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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? Thank you for any comments.

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There is a question about mathematicians that learned mathematics at a late age. mathoverflow.net/questions/3591/… –  Kim Greene Nov 29 '09 at 8:54
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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. –  Jonas Meyer Nov 29 '09 at 9:47
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Community wiki. –  Harry Gindi Nov 29 '09 at 19:18
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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. –  Regenbogen Mar 4 '10 at 16:32
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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. –  quid Dec 24 '11 at 17:45
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closed as no longer relevant by Felipe Voloch, Gjergji Zaimi, quid, Bill Johnson, Alex Bartel Dec 24 '11 at 19:03

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37 Answers

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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I don't really have any advice to give, but at my department, there's a gentleman who just started his undergraduate degree in mathematics. I have not asked him for his precise age, but I think he's at least 50. So 30 is certainly not too old, if there even is such a thing as "being too old".

Don't let yourself be discouraged by the younger students seemingly shrugging off hard challenges which you yourself struggle with; it's just as much a challenge to everybody, they might just don't like to let it show as much (Speaking from personal experience -- I certainly don't like to let others on to how much I struggle with a particular problem, but I suppose with age often comes a certain amount of humbleness.)

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I am indebted to Roger House, an undergraduate for throwing a challenge back to me and showing me the way to Fibonacci matrices. He was 50 at the time, and went on to graduate studies in algebra. Gerhard "Ask Me About Binary Matrices" Paseman, 2011.12.04 –  Gerhard Paseman Dec 4 '11 at 20:29
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It is important to consider that people have different intellectual strengths at different ages. In my teens and twenties computation was my strength and I would happily grind away on page after page of calculations eighteen hours a day, weeks at a time. In fifty five and that doesn't happen anymore. So I do feel I have lost a degree of mental nimbleness and speed. On the other hand I am a better communicator and educator now than when I was young. Someone wrote that age can bring a certain cunningness to solving problems.

Another pertinent issue is whether you have previously been maintaining an active intellectual and maybe even scientific live. You may have important skills, knowledge and perspective you can leverage and transplant into mathematics. I went back to college in math in my fifties and the fact that I had spent twenty five intellectually active years in the software development industry gave me important competitive skills that had a dramatic impact in how well I did in certain math classes. I took an advanced differential equations class that used Mathematica. My background as a programmer and twenty years experience with Mathematica allowed me to attack homework problems quickly with a large variety of methods so that after one hour's work I would have a ten or twenty page Mathematica notebook dissecting the problem I could share with my class. A broad background in relevant areas, attacking a problem in a number of radically different ways, and being interested in communicating and educating others are all strengths I developed with age.

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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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What does this mean? I personally don't understand anything until I can visualize it. –  Qiaochu Yuan Dec 18 '09 at 21:49
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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. –  Kevin H. Lin Dec 24 '09 at 2:04
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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. –  Steven Gubkin Jun 7 '10 at 14:31
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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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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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