flawed? why not go where your scores place you? maybe that is a better fit for you?

 

[eastside00_99]

That's why a person should apply to a range of schools and not just top ten programs (well I guess some can just apply to the very best). What has been going through my mind is that I want to go to the best place possible and one that is also right for me.

What I mean by best place is one with research interest close to mine, good overall ranking, good location, and a place where people get a range of jobs after finishing the program. That is what I think of when I think of best.

This leads into my next criteria which is one that is right for me. It is completely possible to go to say Princeton and be completely miserable. It is competitive I am sure and maybe not suited for those who don't need that push of fierce competition as much. Also, you want to get a Ph.D. and not say well I went to Berkeley for two years and dropped out (I stole these words from someone). I am convinced of that after learning that a friend of mine quite his Ph.D. after a few years. They certainly seem more capible than me from my vantage point, but they said it was just too depressing. They where at a very good school (especially for what area of research they wanted to do).

In regards to the admissions process, yes it is flawed in some ways. One year, it can be relatively easy to get into a program and the next near impossible. No one knows what will happen; not even you. This happened at my school this year. They got a surge of really great applicants for some reason whereas a neighboring school which is ranked much better ended up accepting some of the people that were denied from my school. That has nothing to do with scores or admission criteria but luck of the draw. Now, granted, There is the bear minimum and there is a such thing as a strong application, but missing or hitting both of those does guarantee rejection or admissions.

Then I guess there is the more existential side of the whole thing...

But, Mathwonk, I actually have a question for you: do you know many undergraduates to go overseas to get the Ph.D. I know some probably study at Cambridge for year or something. But, what about in Germany or even Japan?

 

[eastside00_99]

Let me just add, I just don't see what the worry is. I guess I have change my stance on this. As long as one doesn't have debt (and a family to take care of), there is always the ability to study and eventually do research in mathematics no matter the person. Its kind of sickening to see people so concerned with what are good marks, where their degree is from, how many papers one has written, et ceteria. That probably stiffles a lot of creativity in ones life (and not just mathematical creativity). As far as I can gather the hard part of being a mathematician, is the intellectual changellenge of math itself and not how one can put themselves in an optimum position to get tenure at a research institution. The latter is hard of course, but it is nothing in comparision to the former. I am ashamed I even asked about this and have worried about it as much as I have. It reminds me of the former Harvard student who is now a proffessor at Harvard who was completely obsessed with his GPA (argueing to get A- changed to As with his profs) and becoming a mathematics professor at Harvard. The fact that he did it says something tremendous about what people can accomplish, but the way he went about it is well not very respectible or encourageing. I prefer the stories of people solving 40 year problems and then getting the due respect that their work really deserves.

 

[sepowens]

The whole GRE/Top Ten is a load of crap. It is the academic equivelent of a Paris fashion show where the women come out wearing nothing but a basket of fruit on their head and an ugly scarf. Do not fall into it. I do realize that dropping the name of certain schools improves your initial prospects but five years into your career it wil be the papers YOU publish and YOUR reptation in the field that counts.

Look for a program that fits your style of learning and working. Interview the professors (yes, you ask them if they can work with you!) even if just by phone. In other words you need to find not the NAME or the pile of Ivy covered bricks but the PEOPLE you can best achieve your goals with. Contrary to popular belief the top ten have just as many people who could not teach their way out of a wet paper bag as Podunk Community College. The difference is that it is the hardest working students that are fighting to get in there and make up for the inherent deficienies in any institution.

The professor I have most admired resigned after achieving tenure in record time from one of the most prestigious universities in the South to teach at the local technical college. There was no apparent scandal and I finally got the nerve to ask him why. He told me he had studied economics because he loved economics and he had become a professor because he loved to teach economics. He then explained how at the larger institutions it is frowned upon if you get your hands too dirty working with all those nasty students and senior professors are expected to put as much of that nasty teaching stuff on grad students and sit around thinking lofty thoughts. He was the best teacher I have ever known and with him it was not the 'Dismal Science' but an exciting and relevant part of everyones life. And that is the key. Find a school with just a few people like him that still see the beauty and excitement of their field and you will be drug along to your goals rather than chasing them.

 

[JasonJo]

why do you want to get into a school where the criteria for admission are higher than you are able to achieve? do you want to set yourself up to fail? or do you believe the admissions process is flawed? why not go where your scores place you? maybe that is a better fit for you?

maybe so, maybe it is irrational to keep trying. but i can't give up on my dreams. i can't let people try to take that away from me.

 

[jonasK]

http://terrytao.wordpress.com/career-advice/does-one-have-to-be-a-genius-to-do-maths/

http://terrytao.wordpress.com/career-advice/

That's the guy you should be listening to.

 

[J77]

That's the guy you should be listening to.

One guy?

That's narrowing your viewpoint a bit...

 

[mathwonk]

your dream seems misdirected, i.e. it relates to where you study rather than what you learn.

have you considered, for math, such places as university of utah? chris hacon there is a recent recipient of a clay math institute award and a possible fields medal candidate for his recent work.

there are many other outstanding professors there as well, such as aaron bertram, dragan milicic, etc...

 

[pivoxa15]

Do you think it's best to start off in a pure area of maths first then branch out to more applied areas later on?

So in that case start off in a foundational area like mathematical logic?

 

[cristo]

So in that case start off in a foundational area like mathematical logic?

Well, every mathematician should know basic logic! But I don't know what you mean, or whether you are talking about undergraduate studies or not. If so, then are you not forced to take a wide range of courses so you have a basic background in everything?

 

[kaotak]

you'll have to ask if you can get credit for both. the good part is you are learning the material.

dummitt and footem is a good book for use at several levels, from beginning undergrad to beginning graduate.

Sorry to revive the topic. But this remark kind of lurked on my mind. The ind. study is unofficial, so I am not getting credit for it. Should I still ask if I can get credit for the algebra class, which I will take in a year or two from now, if I pursue my independent study? I imagine that a lot of people buy the textbooks the summer in advance to prepare for class.

 

[pivoxa15]

Well, every mathematician should know basic logic! But I don't know what you mean, or whether you are talking about undergraduate studies or not. If so, then are you not forced to take a wide range of courses so you have a basic background in everything?

Offcourse. I was asking about whether one should start doing research in mathematical logic like Von Neumann who did his Phd in foundations of maths then branched out to other fields rather successfully. Not everyone is a Von Nuemann but I wonder how good was that strategy.

 

[mathwonk]

von nuemann?

 

[pivoxa15]

I spelt it right the first time it's Von Neumann :)

I'm only giving an example that's all, nothing personal in it.

 

[mathwonk]

all i can say is that very few people to my knowledge have used the strategy of starting off in one field then switching successfully to another.

i only know a couple of people who have studied math logic. they tend to be very smart people, and can indeed go in other directiions.

i do not think the training in logic particularly helped them though, they were just really smart.

 

[pivoxa15]

So for the average mathematician at which point do they lock themselves into a field?

 

[eastside00_99]

I say once you start working on you dissertation your locked into your field for the next 7 years probably. I really don't know. Mathwonk could probably give some idea about this. But, you work on you disertation for probably 3-4 years and then work for the next 3 to expand on what is in it and put it in publish form. Of course, you want to consider things not in your dissertation and continue some of the proposed future area of research that you dissertation promises. My prof said it is harder today to change research fields because universities want you to have a strong research program (something that could be hard to do if you move around a lot). He himself moved around a lot. He started out as an algebraist working in the field of homological algebra but then becam an analysist working in global analysis and math physics. (That was the big change he did but I am sure he looked at may areas of math in between by the way he talks about it). But, most of the success stories in research (especially people who branch out to other areas) that I have heard is where people get interested in something and their work naturally takes them to other areas of math.

 

[mathwonk]

i started in topology then went to several complex variables, then wound up in algebraic geometry. this was all to the good since algebraic geometry used all those other fields.

because algebraic geometry is so broad, it is possible to change from it to some other fields, especially if you are very flexible and strong. it is not at all unusual for mathematicians to go to physics afterwards, e.g.

or for algebraic geometers to consult with number theorists, or even some algebraists.

david mumford went from algebraic geometry to artificial intelligence. pure math is maybe the hardest, and it is possible to transfer to other fields in old age using what you have learned as a crutch, especially if you have a partner who can provide the knowledge from the new field.

i myself am rather narrow in a broad way, and went to alg geom in 1965, then played in diff top for 4-5 years, then went back to alg geom, in 1977 and stayed for the last 30 years.

i like number theory too and topology but there is big pressure to get grants and that is tough otuside your narrow specialty. i.e. if you are the best expert in the world on callifragilistic bendyles, it is tough to get a grant playing around briefly with spondilishous hardilooliholes.

 

[pivoxa15]

Interesting, so having done topology and algebra at a high level, in general terms, do you think topology is not as rigorous as algebra nor analysis? Why or why not? How would you rank the three fields in increasing order of rigor?

Have you seen physicists switching into pure maths? If so any examples?

 

[d_leet]

Interesting, so having done topology and algebra at a high level, in general terms, do you think topology is not as rigorous as algebra nor analysis? Why or why not? How would you rank the three fields in increasing order of rigor?

What does this even mean? How can one branch of math be any more or less rigorous than another? What does it mean for a branch of math to be rigorous?

 

[mathwonk]

i have not known any physicists who switched into pure math later in life, but of course there is witten, who is a physicist making tremendous strides in pure math at the same time.

different fields of math differ with respect to breadth, and hence in their applicability to other areas. but there are people who master several of them. serre wrote his thesis in algebraic topology, then became a pioneer in algebraic geometry, by introducing methods from topology into algebraic geometry (algebraic sheaf cohomology). grothendieck began in functional analysis, then revolutionized algebraic geometry further with the idea of "spectra" for rings, as well as general homological methods (injective resolutions) for algebraic sheaf cohomology.

 

[Beeza]

There is a professor in out math department who is originally a physics PhD, but I have no idea how long ago he made the switch to math.

 

[pivoxa15]

Is he in applied maths or pure maths. If applied then that isn't surprising.

Any applied mathematicians who switched into pure maths?

What about the rigor question?

Is algebraic geometry less active these days due to it being a mature field?

 

[mathwonk]

alg geom seems very active to me, but you might check out the speakers at the international congress of mathematicians to see which fields are represented most. usually alg geom is one of the most active.

see international congress of mathematicians, madrid 2006.

a quick look reveals little alg geom that time, and more topology (think poincare conjecture) and number theory.

 

[yarp]

What virtues should a mathematician have? Aside from a fully updated knowledge of his/her field, what if (s)he misses the more important qualities like great creativity and problem solving skills? I mean, you can't go anywhere if you understand the books but not most of the problems, can you?

 

[mathwonk]

he/she should love the subject and want to improve, and be willing to work hard to do so. that's about it. extreme persistence and some basic smarts takes care of the rest.

 

[symbolipoint]

Analytical Thinker, Persistant, possibly Inventive (not necessarily creative, but creative is a very helpful quality for a mathematician).

Maybe the "Inventive" quality is nothing more than a general result for being both analytical and persistant.