Should I Become a Mathematician?

[Nano-Passion]

if you are after money, become a salesman. deceiving people is always more lucrative than enlightening them.

I agree, can I post that on my facebook? I will quote you. ^.^

 

[mathwonk]

I am one pure mathematician who is guilty of teaching lots of math courses filled with proofs and short on applications. the truth is i taught what i knew and was interested in myself, and what was in the books we used. now that i am old and a little wiser i might teach differently but i am retired.

my logic in the old days was that understanding the ideas would enable you to apply them yourself, so i hope that is true.

 

[Jack21222]

I am one pure mathematician who is guilty of teaching lots of math courses filled with proofs and short on applications. the truth is i taught what i knew and was interested in myself, and what was in the books we used. now that i am old and a little wiser i might teach differently but i am retired.

my logic in the old days was that understanding the ideas would enable you to apply them yourself, so i hope that is true.

My problem is I struggle to understand the ideas without something real to connect it to in my mind. That's why if I pursue math, it'd be applied math.

Do you think a student who gets bored of proofs and abstractions, but is good with calculations can survive in an applied math grad program, such as this: http://www.amsc.umd.edu/programs/doctorate.html ?

 

[mathwonk]

well i can't tell from a website what the courses are like. even in our department we had professors who understood the importance of applications and emphasized them in their classes. they were recognizable by their class evaluations which emphasized this.

you see i am also becoming [too late?] more flexible in this regard. so you too should become flexible as early as possible and try to learn the pure stuff while also continually asking applied questions to provoke - inspire your professors to respond to them. even the pure guys know really a lot that they can convey if pressed. good luck.

 

[mathwonk]

have you noticed we are over 500,000 views? of course 400,000 of those are mine.

 

[Math Dad]

Greetings Mathwonk,

I am a retired engineer whose main job now is to help my 7th grade and 3rd grade kids on math. I happily find this thread, and plan to spend time to read through it. It's really nice to have a real mathematician around to provide help. Really appreciate.

A little background on myself. I have PH.D. degree on E.E. I thought math was pretty easy as a kid, until I encountered my first setback at Calculus. After a short career after undergraduate, I was getting better academically and then entering graduate school. At graduate school, I took several Math graduate course, including Algebra, Wavelet (both for my related area), and Topology (for no particular reason, just to test the mature of my math.). That was the peak of my academical life. I forget a good part of those stuffs after 15 years professional career ( which relied a lot on Fourier analysis). During that period, I can not find time to study as much as math I liked. Until recently, I have chance to study Calculus again.

My first question is do you really think "Mathematics is a branch of Physics"?

 

[Math Dad]

Professor Mathwonk,

Two more questions, thanks for the attention.

You mentioned (and I totally agree) the book "What is Mathematics" by Courant and Robbins as a good survey for math before undergraduate. Do you know any book play the same role as good survey for math before graduate? If not, anyone come close? If no, can it be done?

How do you categorize the book "Concrete Mathematics" by Graham, Knuth and Patashnik? (Similar question seems have been discussed in post #338~#340, please ignore it.)

 

[Nano-Passion]

As an electrical engineer I think physics at the college level gives people a clearly better background than math. I've met and I've worked with both categories and in most cases the math education seems narrower. I've always been impressed with physics graduates working in various companies. I cannot say the same about the math graduates.

If you want a beter standard of living go to an engineering school and specialize in EE in particular analog design. Within a few years of graduation you can be making over 120K or even more and I am not talking of California where salaries are higher.

Of course some people are purists and dream of shaping the mathematics field. Good luck with that. When we were young and naive most of us had such dreams. Nowadays the education is such that the degrees don't mean much anymore. Most of the people in industry or academia are simply parroting stuff from books and don't understand the science at a very basic level. From a handful of guys creating a treasure of knowledge 100 years ago out of nothing, the scientific field moved into a situation where hundreds or thousands of scientists with large budgets and equipment can barely make some incremental and slow progress.

Some might counter me by saying that there are so much more patents awarded and papers published nowadays. That's true, but 50 or 100 years ago a paper was published when the author had something important to say and today most of the papers are iddle chatter adding very little to what was already said. This is because the system forces increased minimum quotas on scientists while at the same time making them more compliant rather than more inquisitive and curious. Now more and more people go to school and get a degree than ever before. Is the degree type of any importance? I think it is, but less than what some people believe.

My blog: http://excelunusual.com"

Holy cow man, way to crush spirits. While you do make a sound argument.. I would say that there have been scientists throughout history that are ill-mentioned. The few that are known today are just some of the major contributions. You should notice that back then there would have been a large percentage of people not making it into the big names just as it is today. But that isn't to say that the probabilities aren't stacked high against you.. but still... nothing ventured nothing gained. Sometimes, dreams do come true. Albeit, a very small percentage.

 

[mathwonk]

geo77 are you envious of all the hits here, and trying to seduce my viewers? more power to you.

just kidding. "we welcome diverse viewpoints!"

 

[mathwonk]

@ mathdad

no i do not think math is a branch of physics, but maybe a large part is. that quote is from arnol'd who knows a lot more math than i do, but i think he is focusing on the classical branches of math like analysis. of course i do not know any physics so what would i know?

i also think courant and robbins has a lot to offer everyone.

a superb review of calculus with applications would be courant's calculus book, vols 1 and 2.

here is a bargain for both volumes if you act quickly:

http://www.hungrybookworm.com/SearchProducts.aspx?SearchBy=Author&Text=richard%20courant&Media=Books

 

[deluks917]

http://pauli.uni-muenster.de/~munsteg/arnold.html"

I never understood if this article was a joke.

 

[mathwonk]

hey geo77t!: lighten up, perhaps you missed this:

"just kidding. "we welcome diverse viewpoints!"

I welcome your viewpoint here. You are surely right that EE is a better career choice for income.

I would not want to be guilty of leading anyone into the vow of poverty that is pure math

without full disclosure.where is your site? - I would love to visit it.

 

[mathwonk]

everything arnol'd says is kind of a misanthropic but mostly correct comment on reality.

I read and admire a lot of his stuff, but try to come up for air now and then.

I mean, why be grumpy all the time? But his books are wonderful.

 

[Functor97]

As an electrical engineer I think physics at the college level gives people a clearly better background than math. I've met and I've worked with both categories and in most cases the math education seems narrower. I've always been impressed with physics graduates working in various companies. I cannot say the same about the math graduates.

If you want a beter standard of living go to an engineering school and specialize in EE in particular analog design. Within a few years of graduation you can be making over 120K or even more and I am not talking of California where salaries are higher.

Of course some people are purists and dream of shaping the mathematics field. Good luck with that. When we were young and naive most of us had such dreams. Nowadays the education is such that the degrees don't mean much anymore. Most of the people in industry or academia are simply parroting stuff from books and don't understand the science at a very basic level. From a handful of guys creating a treasure of knowledge 100 years ago out of nothing, the scientific field moved into a situation where hundreds or thousands of scientists with large budgets and equipment can barely make some incremental and slow progress.

Some might counter me by saying that there are so much more patents awarded and papers published nowadays. That's true, but 50 or 100 years ago a paper was published when the author had something important to say and today most of the papers are iddle chatter adding very little to what was already said. This is because the system forces increased minimum quotas on scientists while at the same time making them more compliant rather than more inquisitive and creative. Now more and more people go to school and get a degree than ever before. Is the degree type of any importance? I think it is, but less than what some people believe.

You only live once. I would rather do what i enjoy, no matter how useless and poor it will make me, then spend time making money and feeling miserable.

 

[Dembadon]

As an electrical engineer I think physics at the college level gives people a clearly better background than math.

Better background for what? In case you aren't aware, this is a thread about becoming a mathematician. Are you really asserting that physics gives one a better background in mathematics than a degree in, well, mathematics?

I've met and I've worked with both categories and in most cases the math education seems narrower. I've always been impressed with physics graduates working in various companies. I cannot say the same about the math graduates.

Anecdotes are certainly amusing, but the academic guidance section is not the place where they should be used as the basis for decision making. Again, you aren't being very precise with your explanations. What are you comparing a mathematics education to that would justify your feelings of its inadequacy? If you're referring to engineering positions, then your comment about their performance is meaningless, given that mathematics majors aren't required to complete engineering courses for their degree.

Also, with little-to-no knowledge about what is expected of a mathematician, it's pretty audacious to claim that you're in a position to say anything meaningful about their performance within their field.

If you want a beter standard of living go to an engineering school and specialize in EE in particular analog design. Within a few years of graduation you can be making over 120K or even more and I am not talking of California where salaries are higher.

If you really believe that the above scenario is typical of EE graduates in analog design, then it would be nice to see some data supporting your claim. If you don't believe this is typical, you should state that it is a rare case so that students can have realistic expectations. I also think you should take the information you provide more seriously; there are many reading this thread who will make decisions based on what is said here.

 

[vicsmithvic]

When applying to (most) phd programs, should a mathematics undergrad expect to know nearly every detail in a broad range of topics, or does the program mainly look for an ability to research (ie. already published something) and understand high level mathematics?

I'm only a third year yet I already forgot most of the material in first year. I can only prove theorems in those classes if I studied intensely, and i don't think I'll be able to remember all the material in like 20 classes by the time I'm a senior.

I'm at a dilemma: should I review what I learned (which would take a while and I'll learn new topics slower) or just keep on pressing further and further into topics that use theorems that I understand yet can't prove without studying? The problem is that many theorems (and lemmas) are so long and tricky to prove, so the only way I can truly know them is through memorization, which doesn't stick with me in the long term unless I constantly look through them in my coursework.

 

[mathwonk]

vic, try to focus on what you enjoy and love in mathematics. phd programs are long and hard. to survive you have to be enjoying them as much as possible. you cannot know too much. but just do your best.

 

[Functor97]

of course i do not know any physics so what would i know?

I do not mean to be rude, but i think you are being too modest! In several threads i have seen you give mathematical explanations with a physical intuition behind them. By "not knowing ANY physics" do you mean you have yet to get around to Quantum field theory?

 

[mathwonk]

thank you. i guess i mean i don't feel that i understand physics. I kind of bailed in freshman year from the basic physics course because it just was not precise enough for me. I remember one triumph in a homework set where it was very tempting but not quite satisfying to write the solution as a certain imprecise integral. I spent a long time working out exactly what that integral should mean and explained it on my paper. The grader said mine was the first in over a hundred papers to make clear what I was doing.

But as time went on the number of occasions where one had to provide some assumptions that had not been stated in order to make progress just lost me. I need everything to be made clear or I don't know what to assume. I still remember trying to solve problems in a book by a famous physicist like Pauli or someone where he blithely said "well, since space is homogeneous, we may assume...". But he had never said he was assuming that, so of course I did not give myself that hypothesis.

The same thing happened in the basic physics homework, you had to make some assumptions that had not been stated to solve the problems, and I just did not have that gift. In the other direction, I do think physicists often make good mathematicians, because they have good intuition, and just need to learn to be rigorous. So I agree that taking physics classes can help a mathematician learn ideas that underlie much mathematics. Maybe that's what the electrical engineer was trying to say. But he does sound a little grumpy and cynical. He has some cool visual stuff on his site though. You might enjoy checking it out.

I also have no fear at all of being told the realities of the job world, indeed it is valuable information. However, of the two people in my immediate circle, one a (BA) math major working in silicon valley, and one a (BS) EE working in the defense industry, I think the math major makes considerably more. I however, a (PhD + postdoc work) professor in academia, make considerably less than both. But I like what I do and probably would not want to switch with either of them.

 

[Nano-Passion]

thank you. i guess i mean i don't feel that i understand physics. I kind of bailed in freshman year from the basic physics course because it just was not precise enough for me. I remember one triumph in a homework set where it was very tempting but not quite satisfying to write the solution as a certain imprecise integral. I spent a long time working out exactly what that integral should mean and explained it on my paper. The grader said mine was the first in over a hundred papers to make clear what I was doing.

But as time went on the number of occasions where one had to provide some assumptions that had been stated in order to make progress just lost me. I need everything to be made clear or I don't know what to assume. I still remember trying to solve problems in a book by a famous physicist like Pauli or someone where he blithely said "well, since space is homogeneous, we may assume...". But he had never said he was assuming that, so of course I did not give myself that hypothesis.

The same thing happened in the basic physics homework, you had to make some assumptions that had not been stated to solve the problems, and I just did not have that gift. In the other direction, I do think physicists often make good mathematicians, because they have good intuition, and just need to learn to be rigorous. So I agree that taking physics classes can help a mathematician learn ideas that underlie much mathematics. Maybe that's what the electrical engineer was trying to say. But he does sound a little grumpy and cynical. He has some cool visual stuff on his site though. You might enjoy checking it out.I also have no fear at all of being told the realities of the job world, indeed it is valuable information. However, of the two people in my immediate circle, one a (BA) math major working in silicon valley, and one a (BS) EE working in the defense industry, I think the math major makes considerably more. I however, a (PhD + postdoc work) professor in academia, make considerably less than both. But I like what I do and probably would not want to switch with either of them.

Mathwonk, you are a surprisingly modest person. I agree though, I just checked out his site and its pretty cool!

Geo77, your site is very intriguing and I'm sure you spent a lot of effort into this! Best of luck geo77, I will definitely tell people about this.

 

[mathwonk]

actually i was an invited lecturer at the trieste center for theoretical physics in 1989 -

Lectures on Riemann Surfaces: Proceedings of the College on Riemann Surfaces, International Centre for Theoretical Physics, Trieste, Italy, 9 Nov.-1 by International Centre for Theoretical Phy (Jan 1989)

But that is because the physicists (wisely) think math can help them. I had no clue what they were going to do with what we taught them.

 

[DrummingAtom]

I think I'm about to give into math, but applied math not pure. I'm taking Diffy Q/Linear Algebra this semester and I'm blown away by the material. At the start of the semester I thought learning about predator-prey models were going to be boring but it's turned out to be anything but. The graphs almost look like art to me. Differential equations feels like it's a combination of all the math I've ever learned.

The thing that worries me about going higher in math is that it might get too abstract for me. I'll flip through some different Diffy Q books in the library and some of them aren't visual at all. In higher math do the problems get away from the visual aspect and more abstract? Or does it depend on the topic? Specifically, in applied math.

Is it possible that differential equations can get any cooler?

 

[Number Nine]

I think I'm about to give into math, but applied math not pure. I'm taking Diffy Q/Linear Algebra this semester and I'm blown away by the material. At the start of the semester I thought learning about predator-prey models were going to be boring but it's turned out to be anything but. The graphs almost look like art to me. Differential equations feels like it's a combination of all the math I've ever learned.

The thing that worries me about going higher in math is that it might get too abstract for me. I'll flip through some different Diffy Q books in the library and some of them aren't visual at all. In higher math do the problems get away from the visual aspect and more abstract? Or does it depend on the topic? Specifically, in applied math.

Is it possible that differential equations can get any cooler?

Math gets more interesting as it gets more abstract, you just need to develop an intuition for it. Even if you intend to study applied math, I'd recommend taking at least some introductory courses in analysis and algebra (you'll probably have to anyway). They'll introduce you to some of the most interesting mathematics out there and get you used used to dealing with abstraction. Both will completely change the way you see differential equations (think of abstract algebra as the assembly language of mathematics; other fields dress their subject matter up all pretty, algebra tells you what's really happening.)

ps - Yes, DE's get more abstract and less visual; they also get a trillion times more interesting. Differential equations on manifolds is just one of the coolest and weirdest concepts you'll ever experience.

 

[mathwonk]

i like the ode books by martin braun and especially by v. arnol'd.

 

[qspeechc]

The thing that worries me about going higher in math is that it might get too abstract for me. I'll flip through some different Diffy Q books in the library and some of them aren't visual at all. In higher math do the problems get away from the visual aspect and more abstract? Or does it depend on the topic? Specifically, in applied math.

Is it possible that differential equations can get any cooler?

Well, as things get more advanced in maths they of course get more abstract, so harder to visualize. But also, advanced textbooks give less help. For example, they provide much fewer diagrams than undergrad books, if any; they give fewer examples, and usually more difficult examples (this is good and bad actually); they give more general theorems at the outset, rather than concrete examples, then theorems, then generalizations, which is generally what undergrad books do; and so on.

But that is part of growing as a maths student. You have to learn to come to terms with the material on your own. Try to provide your own examples, draw your own pictures, try to simplify matters where you can, be more specific (e.g. if a theorem is about n dimensions think about 2 or 3), add more assumptions to theorems to try make them easier, etc. After all, once you start doing research there is no one to teach you the stuff or draw pictures for you etc.

A diff. eq. book to check out is https://www.amazon.com/dp/0738204536/?tag=pfamazon01-20 by Strogatz. Despite the title it is about differential equations. It is very application based and quite light on the rigorous maths.

 

[GregJ]

mathwonk, read your review on Amazon for Spivaks calculus. Nice

 

[mathwonk]

I once taught all the way through Spivak in 8 weeks to a class of strong returning high school teachers. I graded 400 pages of homework a week. I (and they) learned a lot.

 

[Bandy58]

I graduated recently with a BA in math and physics and chem minors, and this thread caught my attention. I don't want to talk anybody out of the math major, I loved it and I don't regret it. But be very careful.

If you're going to be an actuary or math teacher, by all means, major in math. But you need to seriously consider what you are going to do with the rest of your life before picking a major. Don't be afraid of going in undeclared. I'm now in graduate school for engineering. I have a lot of respect for Mathematicians, almost nothing I do now would be possible without them. As much as I loved doing it, I realized a bit late that I don't want to prove theorems for the rest of my life. Even if you are a successful mathematician, it is unlikely that you will see your work manifest itself in the physical world around you in your lifetime. There are of course many examples of where this was false, but if you think you're going to be the next Shannon or Dirac, you need to realize how immaculate their pasts were (the bit that you are about to establish now).

I guess I'm trying to say, major in math if you're going to be a mathematician, if your primary and overwhelming passion is to work with math. I knew professors in applied math who worked in biophysical type stuff, but realize that what they do is still math. They never see a patient or even a test tube. They don't hear about experiments or results, only theorems and equations. They don't think about organisms or beings, only the few molecules or membranes that matter to their equations. I might be over driving this point, but when you hand someone a resume that says "i just studied math," you are going to end up just doing math.

If you like math as a foundation for physics (like i did), study physics. You will learn all the math you need to know. And If you get a PhD in physics or engineering, you will be able to run mathematical circles around the BA/BS's in math. A PhD in physics taught my topology classes. And nothing stops you from studying some extra math on the side: it will make you a better physicist, or anything really. If you like math for all its applications in DSP (which I'm sort of stuck doing now), be an electrical engineer. The same applies.

If you want to be qualified to work with something, study THAT thing. Not following that was the mistake I made. I studied math because it was fundamental to all the subjects I liked. Now I have trouble proving I'm qualified to with any of those subjects.

Being a mathematician is not pointless. But go into the subject knowing that if you want it to have a point, you have to be able to do something nobody else can or will. Publish quickly.

And if that was TL;DNR, my best advice for someone starting or in school is to not be afraid of failure. Even if a class drops your GPA, you won't be any less intelligent. I'd be better off in terms of working in the field I want to if I had an engineering degree and a 3.0 than I am now with my degree in math and my 3.7.

-Andrew

 

[synkk]

I'm wondering if it's too late to pursue a career in mathematics, I'm approaching 20 years old and I'm thinking of applying to a top 10 UK university, say i got in, would the 2 year difference set me back from any graduate programs or phd if i wish to pursue it? I read a few books and i keep hearing the phrase "Mathematics is a young mans game".

Perhaps I'm being silly, thanks.

 

[Sankaku]

i'm approaching 20 years old

Have you picked out your nursing home yet? Any favourite coffin designs?

 

[mathwonk]

what can i say, I'm 69 and still working on a research paper, although with less energy than 30 years ago.

 

[mathwonk]

seriously, i think if you get in, they will provide adequate programs to get you up to speed.

 

[GregJ]

I'm wondering if it's too late to pursue a career in mathematics, I'm approaching 20 years old...

Heh you're thinking way too much into it. If you can get into a decent university then go for it!

 

[mathwonk]

[tex]x^2\sqrt{x}[\tex]well? why doesn't it work?

 

[Nano-Passion]

[tex]x^2\sqrt{x}[\tex]


well? why doesn't it work?

$$x^2 / \sqrt{2}$$

or $$\frac{x^2}{\sqrt{2}}$$

Right click --> show source to see the latex code.