Other Should I Become a Mathematician?

[U.Renko]

The math graduate student I talked to was very depressed.

Well, that explains a lot.

Honestly: When seeking advice or when you need to make decisions, avoid talking to depressed people.

 

[Mépris]

I was really hoping you could answer my question, being an experienced professor. I will try and make it more clear this time.

I am curious about the level of ability that can be attained, which is different than the ability to get into top schools.

The math graduate student I talked to was very depressed. Even getting into a top 20 school and being top in his class he was still lamenting that he was light years behind the students who started when they were kids and wished he went into another subject he liked: physics- where he could make a contribution.

Now I definitely do not want to be make a critical decision based on a grad students word. I came here to cross check my sources , hopefully from people with experience in academia.

I know that you had a roundabout way getting a PHD, but to my understanding you had an incredibly good start when you were young.
How much of a persons potential is tied to starting math early?
Do you know others who started proof based math in university and were able to succeed?

Hopefully my question is more precise this time!

If you were to read back through this thread, I'm certain you'd find that he mentioned that his math background was somewhat limited when entering college.

That was quite a few years ago and I can only guess but I doubt there were too many Terry Taos then either...

 

[bpatrick]

I am curious about the level of ability that can be attained, which is different than the ability to get into top schools.

...

How much of a persons potential is tied to starting math early?
Do you know others who started proof based math in university and were able to succeed?

A book everybody should read who is having questions about early career in mathematics is:

A Mathematician's Survival Guide: Graduate School and Early Career Development by Steven G. Krantz.

It answers so many questions and has given me much inspiration considering my university education was Musicology and pre-medical, with my graduate education being Trumpet performance ... I didn't see a formal proof until JUNIOR year of college ... aka when I was 20.

If I felt I was in some way inferior to somebody who had blazed through undergrad math and passed the PhD qualifiers when they were 20, I'd have second doubts too, but age has nothing to do with your ability to succeed as a mathematician. Most of the professors I have studied under (a few who were PhD'd by ivy league programs and have wonderful careers) have said that work ethic and the ability to endure failure are much better traits to have than early prodigy status.

As far as I'm concerned, everybody is more or less on equal standing when they get to the point where they can pass all their quals. Some will do it at age 20, some at age 30, and yeah that may make the 30 year old significantly less likely to win the Fields medal (me included), but whatever, I'd rather take the Nobel prize money ... which has no age limit.



Good luck with whatever you chose. That book is more than worth the read. You can probably find it somewhere online without too much trouble ... djvu versions are out there and quite easy to find for free.

p.s. an afterthought I had ... statistically, there may be a correlation between age of getting to the level when you are able to do original research and how "fruitful" your career is. However, I would imagine this is more due to the fact that the "prodigy" may be more socially inept due to discrimination at points in their life, combined with being pushed by guardians and advisers to the point of not having a "normal" social life, hence increasing their mathematical productivity ... like I'm probably not going to ever be a famous award winning mathematician / biophysicist, but I would argue that is because I will spend a large portion of my time with my fiancee (and eventually children) and catching a game plus a few drinks with friends rather than pushing myself totally in applied mathematics. Will I have a productive and fruitful career, sure, but I still think that has much less to do with age, but rather to level of devotion to the field.

 

[Stylish]

Hey n_student. Like you, when I was a freshman I also had no experience with things like proofs. In fact, I had never had any experience with proofs until an analysis/introduction to proofs class in my junior year. Needless to say, I had a lot of trouble with even the simplest of proofs at first.

It was also at this point though that I realized math is what I wanted to do; I originally chose it as a major because I (thought) I was good at it. I spent a lot of time studying for that class, and by the end of it I had more than caught up with my peers.

I didn't just learn how to do proofs though. I realized that hard work and dedication can go a long way, and not just in mathematics. I think you are at a huge advantage because you've already stated that you are "really devoted" and an "incredibly hard worker". Now I am having to spend my time going over all of my earlier courses because I didn't bother trying to truly understand the material, but if you start studying now I'm sure you'll be just fine.

 

[eliya]

I think people shouldn't judge themselves just by statuses. That is, you can't think you're not a good mathematician because you didn't get your PhD from a top 10 school, and aren't teaching in a top 10 school.
I think that mathematicians are people who like doing math, not people who like staring at their diploma that has some big name school on it. If you like doing math then it doesn't matter when you started, where, or how big of a contribution you'll make. What matters is whether or not you like doing math or not.
Yeah, there are benefits for studying at a highly ranked school, or for teaching at one, but remember the following:
If you're in a big department, then it is very likely that there will be a lot of visitors who will give talks in your school. There are also many different mathematicians in your department, and I'm sure they're all very smart and that they are all people you can learn from. Also, sometimes you can be at a school that isn't ranked very high, but is close to other great schools, so you can always make a small trip for a seminar or a talk. For instance, you can go to Brandeis, which has a smaller math department, but be very close (geographically) to MIT and Harvard. Same thing with universities in Chicago and NYC; they're all close to other universities.

Lastly, I think that the math you do in high school requires different thinking than math you do at the university level. I think that people are capable of both kinds of thinking. Being bad at high school math doesn't mean you can't do well in higher level math. Just work hard at your classes, and make sure you really understand the material. Don't think about status. It doesn't really matter in the end.

P.S. Before anyone criticizes me. I'm not saying that highly ranked schools are ******** or that they're unnecessary. I just think people can do well in math at other places.

 

[mathwonk]

Did you know the Fields medalist Hironaka was at Brandeis before he was at Harvard?

 

[Nano-Passion]

Did you know the Fields medalist Hironaka was at Brandeis before he was at Harvard?

According to wikipedia it was kyoto university not Brandeis.

http://en.wikipedia.org/wiki/Hironaka

The university seems to be a very solid one too.
http://en.wikipedia.org/wiki/Kyoto_University

 

[mathwonk]

i didn't know where he got his BA, I meant he was on the Brandeis faculty before he went to the faculty at Harvard. As I recall, he went from the faculty at Brandeis to that at Columbia and then to Harvard. I was trying to illustrate the fact that many less famous schools have outstanding faculties. Hironaka also lived in Kyoto when the ICM was held there in about 1992, and I believe he was also on the faculty there at RIMS.

 

[AcidRainLiTE]

Hi Everyone,

I want to apply to graduate school this year for a PhD (or possibly masters, but with the eventual goal of a PhD) in math. As an undergrad, I did a double major in math and physics with physics being my primary major.

My application is strong, with the exception of my Math Subject GRE scores. I did really poorly on them (43rd percentile or 620 out of 900), mainly because I didn't study correctly. Other than that, I have straight A's or A- in all of my math and physics courses and have good scores on the general GRE (94 percentile in verbal, 91 percentile in quantitative). I also am sure my professors will give me strong recommendations.

My questions is, will my bad Subject GRE scores destroy my chances at getting into grad school this year? I know I could take them again, study properly, and do much better, but that would mean I would have to wait to apply until next year. I would really like to go this year. I graduated in 2010 with my BS, have been working since then, but am ready to go back to school and would like to do so without working another year in the corporate world. What do you think? What are my chances of getting in?

 

[homeomorphic]

Hi Everyone,

I want to apply to graduate school this year for a PhD (or possibly masters, but with the eventual goal of a PhD) in math. As an undergrad, I did a double major in math and physics with physics being my primary major.

My application is strong, with the exception of my Math Subject GRE scores. I did really poorly on them (43rd percentile or 620 out of 900), mainly because I didn't study correctly. Other than that, I have straight A's or A- in all of my math and physics courses and have good scores on the general GRE (94 percentile in verbal, 91 percentile in quantitative). I also am sure my professors will give me strong recommendations.

My questions is, will my bad Subject GRE scores destroy my chances at getting into grad school this year? I know I could take them again, study properly, and do much better, but that would mean I would have to wait to apply until next year. I would really like to go this year. I graduated in 2010 with my BS, have been working since then, but am ready to go back to school and would like to do so without working another year in the corporate world. What do you think? What are my chances of getting in?

Get in where? I don't think it's that important that you have to get into the top schools. You might not get into Princeton or Harvard, but that's not the end of the world. Assuming you aren't broke, you should just apply and see what happens. You won't lose anything except a modest amount of time and money. You can always try again later. If you don't insist on going to one of the very top places, I don't think you'll have any trouble. Just apply to a whole bunch of places. Like 8 places, let's say.

 

[mathwonk]

the grades (and letters) are more impressive if you went to a strong undergraduate school. is that the case?

 

[bpatrick]

You said you have solid grades and also focused a lot in physics, so assuming you went to a good undergraduate institution, you'll probably be fine almost anywhere other than the top math programs in the US. I'd imagine that an admissions committee would see your 43rd % on the GREs along with your solid undergrad physics and math course grades and reason that you did fine on the calculus / differential equations / linear algebra end of it but didn't know much when it came to the algebra/topology/geometry/discrete areas that were tested by the math GRE.

So if that all is the case, I'd imagine you have a good chance at getting into many programs if you're personal statement reflects eventually getting into applied math / mathematical physics / PDE's / etc...

If you're trying to go for ivy league programs or any that focus mainly in pure math, I'd imagine they wouldn't take the risk of investing in you with those test scores, especially since many of the top programs are more "pure math" oriented and wouldn't want to bring in a student who possibly needed remedial work or didn't stand a great chance at passing their qualifiers after the first year.

 

[homeomorphic]

You said you have solid grades and also focused a lot in physics, so assuming you went to a good undergraduate institution, you'll probably be fine almost anywhere other than the top math programs in the US. I'd imagine that an admissions committee would see your 43rd % on the GREs along with your solid undergrad physics and math course grades and reason that you did fine on the calculus / differential equations / linear algebra end of it but didn't know much when it came to the algebra/topology/geometry/discrete areas that were tested by the math GRE.

So if that all is the case, I'd imagine you have a good chance at getting into many programs if you're personal statement reflects eventually getting into applied math / mathematical physics / PDE's / etc...

If you're trying to go for ivy league programs or any that focus mainly in pure math, I'd imagine they wouldn't take the risk of investing in you with those test scores, especially since many of the top programs are more "pure math" oriented and wouldn't want to bring in a student who possibly needed remedial work or didn't stand a great chance at passing their qualifiers after the first year.

Not really. The math GRE barely tests that stuff. It's 50% calculus. If he's like me, he just made a lot of calculation errors or wasn't fast enough. And that's probably what the admissions committees will think. It's a silly test. It's basically all about having lightning calculation reflexes (since it is long enough that one must be some kind of demon in order to get through the whole thing, in terms of pure manual dexterity in writing (sarcasm)) and not being prone to trivial oversights, which, conveniently, are exactly my weaknesses (I think I got 52nd percentile). Not much to do with pure math. That's only a small portion of it. It barely has any topology in it and no geometry. Tiny bit of algebra. Of course, it was 6 years ago when I took it, but I doubt it's much different.

But yes, they will see it as suspect because they are looking for an overall strong application. Sort of like one more consistency check because it's an outside source that isn't coming from the particular institution.

By the way, I know a grad student at a, let's say top 20 school, who did pretty badly on the math GRE. Maybe even in the 30s, definitely no higher than 40s. I don't remember. She didn't get many offers, but just one is enough.

 

[tyler_T]

Not really. The math GRE barely tests that stuff. It's 50% calculus. If he's like me, he just made a lot of calculation errors or wasn't fast enough. And that's probably what the admissions committees will think. It's a silly test. It's basically all about having lightning calculation reflexes (since it is long enough that one must be some kind of demon in order to get through the whole thing, in terms of pure manual dexterity in writing (sarcasm)) and not being prone to trivial oversights, which, conveniently, are exactly my weaknesses (I think I got 52nd percentile). Not much to do with pure math. That's only a small portion of it. It barely has any topology in it and no geometry. Tiny bit of algebra. Of course, it was 6 years ago when I took it, but I doubt it's much different.

But yes, they will see it as suspect because they are looking for an overall strong application. Sort of like one more consistency check because it's an outside source that isn't coming from the particular institution.

By the way, I know a grad student at a, let's say top 20 school, who did pretty badly on the math GRE. Maybe even in the 30s, definitely no higher than 40s. I don't remember. She didn't get many offers, but just one is enough.

Is it even worth reporting a score around 50th percentile to schools that recommend, but don't require, the subject GRE, like applied math programs?

 

[eliya]

Is it even worth reporting a score around 50th percentile to schools that recommend, but don't require, the subject GRE, like applied math programs?

I think you can email the program and ask if they look at the subject GRE scores or not. If they don't then there's no need to report them.
I can't see how reporting a low score will help you in any way. On the other hand, if you don't report it, they can immediately assume that you just did horribly on the exam. However, I think I wouldn't report a low score to a program that doesn't require it.
I should say, I haven't applied to grad school yet, so take it with a grain of salt.

To the "original" poster, there are a few good schools that don't require the subject GRE scores. I think Stony Brook is one of them.

 

[homeomorphic]

Is it even worth reporting a score around 50th percentile to schools that recommend, but don't require, the subject GRE, like applied math programs?

Most places require it.

Actually, someone I e-mailed when applying to grad schools said something to the effect that he considered 50th percentile to be sort of a minimum. Around 50th percentile. But that's just one opinion. People on admissions committees all have their own philsophies and that's why you have to apply to many places.

 

[tyler_T]

Most places require it.

Actually, someone I e-mailed when applying to grad schools said something to the effect that he considered 50th percentile to be sort of a minimum. Around 50th percentile. But that's just one opinion. People on admissions committees all have their own philsophies and that's why you have to apply to many places.

How strong was the program at that schools? (Top 20, top 50, etc)

 

[AcidRainLiTE]

the grades (and letters) are more impressive if you went to a strong undergraduate school. is that the case?

I went to a small private school, Grove City College (http://colleges.usnews.rankingsandreviews.com/best-colleges/grove-city-college-3269). It is pretty strong academically, but I am doubtful that it is very well known.

I am looking to apply to programs in pure math, not applied math. From some of the replies, it seems that may be a bit harder with the low GRE score.

To the "original" poster, there are a few good schools that don't require the subject GRE scores. I think Stony Brook is one of them.

Stony Brook is on my list. The only thing that bothers me a bit about the program is that it has very little in mathematical logic/set theory/foundations of math. Some of the other programs I have looked at (Maryland, Penn State, Illinoise, UCLA, Michigan, Notre Dame) seem to have a bit more in that area. And that is one of the areas I am potentially interested in. Either that or Topology or Geometry. The good thing about stony brook, though, is they would be a good place for me to pursue my dual interest in math&theoretical physics (if I do want to continue in physics), since they seem to have a good theoretical physics department.

 

[homeomorphic]

How strong was the program at that schools? (Top 20, top 50, etc)

Maybe 20-40 range. Actually, I think even he would probably say it's just a general rule that could have exceptions if the rest of the application was particularly strong.

I am looking to apply to programs in pure math, not applied math. From some of the replies, it seems that may be a bit harder with the low GRE score.

I don't think it makes any difference whether it's pure or applied. Typically, you get to choose AFTER you get accepted, whether you want to do pure or applied. They don't even ask, except you might mention it in your application.

Stony Brook is on my list. The only thing that bothers me a bit about the program is that it has very little in mathematical logic/set theory/foundations of math. Some of the other programs I have looked at (Maryland, Penn State, Illinoise, UCLA, Michigan, Notre Dame) seem to have a bit more in that area. And that is one of the areas I am potentially interested in. Either that or Topology or Geometry.

Most of those sound at least somewhat realistic. If you don't mind spending the money, apply to Michigan and UCLA, but be aware that places like that turn down fantastic people. I've known people with seemingly unbeatable applications that apply mostly in the top 15 and they typically only get into 2 or 3 out of 8. No one should count on getting into a place like Harvard unless they already have 2-3 years of graduate level classes under their belt, more or less straight As in their subject, preferably already published, etc, plus fit the department. I think sometimes they just decide to take a chance with someone who doesn't have that kind of record, though. Ed Witten was a history major and somehow got into Princeton. I'm not sure exactly how that happened, except, evidently, his dad was a physicist, so he wasn't just starting from scratch.

 

[mathwonk]

you should choose your school based on whether they have your interests, keeping in mind that your interests can easily change once you join a strong department.

to get a look at your school compared to others, you might take a look at their departmental website and check out where your professors got their own phd's. you will note that they themselves went to good but not super famous schools. if you ask one of your own teachers who got a phd at say notre dame, she can tell you whether you would find that school a reasonable fit.

admissions committees do not look just at one factor, but try to discover from all aspects of it, which candidates have the most potential. i am virtually sure you will gain admission to a school where you can fit in well. those gre scores are not as low as you seem to think.

i do not recommend applying to harvard, unless your letters are incredibly strong, but i do suggest applying to schools comparable to my institution, university of georgia.

i must observe however that set theory is not widely considered a serious research topic, and may not be represented at many places. geometry on the other hand is an extremely serious subject in pure math. ( of course i am a geometer)having looked at your list, i suggest speaking with some professors at those places to see what they think. in this context however, i recall my own story again - i was interviewed and rejected by eilenberg for columbia in 1965. then in 1980 when i was at harvard i met eilenberg again and he apologized for not recognizing my ability. so the story is never over until it's over.

 

[eliya]

Stony Brook is on my list. The only thing that bothers me a bit about the program is that it has very little in mathematical logic/set theory/foundations of math. Some of the other programs I have looked at (Maryland, Penn State, Illinoise, UCLA, Michigan, Notre Dame) seem to have a bit more in that area.

UIC have a few logicians, and they seem to hold a few logic and set theory seminars. I don't know how that compares to Stony Brook or the other schools on your list that in terms of logic and set theory.

 

[gniedom]

Calc midterm tomorrow. Anyone want to help with this suggested problem?
Limits of the form limxgoesto inf xe^-x.
(i) Evaluate limxgoesto inf xe^-x.
(ii) Fix a positive intger n and assume that limxgoesto inf xe^-x.= 0. Show that
it must be the case that limgoesto inf x^n+1e^-x = 0 as well.
(iii) From (i) and (ii), what can you say about the value of limxgoesto inf xe^-x.
for any positive integer s? Explain your reasoning.

 

[mathwonk]

try one of the math or homework threads. (hint: l'hopital)

 

[DrummingAtom]

So this semester is winding down to an end and a couple months ago I was intrigued by Differential Equations but my whole interest has shifted to Linear Algebra. There is a slight disclaimer though when I say I'm interested in Linear Algebra... The class I'm currently taking is a combined DE/LA class and actually it kinda stinks. We learned a whole bunch of LA concepts in about 3 weeks then used them to solve DE's. I went out and self studied some things on my own and the geometric properties/concepts in LA are fascinating.

I'm probably going to spend all winter break studying more LA but I don't really know where to pick up. In class I have learned vector spaces, eigenstuff, matrix operations, linear independence, and a little about basis. This class has been a crash course and although I am picking up somethings I want to know the theory of LA much more because I can feel there is something very deep going on. What are usually the first topics studied in LA from a pure math perspective?

Also, I was pretty disappointed with the presentation of some of the topics in LA because it seemed like they were making things much more complicated than need be. The book I have for class made it seem like the determinant was just pulled out of thin air and never once mentioned it's geometry! After browsing through a bunch of books in my school's library I noticed almost no LA books talk about the geometry of determinants. Is anyone else disappointed by this?

 

[matqkks]

Yes it has been frustrating to see lack of geometric interpretation of LA concepts. Have a look at Gilbert Strang website at MIT to liven this subject.
I have also set up topics on this issue through this forum.
Determinants of 2 by2 gives the area scale factor, 3by 3 gives the volume scale factor.
Negative determinant changes the orientation of the area, volume.
Determinant of 1 preserves the lengths, angles etc.
I have some notes on this topic, let me know via email if you would like a copy.

 

[Nano-Passion]

Yes it has been frustrating to see lack of geometric interpretation of LA concepts. Have a look at Gilbert Strang website at MIT to liven this subject.
I have also set up topics on this issue through this forum.
Determinants of 2 by2 gives the area scale factor, 3by 3 gives the volume scale factor.
Negative determinant changes the orientation of the area, volume.
Determinant of 1 preserves the lengths, angles etc.

At some point I kind of accepted that linear algebra is devoid of geometric interpretations. If others have links that supply the geometric interpretations then that would be appreciated.

I have some notes on this topic, let me know via email if you would like a copy.

Hmm, not to be nosy or anything but I would also like an email of this. That is if you don't have to go out of your way typing it out and stuff.

 

[homeomorphic]

At some point I kind of accepted that linear algebra is devoid of geometric interpretations. If others have links that supply the geometric interpretations then that would be appreciated.

I think it's a pretty geometric subject. However, when you pass to complex vector spaces or vectors spaces with other fields, it gets more abstract and it's not exactly so geometric, but you can pretty much think of it the same way by analogy. The bulk of what I understand about linear algebra was learned after I took the class in the course of learning other things.

I didn't really learn the subject from books, but you might try Linear Algebra Through Geometry. Never read it. I just like the sound of it. For more advanced stuff, I think Linear Algebra Done Right is good.

What are usually the first topics studied in LA from a pure math perspective?

Vector spaces, bases, linear independence, linear transformations, matrices that represent linear transformations. That's the core of it.

Also, I was pretty disappointed with the presentation of some of the topics in LA because it seemed like they were making things much more complicated than need be. The book I have for class made it seem like the determinant was just pulled out of thin air and never once mentioned it's geometry! After browsing through a bunch of books in my school's library I noticed almost no LA books talk about the geometry of determinants. Is anyone else disappointed by this?

Yes. I find it extremely annoying. Why do they insist on being so rigid, formal, and boring? It's a shame.

 

[DrummingAtom]

Yes. I find it extremely annoying. Why do they insist on being so rigid, formal, and boring? It's a shame.

Yeah, I don't know anything about higher level math because I'm only up to Diffy Q's right now. But it seems the biggest mystery to me is why most math professors teach abstractly first then proceed to go back and do examples and conceptual things. The lectures and most of the books I've seen follow this method and I can't understand why. To me, definition, theorem, proof, then concepts is backwards in every aspect; heck sometimes the concepts don't even follow it just ends with the proof.

I really like math and want to know more about it but honestly my "discovering" math is when I sift through the abstract stuff and find out the concepts really aren't as hard as they are made it out to be.

By the way, homeomorphic, I took your advice and checked out V.I. Arnold and he seems exactly like my type of math guy. Visual and intuitive. His article on teaching math was inspiring for someone like me. Once I get Linear Algebra out of my system I'm going to buy his ODE book. Thanks for the recommendation.

 

[homeomorphic]

Yeah, I don't know anything about higher level math because I'm only up to Diffy Q's right now. But it seems the biggest mystery to me is why most math professors teach abstractly first then proceed to go back and do examples and conceptual things. The lectures and most of the books I've seen follow this method and I can't understand why. To me, definition, theorem, proof, then concepts is backwards in every aspect; heck sometimes the concepts don't even follow it just ends with the proof.

There are books that are like definition, theorem, proof that are pretty good. It depends on how it's done.

I really like math and want to know more about it but honestly my "discovering" math is when I sift through the abstract stuff and find out the concepts really aren't as hard as they are made it out to be.

Yeah, pretty much. I'm usually aware from the start that a textbook/prof is not giving nearly as much intuition as they should, but it can be even more striking when you actually understand the subject and see how badly they butchered it. Math is difficult. The fact that it is difficult is part of what makes it so outrageous for them to complicate matters and make it 20 times more difficult than it ought to be.

By the way, homeomorphic, I took your advice and checked out V.I. Arnold and he seems exactly like my type of math guy. Visual and intuitive. His article on teaching math was inspiring for someone like me. Once I get Linear Algebra out of my system I'm going to buy his ODE book. Thanks for the recommendation.

The ODE book is good, but it's a little difficult. I think you'll definitely see his visual, intuitive thinking show through, but it's not an easy book. I think probably my favorite book of Arnold might be the one on classical mechanics, although I don't consider to be perfect. The best place to start would be Visual Complex Analysis. Pretty elementary. Very visual, as the title suggests. Very entertaining.

 

[sponsoredwalk]

You guys should never look at Bourbaki's or Hoffman/Kunze's definition of the determinant so