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Kind of an odd question, perhaps, so I apologize in advance if it is inappropriate for this forum. I've never taken a mathematics course since high school, and didn't complete college. However, several years ago I was affected by a serious illness and ended up temporarily disabled. I worked in the music business, and to help pass the time during my convalescence I picked up a book on musical acoustics.

That book reintroduced me to calculus with which I'd had a fleeting encounter with during high school, so to understand what I was reading I figured I needed to brush up, so I picked up a copy of Stewart's "Calculus". Eventually I spent more time working through that book than on the original text. I also got a copy of "Differential Equations" by Edwards and Penny after I had learned enough calculus to understand that. I've also been learning linear algebra - MIT's lectures and problem sets have really helped in this area. I'm fascinated with the mathematics of the Fourier transform, particularly its application to music in the form of the DFT and DSP - I've enjoyed the lectures that Stanford has available on the topic immensely. I just picked up a little book called "Introduction To Bessel Functions" by Frank Bowman that I'm looking forward to reading.

The difficulty is, I'm 30 years old, and I can tell that I'm a lot slower at this than I would have been if I had studied it at age 18. I'm also starting to feel that I'm getting into material that is going to be very difficult to learn without structure or some kind of instruction - like I've picked all the low-hanging fruit and that I'm at the point of diminishing returns. I am fortunate though, that after a lot of time and some great MDs my illness is mostly under control and I now have to decide what to do with "what comes after."

I feel a great deal of regret, though, that I didn't discover that I enjoyed this discipline until it was probably too late to make any difference. I am able, however, to return to college now if I so choose.

The questions I'd like opinions on are these: is returning to school at my age for science or mathematics possible? Is it worth it? I've had a lot of difficulty finding any examples of people who have gotten their first degrees in science or mathematics at my age. Do such people exist? Or is this avenue essentially forever closed beyond a certain point? If anyone is familiar with older first-time students in mathematics or science - how do they fare?

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    $\begingroup$ There is a question about mathematicians that learned mathematics at a late age. mathoverflow.net/questions/3591/… $\endgroup$
    – Kim Greene
    Commented Nov 29, 2009 at 8:54
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    $\begingroup$ No, of course not, do what you like! As you can see at Kim Greene's link, there are certainly examples of people starting late. But this is really a person to person thing, and no one can predict how you (or an 18-year-old) will fare. $\endgroup$
    – Jonas Meyer
    Commented Nov 29, 2009 at 9:47
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    $\begingroup$ I know one mathematician who left math at the age of 20(with a B Sc), enrolled in grad school in his thirties and got Ph. D. in a very modern and hot topic, requiring lots of study and effort, by 38 or so. He is very good, in my view. So you shouldn't hesitate at all. $\endgroup$
    – Regenbogen
    Commented Mar 4, 2010 at 16:32
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    $\begingroup$ I got my 1st degree at 27, and it was in CS, not in maths. $\endgroup$
    – Dima Pasechnik
    Commented Dec 4, 2011 at 16:36
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    $\begingroup$ In my opinion the material collect so far on this subject seems sufficient to refelect a wide spectrum of opinions. I thus now vote to close. $\endgroup$
    – user9072
    Commented Dec 24, 2011 at 17:45

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I did a Mathematics Batchelors 7 years ago, but was always having difficulty trying to cram in theorems and proofs until they started to merge into one(!!!). Naturally, this didn't pan out too well as a revision method. But looking back on the notes now, that daunting information seems a lot more readable than it did before exams. (I've been reading up on Representations of Groups) So, in summary, No! I don't think you're too old. It would appear that the myths of being too rusty are bunk. Historically, Mathematicians have been known to have done their best work young. Then again, in the past a lot of them popped their clogs a lot more quickly than Mathematicians today. Besides, when if you were a lot younger, you might be just interested in just partying and all sorts of juvenile things at college thus being a little distracted from understanding things properly in the Mathematical World... Quite a lot of undergrads I knew just memorized proofs and exercise questions to get by in the exams, but didn't quite get an intuitive feel for it. The blank looks i used to get from friends with Firsts asking them if they can remember what a Stochastic Process or to get them to write the definition of continuity for a single variable...... :-D

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Depends on what you want. Too old to get the Field's medal? probably. Too old to study mathematics or have an academic career in mathematics? definitely not! I knew a few people who did their master's in math in their late 30's and went on to teach college math.

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Enthusiasm the subject has much more to do with the learning than your age.

The only problem you will have is probably to be able to calculate simple things fast, like regular multiplication, addition and algebraic simplification. These are things that you can only learn with a lot of practice and time. (And this is basically all you learn before the age of 18)

New theory will probably not be a problem for you at all. In my experience, the theory is not an issue, but it is mostly the mathematical self esteem that you need. You NEED to believe that you can and will be able to understand the theory.

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The best professor that I have had at my university got his bachelors degree while in his 40s.

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There is evidence that exercising your brain help you stave off Alzheimer's disease, meaning studying mathematics, learning another languages, etc. all prolong your enjoyable lifespan!

There should be several good books on the mathematics of sound encoding/compression, as well as the mathematics of music itself, but I cannot recommend anything in particular.

I'll list some other books you might find interesting however :

Another nice elementary differential equations text is Boyce and DiPrima. Ordinary Differential Equations by Garrett Birkhoff and Gian-Carlo Rota is slightly more advanced. Folland's Introduction to Partial Differential Equations is a nice light introduction to the more advanced stuff that mathematicians working in PDE worry about.

If you're curious about Stochastic Differential Equations, Baxter and Rennie's Financial Calculus: An Introduction to Derivative Pricing gives a wonderfully simple, but fairly correct treatment of the Black-Scholes pricing formula. I'm afraid it doesn't talk about the Black-Scholes PDE though, which is basically the heat equation evolving backwards in time, but the stochastic calculous is enjoyable on it's own, and fairly elementary.

Wilf's Generatingfunctionology is a wonderful introduction to Generating Functions, which anyone reading mathematics solely for enjoyment should briefly delve into. You might also be interested in Introduction to the Theory of Computation by Sipser, or even Algorithm Design by Kleinberg and Tardos.

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    $\begingroup$ Concrete Mathematics? $\endgroup$
    – sigma_z_1980
    Commented Sep 24, 2011 at 22:53
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bitrex, passion and joy are more important than achievements. If you totally enjoy math or related areas,such as Computer Science, go for it, and achievements will evolve over time. I were doing almost nothing till I turned 26, then realized math is a great thing. Now, five years later I'm still extremely humble (you can easily check by my questions on MO and MSE), but aeons ahead of myself when I were 20, my brain functions much better and I'm working towarrds an advanced degree in CS. If it is someone around you that keeps telling you off, have a closer look at what they do and why you should listen to them at all. In the end mathematicians live a long happy life unlike many others.

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There is one thing I would advise though....don't try and visualise everything. Many a young undergraduate has tripped over that point.

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    $\begingroup$ What does this mean? I personally don't understand anything until I can visualize it. $\endgroup$
    – Qiaochu Yuan
    Commented Dec 18, 2009 at 21:49
  • $\begingroup$ Can you visualise in n-dimensions? $\endgroup$
    – Alex Wong
    Commented Dec 19, 2009 at 21:31
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    $\begingroup$ Alex: Can you visualize 3 dimensions? Actually, not really. We only understand 3 dimensions by understanding the 2 dimensional projections of the 3 dimensions we live in. We visualize 3 dimensional objects by viewing them from different angles -- that's why we have two eyes. Similarly, we can visualize higher dimensional objects by "viewing them from different angles", that is, by understanding their projections to lower dimensions. $\endgroup$
    – Kevin H. Lin
    Commented Dec 24, 2009 at 2:04
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    $\begingroup$ I more often "kinesthetize" 3D objects - I imagine what they feel like. This does not require 2D projection, and it does not generalize well to higher dimensions, but it helps me a lot in dimension 3. $\endgroup$
    – Steven Gubkin
    Commented Jun 7, 2010 at 14:31
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    $\begingroup$ as one of the great italian geometers said: the basic tools of geometry are "projection and section", i.e. reduction to lower dimensions. $\endgroup$
    – roy smith
    Commented May 7, 2014 at 3:27
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