Should I Become a Mathematician?

[Zarem]

Real mathematicians get started young, like ten years old, and have a sort of obsession with it. You can't compete with these people, who may have been at your present level when they were twelve years old.

I can't do any of them at all. One of my professors could do about a third of the problems. But a few students get a perfect score.

You have no hope with the Putnam.

I was never able to understand the Riemann Hypothesis. I once picked up a graduate level book on it and wasn't able to make it past the first page

The best you can hope for is teaching math in a junior college or high school.

You seem quite confident about declaring what everyone else is or isn't capable of, which is interesting coming from someone who was not successful themselves.

 

[symbolipoint]

You seem quite confident about declaring what everyone else is or isn't capable of, which is interesting coming from someone who was not successful themselves.

Zarem, what hornbein and mathwonk say makes sense. Really, individuals do not know for sure unless they try ; and often, keep on trying, hard, for a long time, and must be willing to work through things more than once. Individuals might be geniuses or some might not be geniuses; but regardless, hard, long work is usually necessary. If as mathwonk says, he earned his PhD through many years of hard work, I believe and trust what he said.

 

[mathwonk]

It took me a long time to PhD, but then I published over 30 research papers, and taught over 40 different college math courses. Then in retirement, I began a 3-4 year association lecturing and mentoring brilliant 8-10 year olds with "epsilon camp". That's me in the picture linked below, holding the chair for a youngster working on something related to the construction of the regular pentagon. Of course you and I won't be the kid in the chair, but we can be the one holding it for him.

http://www.epsiloncamp.org/

 

[Loststudent22]

The best you can hope for is teaching math in a junior college or high school. Some enjoy that, but for the most part the students hate the subject and are there under compulsion. The teachers are highly overqualified. Not for me.

Is this what a bitter grad student is like? This entire post was very negative.

 

[mathwonk]

well i would say hornbein's post is one of the more negative ones i have seen here. but it is his sincere feeling about his experience and we cannot discount it. i just think it is not universal. indeed i would say mr hornbein himself may find some good outcome if he modifies his aims realistically. my advice is just to aim at what you want most, try as hard as you can, stay the course for a long time, and accept what comes your way. as long as you are engaged in an activity you enjoy even along the way it will offer satisfaction. I myself did not become famous or win world class prizes but I did some good work and I did my best. I enjoyed as well my contact with top quality minds who were willing to talk to me. I also helped some more talented people to achieve their goals. And even here I try to give good advice for free. As the famous Cech nobel winning poet put it, hey it beats killing and murdering.

more precisely: to quote Jaroslav Seifert:

"Prague! Like a draft of wine her savor, Though she should lie in ruins round me, Though fate from hearth and home should hound me, And choke her soil with blood. Oh, never Will I forsake, though all forsake her! Here with the dead I'll wait, unbending, From early spring to winter's ending, Mute at the door till time awakes her. Though screech-owls call down death and mourning, Though God avert His eyes above, One tear upon His lashes burning Charms from our roofs the hovering curse. All my heart's burden, in this verse, I have brought and sung for you, my love! And Now Goodbye To all those million verses in the world I've added just a few. They probably were no wiser than a cricket's chirrup. I know. Forgive me. I'm coming to the end. They weren't even the first footmarks in the lunar dust. If at times they sparkled after all it was not their light. I loved this language. And that which forces silent lips to quiver will make young lovers kiss as they stroll through red-gilded fields under a sunset slower than in the tropics. Poetry is with us from the start. Like loving, like hunger, like the plague, like war. At times my verses were embarrassingly foolish. But I make no excuse. I believe that seeking beautiful words is better than killing and murdering."

 

[symbolipoint]

hornbein said

The best you can hope for is teaching math in a junior college or high school. Some enjoy that, but for the most part the students hate the subject and are there under compulsion. The teachers are highly overqualified. Not for me.

Is this what a bitter grad student is like? This entire post was very negative.

That is largely the truth. Not all students, but most of them. Expect that any grad student doing some teaching will be teaching students who do not like Mathematics.

 

[xaos]

i think the warnings are valid: 'you have to enjoy it' and 'you have to measure this against the opportunity cost of this path to other paths'. since my master's ten years ago, i have been at it almost continuously, finally reaching up to homological topology. but is only getting 5 pages of work done after twelve hours of semi distracted effort really worth it? shouldn't i be doing something with my life?

i really enjoy mathematics but i hate to program because it takes away time from studying mathematics. however i know i will never teach, so the only other option i see is to learn how to program. surprisingly there are jobs in programming but nobody cares about commutation diagrams.

you don't have to be a genius to understand mathematics, but you don't have to be a fool either. there is great reward in understanding things few others can barely grasp.

 

[FocusOnTruth]

Regarding my late start, I have certainly seen very mixed feedback. I'm not sure I've mentioned this already, but here's my brief background:

-Enjoyed mathematics intensely as a small child and managed to get several years ahead of the curve in the beginning. I could do some basic college level problems as a toddler.
- Environmental and emotional issues interfered with learning much further. My skills regressed, and I underachieved throughout school. (Something not math related but possibly useful in elaborating upon my situation: I had never even read a book until summer before my senior year of high school.)
- I took precalculus senior year and barely passed. I think I could have done better if it was my only focus,but I was terribly behind in every subject, so I was going through great struggles in virtually every facet of life. However, it may be pointless to speculate.
-Going into college, I didn't know how to factor polynomials or how to define a function.
- With persistence, I have improved greatly. I finished Calc I with a solid A and am doing similarly well in Calc II. I also study independently and am gradually making up for childhood and adolescence.

With all that I've heard, I honestly can't say whether or not I'll ever be able to catch up to those who started young and competed in IMO and Putnam. I certainly won't be on their level any time soon. Regardless, I love mathematics and think that having overcome environmental obstacles and personal issues to rekindle my joy in learning is also valuable and may benefit me in ways that years of practice may have not.

Hornbein certainly had a respectable view, but I can't say I agree. Perhaps it's my naivete,but I believe that by pushing myself to the edge of my ability and remaining curious, I can make worthy contributions. I also think I have more options in mathematics than high school and junior college teaching. Of course, time will tell whether or not I'm correct.On a somewhat related note: Since I've gotten a rather late start on academics as a whole, I am indecisive as to whether or not I should study non-math subjects such as humanities and biology. I certainly find all studying enriching, but I fear that by spreading myself too thin I may be incurring to great an opportunity cost. That is, I think it may be better to just focus, for now,on math and more strongly related subjects like physics, coming back to those other curiosities later when I have more time and a well-established career as a mathematician.

 

[Catria]

My grad-level instructors (especially in the courses I dropped) thought that I was one of the most mathematically-inclined students in years, if not their careers as physics professors, since most of the questions I ask in class is about mathematical assumptions and what to do when they aren't verified: non-commutating second-order partial derivatives, discontinuous Lagrangians/Hamiltonians (usually because of the potential term), inability to commute sum and derivative (or integral), inability to commute integration order, inability to commute derivative and integral, time-dependent masses (in discrete-body problems, rather than classical field theory, where time-dependent mass densities are common), and yet I feel that we can discover new physics partially by relaxing mathematical assumptions (ultraviolet catastrophe comes to mind). But they understand, by the same token, why I want to do theory on some level.

And also the instructor of the course I grade homework for has even accused me of caring too much about mathematical rigor... all of which lead me to mathematics (probably mathematical physics) as something I would do if I still want to do research after I cure the mental illness that caused me to consider dropping out of a physics PhD in the first place. Yet I once ruled out mathematics due to a poor experience with real analysis 2 in undergrad, knowing real analysis is a common topic for PhD math quals.

Now, the one roadblock I envision that would preclude success as a mathematician (applied or pure) would also preclude success in PhD programs in general. High-level coursework would frustrate me to no end, especially since I know there is an extant solution to a lot of coursework problems, whereas in research you're the one looking for a solution. And I feel coursework-induced frustration is IMO (IME?) poor preparation for research-induced frustration. For me how I handle frustration is highly source-dependent.

 

[dkotschessaa]

I think the "young man's game" fallacy arises from an error in reasoning, i.e. that mathematicians peak at a certain age because they are a certain age. I suspect it may have more to do with the age that one is indoctrinated into mathematics, which is *typically* around a standard age (mid 20s). Once the indoctrination is complete I think the ideas are less fresh.

I also think that the advantages of youth are largely physical. The illusion is that the young brain is somehow better but that is simply because the body is better. Physical health lends itself to mental acuity. I am finding that withstanding the rigors of grad school is actually more physical than mental. To "keep up" with the younger students I have to exercise a lot and eat well. I cannot study until 2:00 am or take a test on 5 hours of sleep, or skip a meal. Your brain gets old because your body gets old, but there's so many advantages to maturity. I have less innate skill than most of my peers but more balance and a lot of determination.

Hardy and people who think this way about age did not have a lot of information to go on. There are more of us now and so the world will have a chance to see what we can bring to the table.

-Dave K

 

[FocusOnTruth]

I have had some trouble finding out what exactly a day in the life of an industrial mathematician is like. Will I be able to spend most of my day solving mathematical problems, or is that only a small part of the job?

 

[mathwonk]

I do not know the answer to that, but I know the answer for an academic mathematician, in college. Namely most of your day will probably be spent with teaching classes, grading, counseling, office hours, meetings, reviewing grad exams, more meetings, preparing classes, office hours, applying for grants, writing reports, writing planning documents, evaluating staff, reviewing dossiers of potential students or potential hires, writing dossiers for people going up for promotion or awards,..., so you have to be strict about drawing off some reaearch time that is sacred, and shut your door and don't answer even a knock on it for that afternoon or that part of the day. I only had one brief period like this per week in my schedule. Most research got done during holidays, and some at home, sometimes late at night while not sleeping. It is very difficult for the average college teacher to find time to do math. So sometimes try to get leave at a research institution, or take in a summer meeting. If you can get a job at a place that offer sabbatical leave regularly as part of the conditions for employment,. that would be super. I never had that. UGA offered zero sabbatical leave, even after decades of service. Most laypersons seem to think sabbaticals are part of the academic lifestyle, but they are not everywhere. some places offer 6 months leave after 7 years, and recurringly. you should definitely prefer such a place.

 

[mathwonk]

some free math books from springer:

https://gist.github.com/bishboria/8326b17bbd652f34566a

 

[NathanaelNolk]

Hello everyone, I'm starting my undergrad in mathematics and I was wondering: Considering I'd like to end up doing research in mathematical physics, how much courses should I take in the physics department? Should I self-study physics instead? Are there some absolutely required courses in physics (apart from the obvious EM, mechanics, QM, etc) that I should take, like thermodynamics or something of the sort? I was of QFT/GR. Is it even possible for a mathematician to take such courses?
Thanks for anyone taking the time to reply, even though I know the question may be a bit too general.

 

[mathwonk]

I suggest you ask a physicist like zapperz this question, perhaps in his thread :can i get a phd in physics if my undergrad degree is in something else?"

 

[NathanaelNolk]

I suggest you ask a physicist like zapperz this question

Thanks for your help mathwonk, I'll do that.

 

[VCrakeV]

Hello fellow academics. I'm not interested in pursuing a career directly related to math, but I enjoy it to an extent, and so I'm thinking of doing a minor or secondary major in math (primary major is philosophy). Basically, I find myself loving some aspects, and hating others, so I want to know if I would enjoy a minor or major. I enjoy Algebra, derivative Calculus, integral Calculus, complex numbers, and concepts of infinity. But matrix Algebra and matrices in general bore me to tears. I also dislike 3D graphing, and 3D visuals in general. A major would also require some computer science, which I find quite a bore.

So, would I like either degree? What's math like in the higher courses?

 

[lavinia]

Hello fellow academics. I'm not interested in pursuing a career directly related to math, but I enjoy it to an extent, and so I'm thinking of doing a minor or secondary major in math (primary major is philosophy). Basically, I find myself loving some aspects, and hating others, so I want to know if I would enjoy a minor or major. I enjoy Algebra, derivative Calculus, integral Calculus, complex numbers, and concepts of infinity. But matrix Algebra and matrices in general bore me to tears. I also dislike 3D graphing, and 3D visuals in general. A major would also require some computer science, which I find quite a bore.

So, would I like either degree? What's math like in the higher courses?

I was also a philosophy major. I found mathematics answered many questions that stumped philosophers. Also mathematics presents a Platonic universe. Not a bad idea for a philosopher to know one first hand.

 

[VCrakeV]

I was also a philosophy major. I found mathematics answered many questions that stumped philosophers. Also mathematics presents a Platonic universe. Not a bad idea for a philosopher to know one first hand.

I understand the importance, but it doesn't matter if I won't enjoy it. I can always just study whatever math interests me on my own time, in case university programs have too much math I don't like. But might I like such a program?

 

[symbolipoint]

I understand the importance, but it doesn't matter if I won't enjoy it. I can always just study whatever math interests me on my own time, in case university programs have too much math I don't like. But might I like such a program?

Would practicality make a difference? Mathematics develops tools for use to be able to solve problems and make decisions. That is just very broad. You find the specifics in EVERY FIELD. Would you enjoy practical or predictive power?

 

[lavinia]

I understand the importance, but it doesn't matter if I won't enjoy it. I can always just study whatever math interests me on my own time, in case university programs have too much math I don't like. But might I like such a program?

Hard to say. Studying on your own is hard. It requires dedication

 

[VCrakeV]

Would practicality make a difference? Mathematics develops tools for use to be able to solve problems and make decisions. That is just very broad. You find the specifics in EVERY FIELD. Would you enjoy practical or predictive power?

Practicality is important, but it's more important that I enjoy what I do.

 

[symbolipoint]

Would practicality make a difference? Mathematics develops tools for use to be able to solve problems and make decisions. That is just very broad. You find the specifics in EVERY FIELD. Would you enjoy practical or predictive power?

Practicality is important, but it's more important that I enjoy what I do.

What I am suggesting, that if you can handle some Mathematics courses for a "minor concentration", some pain will give you some gain; and that later on, you may ENJOY being able to use some of what you learned to solve problems and either make predictions or make decisions about some applicable situations.

LATE EDIT: VCrakeV started his question in this topic at post #3692. His question seems more like a different topic than, "Should I become a Mathematician".

 

[VCrakeV]

What I am suggesting, that if you can handle some Mathematics courses for a "minor concentration", some pain will give you some gain; and that later on, you may ENJOY being able to use some of what you learned to solve problems and either make predictions or make decisions about some applicable situations.

Do you know what kind of math this usually entails? I understand you're trying to say that there is enjoyment in achievement, but I always find it to be overshadowed by the pain to get it. That's why I want to know if the math is the kind I enjoy, or the kind that is "painful", so to speak.

 

[symbolipoint]

Do you know what kind of math this usually entails? I understand you're trying to say that there is enjoyment in achievement, but I always find it to be overshadowed by the pain to get it. That's why I want to know if the math is the kind I enjoy, or the kind that is "painful", so to speak.

The courses would include but certainly not restricted to Algebra 1, Algebra 2, "College Algebra", at least the Basics of Linear Algebra, possibly Trigonometry (because I suspect that optical engineers would use much of this and should also be other technical professionals),

 

[symbolipoint]

VCrakeV discusses and asks:

I want to know if I would enjoy a minor or major. I enjoy Algebra, derivative Calculus, integral Calculus, complex numbers, and concepts of infinity. But matrix Algebra and matrices in general bore me to tears. I also dislike 3D graphing, and 3D visuals in general. A major would also require some computer science, which I find quite a bore.

You would not enjoy any major or minor in Mathematics. Look at the program requirements for a minor concentration at your school and decide if you believe you would or would not want/be interested in earning minor concentration or a degree in Math.

 

[Logical Dog]

I want to be a mathematician but I am probably too stupid, my favourite things so far have been mostly in discrete mathematics...set theory and logic, loved proofs and mathematical induction when I came across them . I also like vectors and am trying to study analysis on the side, calculus and algebra are my weakest backgrounds, I have very basic knowledge in them and Geometry too, but most of all I have an obsession with numbers and how almost everything else, evaluates to one or can be constructed through them, somehow this always amazes me (dont know why). I only started loving math a few months ago, i ask some very silly questions about it sometimes.. I know it is not a phase.

The question for me is not should, but if I can. @mathwonk great and vast thread..I will be coming here more often.

 

[symbolipoint]

I want to be a mathematician but I am probably too stupid, my favourite things so far have been mostly in discrete mathematics...set theory and logic, loved proofs and mathematical induction when I came across them . I also like vectors and am trying to study analysis on the side, calculus and algebra are my weakest backgrounds, I have very basic knowledge in them and Geometry too, but most of all I have an obsession with numbers and how almost everything else, evaluates to one or can be constructed through them, somehow this always amazes me (dont know why). I only started loving math a few months ago, i ask some very silly questions about it sometimes.. I know it is not a phase.

The question for me is not should, but if I can. @mathwonk great and vast thread..I will be coming here more often.

You mischaracterize yourself and have not spent as much time studying Algebra and Calculus as the other things of your "favorites".

 

[Logical Dog]

You mischaracterize yourself and have not spent as much time studying Algebra and Calculus as the other things of your "favorites".

I am not smart, and have this silly mental illness. Unfortunately there can only be so many people at the higher end of the intelligence normal distribution, let alone be motivated enough.

math is hard, like all rigourous subjects, a kind of reprogramming of ones soul and identity. I know math is the purest and most used form of knowledge, without it we wouldn't have the framework for sciences and modern life today. So, you can pretty do much A LOT OF things. :D
Thank you for the motivation.

 

[symbolipoint]

I am not smart, and have this silly mental illness. Unfortunately there can only be so many people at the higher end of the intelligence normal distribution, let alone be motivated enough.

math is hard, like all rigourous subjects, a kind of reprogramming of ones soul and identity. I know math is the purest and most used form of knowledge, without it we wouldn't have the framework for sciences and modern life today. So, you can pretty do much A LOT OF things. :D
Thank you for the motivation.

Here is how much of the world may view:

One can struggle to learn Algebra 1,2,3, some one or two Trigonometry courses (even if either repeated or delivered in two different courses), and maybe two or three Calculus course (sequence as Calc 1,2,3), and earn some other degree related to or dependent on Mathematics; and then you could some day apply your possibly limited but very important Algebra and common Geometry skills. Many people will think that YOU ARE SMART. You have used your relatively simple Mathematical skills to solve everyday problems and make good predictions in your work. Other people or at least some of them, will believe you are really smart. Now, how smart are you?

 

[Logical Dog]

Here is how much of the world may view:

One can struggle to learn Algebra 1,2,3, some one or two Trigonometry courses (even if either repeated or delivered in two different courses), and maybe two or three Calculus course (sequence as Calc 1,2,3), and earn some other degree related to or dependent on Mathematics; and then you could some day apply your possibly limited but very important Algebra and common Geometry skills. Many people will think that YOU ARE SMART. You have used your relatively simple Mathematical skills to solve everyday problems and make good predictions in your work. Other people or at least some of them, will believe you are really smart. Now, how smart are you?

I will attempt a math degree later for sure, tired of being a bottom feeder in the vast field of math.

 

[symbolipoint]

I will attempt a math degree later for sure, tired of being a bottom feeder in the vast field of math.

You might feel or find later that Mathematics is not the degree objective for you. You can still pick something that uses Mathematics, and you will apply much of or some of what you learn from Mathematics.

 

[mathwonk]

Remark to symbolipoint: the administrators changed the title of this thread after thousands of posts had been logged here. So there is no reason most of the the posts should be addressing the current title. Admitted it is similar to the original one, "Who wants to be a mathematician?" but that one was chosen whimsically to mirror a then current tv quiz show, rather than to be specifically pedantically descriptive.

Anyway, I take no responsibility for the current title nor think it should impose any restrictions on the questions asked here, which are open to all interested in learning about math and learning about learning about math, as far as I am concerned.

 

[symbolipoint]

Remark to symbolipoint: the administration changed the title of this thread (without asking me), after thousands of posts had been logged here. So there is no reason most of the the posts should be addressing the current title. Admitted it is similar to the original one, "Who wants to be a mathematician?" but that one was chosen whimsically to mirror a then current tv quiz show, rather than to be specifically pedantically descriptive. I always regretted the loss of some humor and the homogenization of the threads' titles, for no clear reason. I also noted enviously that some physics oriented threads were allowed to keep their original titles.

Anyway, I take no responsibility for the current somewhat dull title nor think it should impose any restrictions on the questions asked here, which are open to all interested in learning about math and learning about learning about math, as far as I am concerned at least.

The new title change is not bad, but I like the original title better for the reasons you described. The two titles really do make the same meaning enough.

 

[dkotschessaa]

So, I started my first contributions to this thread as an undergrad in my 30s. I'm now 40 about to get my master's. At this point I will not be pursuing a PhD, but I'm really ecstatically happy with what I've done. I grew up in a working class suburban family. I am the first in my immediate family to have anything higher than a high school diploma. My high school counselors (back in the 90s) advised me that "people like you don't really go to college" and tried to send me to tech school.

So yeah, a master's is pretty bleeping good.

I had been feeling the "bug" to move on for awhile from being in school. My son was born in February (3 months early - long story) and now the mental shift from "self investment" to family is complete. It is time to move on, but this doesn't mean it's the end of anything.

Some of my acquaintances refer to me as "a mathematician" and I always sort of correct them. But I certainly came out of school with a different brain than what I went in with. Non-mathematical endeavors seem a lot easier now, or, if they are not easier, they are not scary. Actually, after 6 years in school, I am finding talking to people that do not have a math or science background slightly frustrating, but this is something I need to work on. Not their fault.

I still have to finish the qualifier, but I'm actually, perhaps ironically, taking time off from school to study for it. I couldn't do TA+classes+qualifier+new baby and we were running out of money. I actually can't *wait* to be done and move on to something else. What an awesome, challenging time this was.

I hope I pass the thing in January, otherwise I will have to take it in may. I have to enroll in a class to take the qualifier so I'm doing an online biostats course - but that's a whole other post.

-Dave K