Other Should I Become a Mathematician?

[Advent]

I've only read half topic but it has an insane amount of advice, references, and enjoyable stuff. Thank you all, seriously.

 

[Bearded Man]

I have a good PreCalc book to recommend people. It starts with logic and set theory then moves to the field axioms. It covers a wide variety of topics from there, including the fundamental theorem of Algebra, logs, one-to-one functions and their inverses, trig, imaginary numbers...

https://www.amazon.com/dp/B000H5ESKG/?tag=pfamazon01-20

Though I have yet to read Spivak, I imagine this would be wonderful preparation for it.

 

[Robert1986]

Hey guys. So I'm in my second semester of college as a mechanical engineering major, but I'm thinking about switching to math. The reasons are simple; recently I've found that I'm better at math than any other subject (especially physics, which is likely what I'll be spending most of my time doing for the next few years considering my current major), and I just think math is cooler than any other subject I've seen so far. The reason I'm really hesitant to do so is because firstly, I have no idea what I'd do with my degree after I graduate, and secondly, and this may seem a bit shallow, I know that I'll likely be making more money as an engineer than as a mathematician, especially right after college. So I guess my question to you guys is what are some of the more lucrative career options for someone with a math PhD (I know that I'll be going to grad school regardless of my major), and what would I likely see myself doing for those first few years after I graduate? Thanks for all the help, sincerely.

EDIT: I should probably add a few more points. In a perfect world I'd major in math and get a job as an engineer (or at least in an engineering company). This is because I love math and I feel like I'd get a TON of satisfaction out of doing useful stuff for the world while also doing what I love. So I guess I should rephrase my question; how easy is it for someone with a math degree to work in an engineering firm? And I know that this will likely vary greatly from person to person, but, mathematicians of the board, how much satisfaction do YOU personally get from doing the more "normal" things that a mathematician does (research, possibly teaching, etc.).

Not true (the part about making less as a mathematician.) I read a Forbes article and the three majors that made the most money in the private sector were: Engineering, Math/CS, and Pharmacology. And, to be honest, I would imagine that there are some engineering disciplines that are causing this engineering average to go way up. ME is probably pretty good money-wise but not as good as ChemE, AE or BME, I would imagine.

Now, let's say you major in math. You say you are going to grad school. Now, what can we have you do so that you can a)make money and b)have a career you enjoy. Well, at my school, we a Ph.D. program called "Computational Science and Engineering." It is like a mix between Engineer CS and Math (and you basically get to pick the field of engineering and proportions of each component, within some loose guidelines.) It is a pretty hard program I understand, but I think if you do it you could major in math, do a lot of math in grad school and come out and get a job in an engineering firm. Everyone wins. Here is the website for the program I mention: www.cse.gatech.edu.

 

[mathwonk]

making money is largely about being flexible and making choices that enhance your earning potential. there is no salaried job that earns the big bucks. professors do better than average but do not earn a lot at most schools. but they get lots of freedom to control their own hours, as long as they bring in grant money for the school. raising your income in a university setting eventually forces you to go into administration where salaries are higher.

if you work in an engineering or internet company with your math major, your income will still depend on your willingness to do more for the company than just what you majored in. If you want to earn more you will find yourself needing to learn to manage more people, make good decisions, and help broaden your company's markets. I.e. again the bigger bucks are in administration than in day to day nuts and bolts work.

The most valuable thing you can learn from a math major is not how to solve canned polynomial or differential equations, but how to apply logic and creativity to analyze and solve a variety of problems.

 

[dkotschessaa]

Was looking for the "like" button for mathwonk's last post. Been spending too much time on Facebook and not enough time here.

 

[mathwonk]

In the same vein, if you are a researcher getting older, and your friends want you to become an administrator, but you would rather remain a researcher, think about it. Your seniors served as administrators and helped you advance your career. Maybe it is your turn. Not only will your pay go up, but you have chance to choose the direction of your research group, and to support the young talent in your department.

 

[analyzer]

Hello, everyone. I probably want to become a mathematician. When I was in high school, mathematics was the only subject in which we were required to think. I should mention, though, that most of the mathematical problems we were faced with were one-step and done, and involved no calculus. Perhaps I liked math at that time because I was the best student in my course.

After graduating from high school, I went through a period of crisis. I sort of became paranoid. I used to have delusions. Previously, I had been diagnosed with obsessive compulsive disorder. Now, I am 26. I have been taking medicines for the past ten years.

At 22, I decided to enroll in a 3-year technology program (I believe the equivalent in the U.S. is an engineering technology program). Soon after enrolling, I became discouraged. I couldn't keep pace. The program is offered by one of the few decent universities in my country. I realized that I lacked many mathematical concepts (precalculus concepts).

Then, I went to a less competitive program in another institution. At last, I completed two years of study of electricity and electronics. There, I realized that I'm not good at manual tasks, like soldering little electronic components on a board. But I excelled in the math and programming courses (you should take into account that the insitution is noncompetitive.)

I read over and over that math teaches one problem solving and logical reasoning. My parents are willing to pay the money if I enroll in the math program at the university which I first attended. But I'm not sure.

I have been studying math on my own (precalculus) with the Spanish version of a book titled Algebra and Trigonometry with Analytic Geometry: A problem-solving approach, by Varberg and Fleming. This book features in each section a difficult problem. I have tried to solve some of these problems. I succeed at times. But, for a real mathematician, these are "mickey mouse" problems. So, given the facts that I have unsuccesfully tried to solve some of these problems and that I am already 26, I am hesitant that I can become a mathematician.

On the other hand, I have not had a real job. Currently, I work with my father. He's got a print business. So, if I choose to go to college instead of getting a real job (thus still depending financially on my parents), I may be ruining my future.

Can someone guide me?

 

[dkotschessaa]

Analyzer,

I'm not a mathematician (yet) but a few years ahead of you in age having gone back to school for math after quite awhile absent, and with a few of the same difficulties.

I would advise you to absolutely not worry about having problems self-studying, and would say not to compare yourself to "real mathematicians" at this point, because you're just not one yet. What I've figured out is that to be a mathematician you have to learn mathematics (a seemingly obvious statement) and to do that you have to go to school and struggle for awhile. Just go back to school and do the work and study and do not question your innate ability. I am passionate about math despite the fact that I am in some senses quite terrible at it. I studied for about a year on my own, and then it took me another year of school for my brain to start getting into shape.

Don't assume that any mathematician can solve any problem instantly, like they are some sort of huge repository of mathematical wisdom. I've seen brilliant professors struggle with problems in class that were in our calculus book. A lot of the young students are baffled by this because they think that math professors should just be problem solving machines. It's not like that.

What they do know how to do is do the required research and reading to be able to come back and solve the problem. They learned to do that in their studies, just like you will in yours. (And I also recommend G. Polya's "How to Solve it" which has helped me in this area).

When I see people like you worrying about being 26 it makes me nervous, because I am 35 and it makes me think I'm supposed to be worried about something. I am aware that I'm not the norm in age and that by the time I get a Phd I will be in my 40s. But I reason thusly - if I work now and get my Phd in my 40s I will be 40 something and have a Phd. If I decide not to do it, then I will eventually be in my 40s anyway and will not have a Phd. If I had gotten my Phd in my 20s I will eventually still be 40 and have a Phd. So in 2 out of three cases I will be a 40something year old Phd. In the third case I will still be in my 40s and thinking that maybe I should have continued to work at it when I was in my 30s. Now how long do I really want to keep that up? So I'm just going to do it now and stop worrying about it.

I realize I've rambled on a bit here in mathwonks thread. Please, mathwonk, let me know if anything I've said here does or doesn't make sense. I don't want to give bad information, but I think I have an idea what I'm talking about here.

-Dave K

 

[analyzer]

Thanks for replying, dkotschessaa. I can see I'm not alone.

You are passionate about math. That's the most important part. For math being hard, one cannot succeed if one is not in love with it.

Regarding my situation, I don't know if I am passionate about math since I haven't even scratched its surface. I want to know more, for sure. But I believe trying to solve hard problems on books on one's own resembles research.

I have gotten stuck with problems for months, and that's discouraging, but one does learn a lot in the way. Besides, one refines one's reasoning skills. And that's what it's all about. A rigorous undergraduate math program should open many doors.

If there's a place where I want to spend most of my energies, that place is university. I don't want to inherit my dad's business. I don't want to do repetitive tasks or manual tasks for eight or more hours a day.

 

[sahmgeek]

When I see people like you worrying about being 26 it makes me nervous, because I am 35 and it makes me think I'm supposed to be worried about something. I am aware that I'm not the norm in age and that by the time I get a Phd I will be in my 40s. But I reason thusly - if I work now and get my Phd in my 40s I will be 40 something and have a Phd. If I decide not to do it, then I will eventually be in my 40s anyway and will not have a Phd. If I had gotten my Phd in my 20s I will eventually still be 40 and have a Phd. So in 2 out of three cases I will be a 40something year old Phd. In the third case I will still be in my 40s and thinking that maybe I should have continued to work at it when I was in my 30s. Now how long do I really want to keep that up? So I'm just going to do it now and stop worrying about it.

 

[dkotschessaa]

Thanks for replying, dkotschessaa. I can see I'm not alone.

You are passionate about math. That's the most important part. For math being hard, one cannot succeed if one is not in love with it.

Regarding my situation, I don't know if I am passionate about math since I haven't even scratched its surface. I want to know more, for sure. But I believe trying to solve hard problems on books on one's own resembles research.

That's a good way to look at it.

If there's a place where I want to spend most of my energies, that place is university. I don't want to inherit my dad's business. I don't want to do repetitive tasks or manual tasks for eight or more hours a day.

Do it man!

 

[mathwonk]

Thanks for the good counsel guys. Dave I appreciate and in fact depend on the input from people like yourself. I feel an obligation to weigh in here when someone explicitly asks for my view, and I have something to say, or but only then.

 

[AcidRainLiTE]

Hi everyone. I was wondering what you think of Lehigh's math PhD program. I recently applied to grad schools and was accepted into Lehigh (my top choice was Stony Brook but I didn't get in). What do you know about the school? How strong is its graduate math program (I am interested in pure mathematics)? One of my main priorities is to be immersed in an environment with experts in the field and surrounded by bright and passionate peers/grad students. I also really want to feel pushed and challenged and don't want to be in a sub-par environment. I may also like to ultimately teach at the grad level and so I am also interested in how attending Lehigh for my PhD would affect my career options. What do you know about the school? Any advice is appreciated.

For the record, I am still awaiting responses from Pitt, Penn State, and Maryland. It is kind of late in the game, though.

 

[homeomorphic]

I also really want to feel pushed and challenged

You should probably be more concerned about feeling TOO pushed and challenged. That's what grad school is all about. One of the profs here jokingly said something like "the purpose of grad school is to suck all the joy out of life".

But it's not a joke. It's not uncommon for the drop-out rate in math grad schools to be 50%. That should tell you something.

Many will enter. Few survive.

I don't know anything about Lehigh's PhD program.

 

[mathwonk]

i do not know anyone there personally but a quick look at their faculty list shows they have their own phd's from top places like SUNY, Harvard, Princeton, MIT, Stanford, Rutgers,...so I would not worry about how good they are, they seem quite good. Indeed it is really hard to find a school these days that does not have very good math faculty. With all the in migration from eastern europe and asia, they just keep getting better and better.

More relevant is whether they specialize in areas of interest to you. So take a look at their fields of specialty.

 

[AcidRainLiTE]

It looks like they have a good number of people specializing in Geometry/Topology which is one of the primary areas I am potentially interested in. I say potentially because I really need a bit more exposure to the various areas before I know what I want to specialize in.

On the other hand, it looks like they have only one person doing algebra/number theory, which is a bit concerning. That is, unless the people doing algebraic geometry are essentially involved in algebra with the addition of its use in geometry. I am not familiar enough with the field to know.

One of my other interests is the interface of math and theoretical physics. It looks like they have people specializing in Differential Geometry, which is closely tied to physics. No one seems to be working specifically on Mathematical Physics, though.

I will probably take it if they give me funding.

 

[mathwonk]

what is your assessment of university of georgia in athens?

https://www.math.uga.edu/mathematics-research-uga

 

[AcidRainLiTE]

Looking over UGA's program has made me doubt whether I want to go to lehigh. It looks like they have a larger range of specialties to choose from. They have people working in algebra, geometry, topology, mathematical physics, and analysis. I guess that is one of the benefits of a large university--you get greater diversity of specializations. Since I am still fairly uncertain what I want to specialize in, a university that offers a lot of choices may be best.

I would say UGA would be awesome for me except for one thing. They don't have courses in foundations/axiomatic set theory. Mathwonk, I know you said before that set theory isn't considered a big area of research, but I still find myself very interested in it. I really want know about ZFC, cardinals, the continuum hypothesis, logic & set theory, godel's theorem, the work of tarski, etc. For some reason my mind just 'locks' right into that stuff. To really thrive, I feel I need to be involved in thinking heavily about those things, even it is not my main area of research.

 

[homeomorphic]

Just study it on your own over the summer or do a reading course.

Also, putting large amounts of time into things that don't have to do with your research can come at a high price. It's potentially beneficial, maybe, but you'll find that it can make it hard to do what needs to be done if you over-do it. I have a similar problem with physics eating up large amounts of my time, although I am a topologist. The physics is finally connecting back up to my research, but it's still only in a tangential way and is a hazardous distraction from finishing my thesis. The physics connection is getting really interesting, now, and will help me a lot motivationally (potentially, in a genuine mathematical way, even) if I can understand it better, but it's dangerous because I'm trying to graduate and it takes a lot of work. And this is something that IS at least tangentially relevant to what I'm doing.

Some day, I'd like to understand Godel's theorem, but for now, I have to restrain myself.

 

[bublik13]

Hello mathwonk,
I am currently a high-school student in Canada. You seem to be a very dedicated and talented mathematician (I read quite a few pages in this thread). Anyways, I was wondering really how good at math you have to be to become a mathematician. It seems as though only geniuses can succeed and that you have to be the best of the best to hold a steady profession. I'm fairly good at maths - I am participating in math competitions and getting good scores (highest score at my high school, for most of them). I want to become a mathematician. Math just keeps my brain running efficiently and makes me happy when succeeding in solving hard problems. What bothers me most is there are always people who do better than me on local competitions. I think that someone who says they want to become a mathematician must be at least, one of the best (in the age group).

I guess the roots of my question are simply asking how realistic it would be to become a mathematician. How skilled do you have to be to even consider going in that direction? Almost everytime I write a national math contest, I get discouraged that so many people are getting better scores than me, even though myself I do try and think I get a good score to my standards. Its simple to think that if I WANT it, then it will happen. But math is one of those things where you can't just limit yourself to reading a textbook, it requires a higher level of thinking (strategical thinking, proofs, etc.).
It would be helpful for me to know your own high-school experience and really how dedicated you were to math from the beginning.

So, any help would be greatly appreciated. I know I have just written a cluster of my own personal views on math, and I just want an opinion from someone who is very experienced in the field.

Thanks in advance, and sorry for the long post :)

 

[Dr. Physics]

Sorry I posted a thread about this but could not find any suggestion. I hope here it will help.

-------------------------------------------------------------------------------------
I have come across various resources in Forums and Outside Forums and I have found that Mathematics is the best career in research and jobs. Now I have been very much interested in Mathematics. I have started solving various High Level Mathematics which are out of my syllabus. I am a 12th grade student studying and living in India. I wish to pursue my further career in Mathematics at IISC, Bangalore [Famous institute for physical science and have tough syllabus for maths]. I want to ask question that is Mathematics a really good interesting subject in areas of research and industrial jobs?
First I was very much interested in Computer science and wanted to do Engineering but later I stumbled upon Maths which has changed my mind.
I want to career as to become a Computer Scientist. I would like to know what should be done to acquire that level of qualification. Is Computer Scientist a lucrative career.
Does IISC's Mathematics curriculum suits that qualification [http://math.iisc.ernet.in/courses.htm || http://www.iisc.ernet.in/ug/UG-Math.pdf]
If that does not then I might try to do transfer in Caltech for Undergraduate Major in
Applied + Computational Mathematics, Is that good decision.
And doing MBA after Doctorate is a good career in Mathematics.
Thanks

 

[dkotschessaa]

Hello mathwonk,
I am currently a high-school student in Canada. You seem to be a very dedicated and talented mathematician (I read quite a few pages in this thread). Anyways, I was wondering really how good at math you have to be to become a mathematician. It seems as though only geniuses can succeed and that you have to be the best of the best to hold a steady profession.

If that's the case I'm in big trouble!

Where'd you get this idea? How many mathematicians do you know?

-DaveK

 

[homeomorphic]

If that's the case I'm in big trouble!

Where'd you get this idea? How many mathematicians do you know?

I wouldn't say you have to be a genius, but I would say it's very, very difficult and competitive and does take some talent. But I think a lot of it has to do with qualities other than intelligence. There aren't very many faculty positions compared to the number of PhDs.

 

[AcidRainLiTE]

bublik13, I know you are waiting for a response from mathwonk, but in the meantime I want to chime in here.

When I was an undergrad, I recall feeling the same thing. I was a physics major, and was constantly considering switching to math. For some reason, though, I had this idea that you had to be a genius to succeed in math. The way I saw it was that you had to be able to prove crazy theorems and how else are you going to prove those theorems except with a flash of brilliant creativity? Needless to say, I ended up majoring in math. And my prejudices turned out to be false. You don't have to be a genius to succeed in math.

Personally, I think all of this competition about being the smartest, brightest, and most successful in the field is a whole bunch of nonsense. Why does it matter that much? I am not the brightest person in the world, there are many people who are much smarter than I am. But the truth is that I like math and I care about it. I am far from the best, but I think that the combination of a decent amount of ability and a lot of drive will go a long way. That's my opinion anyway. But I am just a hopefully soon-to-be grad student. I look forward to hearing mathwonk's response.

 

[homeomorphic]

Most people who go to grad school feel like a million bucks when they finish undergrad because, in order to make it into a good grad school, you have to be good, so you're hailed as some kind of math hero when you graduate. But then, you get to grad school and everyone was a math hero in undergrad, so you don't feel quite so smart, anymore. And then, some people don't make it through the program. Then, more people are weeded out when it comes time to apply for math jobs. Then, if you go more for research, you do a postdoc, and then, you have to get through a bigger bottle-neck to get a tenure-track position at a research-oriented department. The people who don't make aren't necessarily less smart or deserving in every case, but for one reason or another, they don't make it through to the end. Relatively few make it to the end. Of course, it's a bit easier if you are more into teaching. In that case, you just have to finish your PhD and get students to like you and say good things about your teaching and go for a more teaching-oriented department.

There are all different levels of mathematicians.

I probably won't make it as a professor, but that doesn't mean I can't be a mathematician. I will try to still do it, even though I'm going to have to have a different day job to pay the bills.

 

[mathwonk]

I think you have what it takes to get a math PhD and become an active researcher. You are already excelling most of your peers in high school, and it seems likely that high school in Canada is harder than in the US on average. Plus you have the interest. There is less interest among American students for becoming mathematicians than there is demand. hence it is a relatively good area in which to seek advancement.

But your definition of "succeed" may differ from others. Most of us, even good average mathematicians, will never get a Fields medal, or a Guggenheim fellowship, or a job at a top university, or maybe even have serious difficulty getting an NSF grant, other than occasionally.

We may have difficulty getting a professorship at any university, but I am not sure about this. If a mathematician is someone who understand a significant amount of mathematics, and some part of it very well, and tried to create new results, with some success, this is not at all beyond the reach of many people.

Getting into grad school and getting a PhD is very hard, but there is a demand for math students in the US, so it is not as hard as you may think. Getting a university job as a professor is harder. For that, one is competing also with PhD's from outside the US.

My son majored in math at school and has a job he seems to like at a high tech
company providing a valuable service to large businesses. He does not create new mathematics, but has an intellectually challenging task making sure his company solves the real world problems of its clients. It is financially better compensated than academics, but also more stressful. His problem solving skills are useful, and have been supplemented by management skills and planning.

It seems to me that if your just pursue it as long as you enjoy it, it cannot hurt you. Even if you move in a different direction at some point, you will have skills, knowledge, and degrees that are rare and helpful.

If anything, the person who succeeds "all the way" may eventually have more regret for having chosen a field with limited earning power. In my experience those who drop out along the way actually often find jobs they like even better. Or at least, except for one lawyer with health problems exacerbated by stress, I have never known anyone who left academia for the private sector who wanted to go back.

 

[mathwonk]

So you do not have to be a genius to be a mathematician, just fairly bright and definitely hardworking. But not everyone will enjoy the work after they get there. At the "top" are people with prestigious well paid pure research jobs at institutes, or maybe professorships at top schools, good salaries, lots of amazing students and colleagues, and money to travel and time to discuss and do ones research.

But for most people it is at best a professorship at an average university where teaching elementary classes is a fact of life for decades. I started to say uninteresting classes, but one can always try to make them interesting. Still math is a service department at most schools, and many if not most students will be there reluctantly. So teaching and grading can be a largely thankless task that never goes away.

Even if you finish your PhD, you may find yourself at a below average school where teaching loads are heavy and promising students are few, and research support is essentially non existent. At this point you may wonder why you spent all those years perfecting your thesis on a small topic you have no time to consider again.

But for many of us there is a middle ground, the need to teach tedious classes is balanced by the opportunity to teach stimulating ones, and there are colleagues with whom it is helpful and fun to discuss math. There may even be travel money for summer visits to research meetings.

If thinking about math is what gives you pleasure and you prefer doing that to anything else, this balance is pretty reasonable. For some us also there really was never a choice, we didn't even consider the options or the conditions, since as my colleague put it "doing math holds my molecules together".

 

[dkotschessaa]

Mathwonk,

This might seem like a strange question, but is it necessary to be employed in mathematics to enjoy mathematics? I'd like to think that even if my "job" is teaching calculus or even pre-calculus there is no reason that I can't pursue some kind of research on my own time, or even publish papers. It also seems that there are other "causes" that one can get involved in, or outreach programs, etc.

-DaveK

 

[dkotschessaa]

I ask because I am already employable in my own field (information technology) and right now I am learning math largely for the pleasure of it. At this point I am seriously considering taking it "all the way" to the Phd. level, but it's more about what I can learn at this point then what I can "do" or what I want to be when I "grow up." (When does that happen anyway?)

-DaveK

 

[mathwonk]

great question dave. i think of hurkyl as someone like this. a really smart guy who knows a lot of math and learns and works in it, and much smarter and more knowledgeable than many PhD's.

I had the same situation as a non PhD lecturer who was learning and teaching math when I met a crusty old bird named Paul Halmos. I told him i didn't care if I got a PhD as long as I was doing good math. That so and so looked at me and said "That's a cop-out!"

Now that was a manipulative arguable thing to say, but it magnetized me. Nobody was going to say that to me. So I went back to grad school and got my PhD. What I learned there was this: even though I knew more math than my PhD holding colleagues at the community college, I had never done any new math myself, and they had. That is what a PhD gives you.

It is raising your game to a "new level" to borrow a very tired cliche'. Afterwards you are no longer an outsider looking in, but an insider.

I still was unable to get an NSF grant because I had not published but i did have enough street cred to get invited to a brief visiting position at better school. While there I was dissed as a lowly barely literate striver. They gave me a huge teaching load compared to their own and offered me little support. But one day a famous man came and spoke and I listened, awed by everything he said. At the end he asked a question, and it happened that I had answered a special case of it in my thesis so I raised my hand and said, well it is easy in one case, namely,...

I saw his jaw drop as he stared at this no name punk kid who knew the answer to his question. What a thrill. And all the people there who had given me no credit changed their tune instantly, like ... who are you? I loved it.