math phd quora

Math Misery?

"do not worry about your difficulties in mathematics. i assure you, mine are still greater." -albert einstein, should i get a phd … in math.

If you’re asking this question, then the answer is “Yes, go and work towards a PhD.”

Now for some details.

Every so often (about once a semester), I have a student, a friend, an acquaintance, a client, etc. ask me if they should “get a PhD in Mathematics”. But that’s actually not where the question ends nor is that really the question. Usually the back story is as follows:

• The person is thinking about graduate school in a technical discipline because they happen to be reasonably good with mathematics (and for the sciences, being reasonably good, at least mechanically, at mathematics is a prerequisite).
• They have a burning desire for something beyond what their undergraduate curriculum offers.
• They’ve been in the workforce for some time and now want to go back to graduate school — these folks often have a science, engineering, or math undergraduate degree and their work environment has been technical.

From here the following types of statements are said when the individual goes to seek out the opinions of friends and colleagues for getting a PhD in Mathematics:

• Don’t get a PhD, you’ll have no job prospects.
• All you can do with a PhD in Math is teach and you won’t make a lot of money.
• You’ll be overqualified for industry positions.
• Don’t get a PhD, you’ll be an expert in something that only 10 people know about.
• You have to publish papers all the time to keep your professor position.

Some half-truths, some full-blown lies.

Zeroth, who says that there are no job prospects? What is their background? Where / how are they making this claim? Every time I ask these sets of questions, the demographics of the folks who discourage others from further academic pursuit of mathematics are folks who themselves have either failed out of a PhD program or had made their decision to stop further pursuit because of someone else who told them not to. It would be like me saying to someone, don’t pursue a career in Graphic Design, you’re just going to spend the whole time touching up other people’s crappy design work. I’m not a Graphic Designer! I don’t work in that capacity! And even if I did work in that capacity, then seek out a few other opinions! This guy is an awesome graphic designer (he’s my brother).

First, check out 101 Careers in Mathematics . I haven’t read it, but the title alone should be convincing.

Next, at a personal level. I work and have worked as a mathematician in industry. I also teach part-time. I regularly get messages or phone calls from recruiters about full-time opportunities for someone with a strong mathematical and technical background. Depending on the recruiter, it can be hit or miss. Some recruiters don’t really understand the expertise and just see math, math, math, everywhere on my resumé. The recruiters that don’t understand my background will send me full-time positions for Bachelor’s degree candidates. Technical recruiters tend to have a better time understanding the various backgrounds. I am overqualified for some positions, mis-qualified for others, underqualified still for others, or a perfect match. This qualification problem is going to happen no matter what degree one holds. The best thing I can do for myself is to see which positions are within my technical expertise, but for which I am underqualified and start learning those topics. I may not want to apply for that job, but it’s an indication of something I don’t know.

I ran a Math department for a few years in the corporate world with three US offices directly reporting to me and a total of eight global offices over which I had policy oversight. I didn’t do the math in the Math department — I hired people with math and computer science backgrounds to take care of the day-to-day mechanical work. What I had to do was set up sensible and rigorous math policy, field technical questions from clients, create efficient processes, explain the mathematical underpinnings of certain methods to non-math savvy regulators, etc. — in effect, I was a business manager with a very technical background. That is exactly what was needed for that position. The company needed someone who was external facing who could speak about mathematical topics with proven authority in the field without speaking in subscripts.

I now work in a consulting role. I work with organizations to help streamline business processes so that they are cost-efficient without sacrificing quality. How do I do that? I write programs. I analyze the entire product development life cycle and see where bottlenecks are. I track relevant and necessary statistics to measure how effective these processes are. I also run pre-analysis to give a sense of what the expected gains are of a new process or method. And it doesn’t stop there. I also look at existing technical code and see where things can be more efficient.

Some of my clients are also individuals who are working professionals. Some are going through a career change, others just feel that they are falling behind the times and want to get “caught up”. Career changes often requires going back to school, taking some type of graduate school entrance exam, taking a statistics course, etc. Those who feel they are falling behind really just want to learn how to program. I’ve worked with company vice presidents, small business owners, working professionals returning to school for an MBA (for example), medical doctors, finance professionals, and even aspiring math teachers. I have yet to work with a school — I would love to do that, but I’ve found that there’s an immense amount of red tape. Anyone know how I can go about working with a school — math training, professional development, software development, leadership training, classroom management, “cool math stuff seminars”, etc.?

Finally, it is true that there are many teaching positions available with a PhD in Mathematics. It is also true that it is not all fun and glamour, living the life of luxury of an esteemed professor’s life. But tell me, how many other career choices are that glamorous? And if you wanted glamour, go do something else! Either that or solve a popular and open problem in mathematics. Then you’ll have fame! People confuse the fact that there are many teaching positions with there are only teaching positions.

If you are thinking about working towards a PhD in Mathematics and do not want to teach, then absolutely, you must learn to program. Without a reasonably strong programming background, there are fewer industry positions available (“fewer” does not equal “none”). If you do want to teach mathematics, I’d still encourage you to learn to program. It will help with teaching. Students will want to see the theory in action and not just in an academic setting. This is how I teach many of the “applied” courses or units like Graph Theory, Probability, Statistics, Personal Finance, etc.

The point here is that the degree is the degree and in some sense it’s irrelevant, but, if you have the degree and can actually put it to use, there are opportunities beyond teaching. A PhD in Mathematics is not somehow making a person unemployable. It just means that the type of employment one will find is different.

“Getting” a PhD

One does not “get” a PhD by hanging around in the system for a bunch of years. Unlike Bachelor’s and Master’s degrees where the majority of the requirement is to complete coursework in an academically satisfactory way, a PhD is not quite the same. There are few courses that one actually takes as “requirement”. The majority of the time is spent doing research, writing papers, giving talks, and even perhaps, networking within the math community.

Several of the people who have been interested in a PhD were under the impression that the process works as follows: 4 years for a Bachelor’s, 2 years for a Master’s, and then 4 years for a PhD. That may be a reasonable average for the length of time that it takes, but the content is different. The Bachelor’s programs are coursework heavy, with perhaps a senior project that is professor-led. The Master’s degree also tends to be coursework heavy. But there are two types of Master’s degrees. There is the Master’s degree that is not research-oriented, and then there’s a Master’s degree that is research-oriented. The research-oriented degrees are typically set ups for entrance into the PhD program. The non-research-oriented degree is coursework heavy and does not often require the same focus on theory as the research-oriented Master’s degree does. The two degrees have a lot of overlap, but there are nuanced differences in coursework.

Getting into a PhD program often requires the completion of the Master’s level coursework. Some programs award a Master’s degree and then require that the student “reapply” for the PhD program by successfully passing a grueling set of exams known as “Qualifying Exams” (“quals”). Once a student has passed the quals, they are admitted into the PhD program and are now considered to be a PhD Candidate. Other programs have one of two tracks — a Master’s track or a PhD track. If one enters the PhD track, it’s do or die and there’s no Master’s degree awarded regardless of the outcome. If one enters the Master’s track, then they have to apply to a different university for their PhD.

Your Advisor And Your Research

As I said earlier, the PhD is not a degree that one just “gets”. There is a “Master / Apprentice” type relationship between the PhD Candidate and his/her Advisor. There are many, many horror stories of tyrannical advisors who work their apprentices into the ground. I’ve been witness to a few of these incidents. It’s a bit scary and terrifying to have one maniacal individual control several years of a person’s life. For this reason, if you are pursuing a PhD in Mathematics (or any field), choose your advisor very carefully. You will be working with him/her closely for many an hour.

I had the great fortune of having probably the best advisor a student could have. Not only was he a capable and energetic researcher, he was patient, thoughtful, kind, and knew how to work with a variety of personalities and work habits. He left me alone to fiddle. I did a lot of work under him. He pushed me to present and publish. But in all of this, he was never once a tyrant. This is the type of person you want as your advisor. So, when you are working on your Master’s degree towards your PhD, pay close attention to graduate and research faculty. Interact with them. See how they treat their graduate students.

Your advisor, if you are able to cultivate a healthy relationship with him/her, will be your mentor for your life. It really is a Master / Apprentice relationship. You just have to decide if your Master is a Sith Lord or a Jedi Master and then you have to decide what you will become.

Your research is your baby. Nurture it, grow it, cultivate it, and stay with it. That’s a mistake I’ve made. I haven’t kept up with research mostly because I am not working in academia full-time. Regardless, I still make it a point to read the latest in the literature and keep fresh in my mind the things I worked on. One day I will get back into it.

Your research trajectory isn’t necessarily going to go the way you planned. You may start out studying Partial Differential Equations, but before you know it, as you wind through the maze that is Mathematics research, you may find yourself deeply immersed in Stochastic Calculus. Don’t pigeonhole yourself from the outset. Let research take you where it takes you and be excited about everything.

Research is not easy business. There are going to be many, many failures. Some even soul-crushing. My first soul-crushing failure was when one of my research papers was already published in full-generality! I had done an extensive literature review and had found nothing on the topic. Every few months I would do searches and nothing. Then once I had all my results ready and the paper written, I did one last literature review and wouldn’t you know, someone had already published it!

Research is open-ended. There is no textbook solution to the problem you are working on. There is no readily applicable theory. There are no existing methods. This is what you are doing. You are crafting the theory. You are devising the method. You are working on an unsolved problem, however esoteric as it may seem.

Failures define us just as much as our successes do. The sooner we can learn from our mistakes, overcome the setbacks, and get back on our feet, the closer we are to success. Working towards a PhD is not for the weak-willed and it isn’t a degree one just gets.

As I said at the beginning, if you are contemplating working towards a PhD, then do it. Do your homework with respect to who your advisor is, what research specialty you may want to start with, what the university program looks like, what the Math department looks like, etc. Ignore all the silly reasons that people give you about job prospects and the like. Anyone who tells you “don’t learn anymore”, isn’t your friend. Jettison them from your life, immediately.

10 thoughts on “ Should I Get A PhD … In Math? ”

Thank you for your post! I also really enjoy mathematics. I graduated with a Bachelor in Health Science with a minor in business with College Algebra and Calculus 1 courses completed. So fun. I am currently signed up to complete my Masters in Accounting degree, however, I also want to pursue mathematics. I considered completed my Masters in Accounting with a minor in mathematics, and then going on to a PhD in Mathematics. The reason I am considering a Masters in Accounting is due to the “job security,” as well as I kind of enjoy accounting, and the potential to work from home. I know I really enjoy mathematics, and it is one of the subjects that I caught on to the easiest throughout school. I didn’t have to study near as long with math, as I did with other subjects. (1) Moreover, would me pursing a Masters in Accounting with a minor in mathematics, and then going on to pursue a PhD in Mathematics a smart choice? Or should I plan to pursue a Masters in Mathematics, and then go on to the PhD in Mathematics? As a note, the path I would like to pursue with mathematics is to teach mathematics one day. Learning to program sounds cool too. Also, knowing what mathematics scholarships are available out there would be very helpful. (2) Do you know of any math scholarships that I can apply for? Thanks! Melissa Coppola

Thank you for the post…i am having few questions …. what are the benefits that a PhD in mathematics person get…..why should one do PhD in mathematics ..i mean a person is interested but he/she is confused in why one should do PhD ..what are the benifits in future after completing PhD . please reply for the same

Thank you for the post. I have dreamed of learning advanced math since I was in primary school, I have loved math so much, that I had spent my secondary school summers on learning math, solving math questions and equations, I had such a desire for learning math, that it was all I was thinking of and practicing, and I was very good at it. Now, when I graduated from secondary school, I was one of the top students in my country, and though I wanted to pursue a degree in a math related subjects, I ended up pursued to enter medical school, which ended miserably with a low GPA in Health Science. ;( Now I find myself dreaming about math again, wishing if things where different Anyways, do I have a chance? I did not study math at college, I am eager to study math again, I would love to spend up to 12 hours a day every single day studying math, I would feel energetic and happy. Do you have any advice for me, thanks.

Thanks for writing! I don’t know your exact situation, but if you have the time and resources, then absolutely pursue mathematics as you’ve wanted to all along! Generally, and broadly speaking, if you’ve been out of touch with mathematics (formally) for a while, don’t be surprised if it takes a little bit of time getting yourself back up to speed. Be patient, continue to work at it, and always try to ask ‘why’ when studying! Let me know how you are proceeding!

Thank you so much! Weeps.

You’re quite welcome!

Thank you for the post. I’m currently preparing to apply to a graduate program this January after 5+ years of community college teaching. This is great advice and quite encouraging.

By the way, what you say about your advisor is absolutely true, he taught my undergrad multivariable calculus course at Ball State when he was a postdoc. He was fantastic.

I’m so happy to know that this has helped in some way! And yes, Giray is great.

Thank you for this. I really want to study mathematics.. but right now I feel like a lot of door are closed since I pursued a different path. I still have a yearning. I have to see how that path will unfold. Your piece has helped a lot! Thanks

Thank you so much for your words! I’m glad this has helped. Feel free to get in touch if you need a sounding board!

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Too old for advanced mathematics? [closed]

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?

• mathematics-education
• soft-question
• 5 $\begingroup$ There is a question about mathematicians that learned mathematics at a late age. mathoverflow.net/questions/3591/… $\endgroup$ –  Kim Greene Nov 29, 2009 at 8:54
• 4 $\begingroup$ 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 Nov 29, 2009 at 9:47
• 4 $\begingroup$ 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 Mar 4, 2010 at 16:32
• 1 $\begingroup$ I got my 1st degree at 27, and it was in CS, not in maths. $\endgroup$ –  Dima Pasechnik Dec 4, 2011 at 16:36
• 3 $\begingroup$ 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 Dec 24, 2011 at 17:45

37 Answers 37

This is indeed not a typical math overflow question, but never mind that.

Of course you can learn mathematics at the age of 30 after having stopped studying it at the age of 18! Examples are abundant -- in almost every math department I've ever been in, there are at least one or two older graduate students that took some years off (after high school, after college or both) and did quite well upon their return.

Being older than 18 may not be a bad thing. Many 18 year-olds are neither well-prepared nor well-motivated to study mathematics (or something else) at the university level: a lot of them are there because their parents want them to be, and most of them are there because their parents are paying.

It is true that essential skills get rusty after years of disuse -- when I teach "freshman calculus", older students often do not do very well, even if "older" means 21 or 22: they've forgotten too much precalculus mathematics. But you have been learning about calculus, differential equations and linear algebra on your own and enjoying it! You're looking forward to reading a book on Bessel functions!! You're well past the point where older, rusty students have trouble. You can do it, for sure, and it sounds like you want to, so you should.

By the way, 30 is not remotely old. I am a few years older and I think better and more quickly now than I did when I was your age.

• 108 $\begingroup$ We can safely file that quote under "Hardy has been known to talk like a pompous ass". $\endgroup$ –  S. Carnahan ♦ Nov 29, 2009 at 21:54
• 40 $\begingroup$ When you encounter Hardyesque opinions on older mathematicians, it's probably worth keeping this comic in mind: xkcd.com/447 $\endgroup$ –  Harrison Brown Nov 30, 2009 at 2:09
• 37 $\begingroup$ @fpqc: When I was your age, teenagers were more respectful of their elders. @SC: On the contrary, Hardy wrote his famous book after he himself stopped doing mathematical research. Many contemporaries and historians have written about his state of mind during the writing of his book; I believe the phrase "clinically depressed" would now be used. I think it has meaning only as a personal statement, and a dark one at that. $\endgroup$ –  Pete L. Clark Nov 30, 2009 at 2:31
• 31 $\begingroup$ Anyone who actually doubts the productivity of older mathematicians has only to look at Gelfand's output in his later years. $\endgroup$ –  Qiaochu Yuan Dec 1, 2009 at 19:27
• 17 $\begingroup$ Well,does the fact that Karl Weierstrass-one of the founders of rigorous analysis-got his doctorate with a treatise published when he was 39 after many years working as a teacher and studying on his own and continued to publish until his death in 1897-count as a good counterexample, fpqc? Keep in mind-this was in an age when people lived much shorter lives and in much poorer general health. In fact,he died immobile of pnuemonia and continued to work when he could until his death. And we haven't even mentioned his remarkable career as a doctoral mentor to such names as Georg Cantor. $\endgroup$ –  The Mathemagician Mar 19, 2010 at 23:06

Dear bitrex: your enthusiasm is heart-warming!

I have had students much older than you and they have always been a joy to teach: their maturity more than compensated for their potential knowledge-gaps and they fared very well on their exams.

The nicest success story is a professional cellist who didn't even have the "baccalauréat", a French diploma for the end of secondary school usually taken at age 18. He started learning math because he had married a math teacher (!) and became an excellent student. He passed his D.E.A. (a sort of undergraduate thesis) brilliantly and unfortunately couldn't accept my suggestion to do a Ph.D. because of his professional activity ( I sometimes hear him at concerts...).

So my advice is to go on with your mathematics: I can't predict the future but my feeling is that your age is not very relevant. Good luck!

With all this unanimous enthusiasm, I can't help but add a cautionary note. I will say, however, that what I'm about to say applies to anyone of any age trying to get a Ph.D. and pursue a career as an academic mathematician.

If you think you want a Ph.D. in mathematics, you should first try your best to talk yourself out of it. It's a little like aspiring to be a pro athlete. Even under the best of circumstances, the chances are too high that you'll end up in a not-very-well-paying job in a not-very-attractive geographic location. Or, if you insist on living in, say, New York, you may end up teaching as an adjunct at several different places.

Someone with your mathematical talents and skills can often find much more rewarding careers elsewhere.

You should pursue the Ph.D. only if you love learning, doing, and teaching mathematics so much that you can't bear the thought of doing anything else, so you're willing to live with the consequences of trying to make a living with one. Or you have an exit strategy should things not work out.

Having said all that, I have a story. When I was at Rice in the mid 80's, a guy in his 40's or 50's came to the math department and told us he really wanted to become a college math teacher. He had always loved math but went into sales(!) and had a very successful career. With enough money stashed away, he wanted to switch to a career in math. To put it mildly, we were really skeptical, mostly because he had the overly cheery outgoing personality of a salesman and therefore was completely unlike anyone else in the math department. It was unthinkable that someone like that could be serious about math. Anyway, we warned him that his goal was probably unrealistic but he was welcome to try taking our undergraduate math curriculum to prepare. Not surprisingly, he found this rather painful, but eventually to our amazement he started to do well in our courses, including all the proofs in analysis. By the end, we told the guy that we thought he really had a shot at getting a Ph.D. and have a modest career as a college math teacher. He thanked us but told us that he had changed his mind. As much as he loved doing the math, it was a solitary struggle and took too much of his time away from his family and friends. In the end, he chose them over a career in math (which of course was a rather shocking choice to us).

So if you really want to do math and can afford to live with the consequences, by all means go for it.

• 9 $\begingroup$ FWIW, I think this is an excellent answer, esp. in context of all the other answers' unbridled enthusiasm. In all subjects, it's common for students who love the subject to consider "getting a phd" simply the next logical step. In reality, there are many factors, including lifestyle and career outlooks, that will weigh in along with the pure love for a subject in determining one's happiness or success. What I get from this answer is "Just because you love the subject does not mean a phd is right for you"--something I think a lot of current/former phd students wish they'd thought about. $\endgroup$ –  OctaviaQ Oct 14, 2011 at 15:18
• $\begingroup$ ... and this caution may be especially relevant at an older age, when you're more likely to, say, have to ignore an existing family, vs. putting off creating a family. I think @Deane is giving the very wise advice that, even if age does not preclude the mental ability to succeed, it may have an effect of the perceived magnitude of the sacrifices required to succeed in the path. $\endgroup$ –  OctaviaQ Oct 14, 2011 at 15:27
• $\begingroup$ "You should pursue the Ph.D. only if you love learning, doing, and teaching mathematics so much that you can't bear the thought of doing anything else, so you're willing to live with the consequences of trying to make a living with one..." This advice is directed at someone who works in the music business, is it not? I'm sure it is familiar to bitrex if he knows any aspiring professional musicians, because the same advice applies to them, much more strongly. $\endgroup$ –  Elizabeth S. Q. Goodman Dec 5, 2011 at 3:18
• 3 $\begingroup$ When I interviewed at my school, I met another faculty member whose job it turned out I took. A few years later he returned for a visit, having moved to private industry, and was then earning triple my salary. Guess what, I don;'t envy him! I enjoyed doing what I got to do. Go figure. $\endgroup$ –  roy smith Aug 6, 2012 at 5:50

Here is an example that no one has mentioned yet. Raymond Smullyan is a well-known mathematician who has had quite a career, publishing many books and papers on recreational mathematics and logic. He got his undergrad degree at around age 35 and his PhD at age 40. It didn't seem to hurt him much. He is now 91 and is still publishing(!). So yes, these people exist!

In my late 20's I was a lugger in a meat market. I got my PhD in my mid 30's, and spent the next 3 decades on the faculty at UGA. To be honest, getting a PhD was hard and not especially lucrative, and certainly not everyone in my graduate class has earned a living doing math at the college level. But I would not have wanted to do anything else. I have met many brilliant and generous people and been privileged to discuss math with them all these years. If you pursue your goal but don't find a suitable college teaching job, and you like discussing math with interested kids, I suggest looking at private high schools. Some of my most rewarding teaching occurred when I volunteered one year at a good local high school.

• 1 $\begingroup$ youtube.com/watch?v=fdkVsnZk2MI $$ $$ $\endgroup$ –  Will Jagy Nov 11, 2010 at 5:22
• 13 $\begingroup$ Dear Roy, As I already told you, the privilege was ours. $\endgroup$ –  Pete L. Clark Nov 11, 2010 at 5:32

I turned 40 late this past year after a long and unhappy life taking care of sick family and then enduring my own illnesses that have slowed my progress considerably. But I'm nearly finished with my Master's in mathematics after getting a subpar bachelor's in chemistry and I'm planning for my PHD. My health is the number one concern here as far as being able to do it. I know when I'm on my A game, I'm as good as anybody. The problem is that happens less and less these days

Am I scared? SURE. Especially hanging around with 19 year olds who can run rings around me because they don't need to sleep........ But I can't give up now. I've suffered and lost just too much. And anyone walking the same path shouldn't have any other attitude except that. PERIOD.

I've got a Master's degree almost, some terrific grades in some very hard graduate mathematics courses and some not so great grades and incompletes. I've learned some awesome subjects and had some fantastic teachers.I've been reviewing textbooks for the Mathematical Society of America pro bono for almost 2 years and I LOVE the job. I have a blog on mathematics I don't write in often enough,but I intend for that to change.I have the same philosophy on mathematics that the late great science fiction writer Fredric Brown had on writing: His wife said after his death he hated to write,but LOVED having written. I love having written mathematics......

I don't even care about grades anymore. I was obsessed by it once,but you know what? After watching half your family die slowly in agony of cancer and seeing entire families live out of their cars after falling behind on their mortgages,it really puts a perspective on things. I doubt the fact I got a C+ in advanced ordinary differential equations because I got sick the last 3 weeks will matter if I publish 6 significant papers on additive number theory over the next 2 years, do you guys?

Yeah, I know, in academia,what I just said is heresy. But you have to keep it real.

I'll make it or I won't. I'll get a PHD in mathematics and spend a few years making contributions and teaching or I'll die of a massive heart attack trying. It's as simple as that.

• 32 $\begingroup$ Too much information. $\endgroup$ –  Todd Trimble ♦ Dec 4, 2011 at 21:15
• 10 $\begingroup$ Probably,but I think I made my point. We're all human here and posts like this-once in awhile-are positive to remind us of that. $\endgroup$ –  The Mathemagician Aug 10, 2017 at 17:44

Quick answer: No, you are not too old. Yes, such people do exist. It sounds like you're off to a good start. Don't let your age worry you.

I dropped out of college when I was 21 to work as a software engineer. Admittedly my work was technical, but my background in abstract mathematics was basically nonexistent. Two+ years ago, when I was 34, I decided to get a PhD in math. I returned to college to study math, basically from scratch. Like you, I'd learned some math on my own, but I feel I made faster progress in a more structured environment working with people who were also trying to learn math. It was a great decision. I'm now a first year graduate student, well on my way to a second career in math.

• 11 $\begingroup$ At Princeton, no less! Go, Cotton! $\endgroup$ –  Eric Zaslow Mar 8, 2010 at 4:40
• 5 $\begingroup$ A bit of a side question, how did you manage to pay the bills? Did you find a job as a TA straight away, live off savings...? $\endgroup$ –  finitud May 5, 2014 at 23:07

First of all, bitrex, of course you're not too old, and it's probably your imagination that you're slower now than you were at 18. What's more likely is that you now have a better awareness of what you're missing, so it seems slower, even though I'll bet that you're actually learning better. "Cognitive decline" (or at least any decline which would affect doing mathematics) doesn't set in until your 60s, and even then it's highly variable.

I think it's sad that anyone feels this question even needs to be asked. One of the things I find most frustrating about mathematical culture is how impressed everyone is when good mathematics is done by younger people, as though your age appeared next to your work, like in a grade-school art contest. I really hope the Chern Medal supplants the Fields as the premier prize--I think providing something aspirational to over-40 mathematicians will have a very salutary effect on the field as a whole, to say nothing of the salutary effect it will have on a lot of individual over-40 psyches.

But here's something odd that I've noticed: the mythology about "older mathematicians" seems to cut women more slack. I guess sexism can cut both ways.

• 6 $\begingroup$ I thought the justification for the "under 40" requirement for the Fields medal was to encourage future research. This is still a bit of a cop out, but it's worth noting. $\endgroup$ –  Cory Knapp Nov 29, 2009 at 21:29
• 2 $\begingroup$ The mythology I've heard is that men might be brilliant at math at a young age and then decline, whereas women might be pretty good for years (but never brilliant, is the implication). If that's what you're referring to, that addition always reeked of a post-hoc justification of the same old sexism to me. $\endgroup$ –  Elizabeth S. Q. Goodman Dec 5, 2011 at 2:13

I started college in Jan 2007 when I was just about to turn 27. At the time I knew nothing : I didn't really remember trigonometry. I didn't know what it meant to raise a number to a negative power. I'm graduating this December (at 29; I was motivated enough by feeling like I was years behind schedule that I was able to finish this degree in 3 years), in the process of applying to graduate schools, in 3 graduate classes now.

Yes, I do regret that I didn't do all this sooner. And honestly it still feels weird. Sometimes I go to class and it just seems so strange that I'm actually going to college. Still, overall, this is one of the best things I've ever done. I guess you have a couple years on me, but it doesn't matter.

The unfortunate thing is that, at least at my school, you don't get to do much mathematics until your junior year, so you may be in for a long slog of general education classes you are not particularly interested in. (I actually think this is a big problem... but that's a whole different issue I guess.)

Also, you say "I'm getting into material that is going to be very difficult to learn without structure or some kind of instruction." Maybe. But it's also possible you just haven't yet developed the skills/habits to learn that kind of thing.

• 6 $\begingroup$ Re "the unfortunate thing" -- this is a common story at many places. I think much of the reason why I entered mathematics and not any other subject was that the mathematics program at the University of Alberta allowed students to jump right in and learn mathematics in a very "aggressive" mode from the beginning. I found the intro courses in most subjects to be devoid of any real expectations on the student. I was in university for a challenge. Challenge me!! That's how I felt. $\endgroup$ –  Ryan Budney Dec 19, 2009 at 20:27

One of the ablest mathematicians at my grad school went to Julliard and taught music until he was 30. He then spent 6 years at the U. Wisconson and got a PhD degree under Walter Rudin in function theory. He is a very successful professional mathematician.

My 2 cents (I'm too poor for 5 cents ;) )

I have a very problematic educational impediment, I am moderately to severely disabled, and it strongly effects my ability to learn mathematics. I'm not equating the problem of "being too old" and "being disabled", but just as a success story.

I will be completing my mathematics undergraduate degree in my 6th year at UC Berkeley (next year).

I would not let anything stand in your way if you want to learn mathematics. It is an amazing subject and I wish I could tell more people about why it's amazing. Your enthusiasm indicates to me that no impediment could stand in your way.

Pacing may be an issue since you are not working with an instructor... that's a different topic but I believe there is a post on here about pacing for learning new mathematics (for some reason I think I even posted it ><)

I have friends who are your age and older that have succeeded at UC Berkeley in mathematics, and, not to exaggerate, they made it through what is for most people a rather intense curriculum (from my vantage point, which is, of course, quite limited).

I never doubt the capabilities of the well motivated, so I believe you can do it! Keep with it! It only gets better :)

I agree with the consensus here: it is definitely not too late to be learning math. The fact that you have mastered several books worth of material on your own, without the benefit of an instructor, is proof enough. There is nothing to stop you from continuing in the same mode if you wish.

However, it sounds like you have heard the siren call of mathematics and would like to get into it in a bigger way, and more rapidly. As a mathematician I can only encourage you. Sure, there are some disadvantages to starting later in life, but there are compensating advantages as well.

My own testimony: I did complete a bachelor's degree in math straight out of high school, so I do not quite fit the profile you are looking for. But after working 23+ years in the software industry, I returned to grad school in 2002, completed my master's in 2004, and finished my PhD this last June (2009) at the ripe age of 51. I don't think my thinking is any slower than when I was young.

Whether you should return to school is a personal decision, and it no doubt depends on many factors. But that is really a separate discussion, a separate thread. The answer to your immediate question is that age should not be a barrier (especially for a young-un like you).

I always feel very encouraged when I come across threads like these. I'm in a similar position. I was a math major at Georgia Tech. I lost my way and ended up in pharmacy school. I'm now in my last year and plan on going back to Tech to finish my math degree as soon as I'm financially able (hopefully after one year of working as a pharmacist), after which I want to go to grad school. It's great to hear such positive stories from others.

If everything goes as planned, I'll be 30 when I enter grad school. So no, you have no reason to feel you're too old. I know of several mathematicians who obtained their PhDs in their 30s, and even a famous one who got hers at 41.

You are NEVER too old if you love it. And this is coming from someone who is 47 and working on their PhD in probability.

• $\begingroup$ Just reading this message now. Really hope you made it, Peter. My health combined with financial problems ultimately got the better of me and ended my career-for now. I'm hoping a business I'm working on in math education gets me one more chance before I die. $\endgroup$ –  The Mathemagician Feb 18, 2020 at 5:09

I just turned 30 myself, and I'm in almost precisely the same boat. I read mathematics "religiously". I keep thinking of going back to school, but I've been too timid about it. I think the biggest obstacle I've felt learning on my own (or trying to) is the lack of a "click" to make sure you really understand the material. Rather than a test, exam, or problem sheet, you have to figure out how to verify your answers in more than one fashion. I'm sure that can be a great boon, but it also slows you down.

It's very good to know I'm not alone in this boat!

I just read that coffee table book full of mathematicians' biographies: "Mathematicians: An Outer View of the Inner World". The most striking part of it was the variety of backgrounds. While the majority of featured mathematicians were interested in math early, or had parents with analytic/technical backgrounds, a significant fraction of them only became interested in mathematics while in college, and some later than that.

BTW, you said you came to mathematics from music and acoustical applications, and that you're starting to feel overwhelmed by the math of those waveforms. There are actually many other connections between music and mathematics, and some of these other areas may be fruitful to you. For example, look at Combinatorics for the study of melody or harmony. But along the path you've described, of Fourier and DST and Bessel functions, take a look at this free online edition of "Music: a Mathematical Offering", by Dave Benson and Cambridge University Press: http://www.maths.abdn.ac.uk/~bensondj/html/maths-music.html . It looks terrific, and I'm going to download it myself now.

Also, it's very common to not understand some new mathematics the first time. Professional mathematicians will often plow through a difficult paper on the first read, skipping over equations to get the general idea of where it's going. Even Feynman recommended this technique. Don't let yourself get stuck trying to understand an equation, but keep going. Then you can come back and read it again, either immediately or later, with more understanding.

As someone doing something similar, the biggest problem for me has been time as I recently got married. The coursework part of things isn't that bad but doing research on a topic takes focus and a lot of time just thinking and reading about a problem.

I don't always have as much time as some of the younger students who can essentially dedicate most of their waking hours to studying mathematics.

I started at 32, almost 33. I've been worried that I've lost my best years but I'm getting through Analysis fairly well, teaching myself topology and preparing to take number theory & a real probability course in the spring.

In my second semester the topology (Munkres) and the Analysis (Rudin) were beyond me, but just a bit of work went a long way. Much of Concrete Math (Knuth) was beyond me last year as well, but I'm able to get what I want from it as I need to.

I'm slower in a lot of ways than I was when I was 18, but as some have said maturity does a lot for a person. There's no way I'd have done as well as I am then. Also, speed isn't what's important for mathematics. It's great if you have to take the Physics GRE and need to calculate on the fly, but I've found I tend to be able to grok proofs at a deeper level than I would have.

Also, professors love the work ethic us "older" people have.

The only suggestion I can offer is find a program that you fit well in, whether big or small, with strong guidance or with a lot of independent study and find a professor you enjoy working with if at all possible.

I couldn't be happier and my life couldn't be better were I to have chosen a different path. Give it a try, the worst that happens is you decide it's not for you.

I am a PhD candidate in Comp Sc and will soon touch 30. And I don't think I've grown slower during the years. My intuition has probably never been "better" and I have nurtured the humility to understand that I am far from perfect, even in my opinions and thoughts. But the pursuit is to be perfect and I know that I can do a great job.

My question to you is: Are you sure that the "slowness" as you've got "older" is really true or is it something you've learnt from the popular culture ? It is easy to get biased, very difficult to be true. This is, in particular true about the scientific theories of the effects of age on mathematical ability. Just take note of how many papers are published each year contradicting the earlier theories.

From my personal experience I can say that when you enter the graduate school late, the expectations of the people around you are different -- most likely you'll have considerably more responsibilities like family, planning for the future, etc. So you surely need a stronger will power and time management skills than the under 25. This is an opportunity.

• $\begingroup$ 'something you've learnt from popular culture': Excellent comment, agree) $\endgroup$ –  sigma_z_1980 Sep 24, 2011 at 22:39

Wow - this is totally encouraging. I just turned 50 in March and within the last year and a half have become obsessed with numbers. I am compelled daily to find the prime factors of zip codes, addresses, and RSA numbers. I saw the Christmas lights on my house in binary. I love the patterns and personalities of numbers.

Though I am not as wizardly as you all, I blew through an elementary algebra text in a weekend, find that geometry is returning easily, and I'm on my way to really enjoying trig and calculus, although I really want to explore discrete mathematics.

So reading through these posts has really boosted my confidence and enthusiasm. Thanks to all!!

• $\begingroup$ The older I had become, the sharper my mathematics intuition had become. As an undergraduate in CS, I had a math minor but I did not fully embrace the math. To what you said about your sensitivity about the patterns and numeric relationships, I concur. Everything around me has come alive from the equations that describe my inversion table to approximating the volume of my odd shaped pool. Mathematics is no longer a one night stand, she is now a full mistress! $\endgroup$ –  Mark Irvin Nov 10, 2015 at 16:32

I think the myth of being "too old" is a stereotype threat like others that tend to push people out of mathematics at various stages, at least in my experience in the USA. But it's not just about mathematical abilities, it's also about how you communicate, write or socialize; that affects whether you learn from others, whether they recognize your contributions to mathematical thought, and so on. Embarrassment and egos can get in the way of people who should be studying together and learning from each other. If you're studying math in college now, I hope you will reach out to some of your younger classmates and work with them.

A couple more words of encouragement. Sharpening and focusing one's mathematical thinking, as well as learning mathematical content, often feel like slow processes (or come in spurts), and repetition may be required; however the progress one makes in a year can look impossibly far before one makes it. I think that contributes to feelings of inferiority that people so often have when it comes to math. You should do more math in college, if you want to. But if you're keeping your job and have a real life and yet have room for math, you're in a great position, and the main obstacle might be figuring out how to contribute to the community. We don't just need published papers on new work; we also need time-saving sources, such as masters' theses, that clarify, organize, and modernize old work. Either way the trick would be getting math into circulation when you're not affiliated with a university. Contact with professors would help.

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.

I would not necessarily say that you're too old to learn mathematics. I'd even say it may be an advantage. Many mathematical problems you'll encounter during during your studies can be solved easily if you accept and understand how mathematicians proceed when they come across problems. This normally requires one thing: patience. It is normal to be stuck on a problem for days or even for weeks (my experience sometimes!). However, many (young) people tend to becoming very frustrated if a solution isn't obvious. Mostly, indeed, it isn't. These are then the interesting problems. There is a saying that the older you are the more patient you are. If you combine this with motivation and passion about mathematics and still some curiosity, you'll have no problem in succeeding (no guarantee, though, but it becomes more likely ;) ). My opinion is that you never become too old to do something academic. My dad for instance wanted too learn something about electrical engineering. So, he read some books about it and is able to solve the problems these books contain. And, he studied law and is 55 years old. I think this shows that with enought motivation you can do anything. Perhaps you'll have a decreased memory capacity compared to your fellow students, but only perhaps. I think, you never know, if you don't try. So just try it.

To encourage you there are two people in my Department who are about 40 years old and have just started their Ph.D. One of them was out of touch for nearly twenty years!

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.)

• 2 $\begingroup$ 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 $\endgroup$ –  Gerhard Paseman Dec 4, 2011 at 20:29

It has been done many times. Someone retires from his/her first career, then goes back to school. Occasionally even getting a Ph.D. in mathematics, and having a second career as a mathematician.

Well, you can't be sure that you will do an academic career.

But you're definitely able to study mathematics.

Here are my 5¢:

You should not study mathematics unless you love the process of learning, problem solving, etc. I think the right motivation is the joy of studying, not a career. (But don't be upset if studying is hard for you — there is no royal road, it is hard for everyone.)

Also, it is not possible to get an insight into the real mathematics from applied topics and random books. As a first step, you should try to take some rigorous courses from working mathematicians and find a good advisor.

So give it a try.

I'm 29 (turn 30 in Spring) and I returned to finish my undergraduate degree in 2007 in mathematics after working in computers for 8 or so years (after dropping out of 1st college). I'm finishing up this Spring.. currently on my last required course for the major. I can tell you from direct experience that you're not too old. I initially returned to study biology (I was interested in bioinformatics) and starting taking math courses... taking these courses turned me onto math... at 27.

My first class back was an introductory Linear Algebra course; last math class was 7 years prior (a discrete math course) and took calc 2 8 years prior. I struggled for like 6 weeks and finally things started to click... the key was that I just worked at it; kept on trying. I was slower at doing the maths than my classmates, the majority of whom were 19 years old. While the beginning of the course was a struggle, the rest of the course was very clear to me after I put the time/effort in.

My second course was a vector calculus course and I found it easier than the first course I took upon my return. It was easier because I knew how I needed to approach the material better and I was more disciplined to follow that path. I compare this mindset to my mindset when I first was in college getting my CS degree; I was a space cadet... most people that age (18/19) tend to be. But now I know that I enjoy learning the different areas of math and the way to do that is to put in the time/effort to study and work on problems. I just didn't have the patience when I was younger. This was a very enlightening thing I learned by taking a 2nd math course.

From then on I have taken a variety of courses from ODEs, non-linear DEs, geometry, topology, more advanced linear algebra, and others... and I have greatly enjoyed my time learning the materials, even if I have lived int he library the past 2 years :-). One thing I've noticed is that being older, I tend to want to know the whole story. I am an applied math major and unlike my younger classmates, they take a lot of the theorems and methods for granted while I am interested in the why and how that got created. From what I've seen, this spans the pure and applied math realms at times.

Anyway, sorry to ramble on like this, but I just wanted to illustrate that it is possible and that you can do it!

Go for it! Good luck!

It's never too late, my dream when I was kid to become a doctor in math, am 42 yrs old now, I could'nt study cause my financial situations, i was top student in math, I just enrolled to finish my last year in B.sc math, then am looking to apply directly for Phd math. I left school at age 23. I feel very strong and more smarter than before. good luck to all.

My experience is the older I get the quicker I am at learning new things, in mathematics or anything else. Maturity goes a long way at quieting the mind and a quit mind is much quicker at learning new things than the buzzing mind of the 18 year old that is still trying to figure out what is relevant and what is not. If anything your age is an asset so you should definitely go for it.

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What is the worst mental health advice/treatment you ever received from a mental health professional? originally appeared on Quora : the place to gain and share knowledge, empowering people to learn from others and better understand the world.

Answer by Dr. Abbie Maroño, PhD in Psychology and Behavior Analysis, on Quora :

When we turn to mental health professionals, it is often during our most vulnerable moments, seeking support and guidance to navigate through challenging times. These practitioners play a crucial role in nurturing our wellbeing and aiding in our recovery process. The field of mental health is of paramount importance, and it's worth noting that the vast majority of professionals within this industry are not only well-trained but are exceptional in their dedication to supporting the mental and emotional health of their clients. Their expertise and compassionate care are invaluable to individuals and communities alike. However, as in any profession, there can be instances where the standard of care does not meet expectations, leading to outcomes that can be detrimental.

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In this case, the clinician's advice for the individual to seek out a romantic partner as part of their journey through PTSD was profoundly misguided. This recommendation overlooked the potential danger to others and the individual's tendency towards harmful behavior. Encouraging someone with such a profile to pursue romantic relationships without addressing these critical issues can exacerbate the individual's challenges and, more alarmingly, put others at risk.

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The unfortunate outcome of another person being harmed as a result of this advice highlights a severe lapse in professional judgment. It serves as a stark reminder of the responsibilities mental health practitioners hold not only to their clients but to society at large. The wellbeing and safety of the community must always be a paramount consideration in the treatment process. This incident underscores the need for continuous professional development, adherence to ethical standards, and the importance of a thorough risk assessment in mental health practice.

In conclusion, while the mental health field is crucial and filled with dedicated professionals who make a significant positive impact, it is essential to remain vigilant and proactive in ensuring that the care provided is safe and in the best interest of all individuals involved.

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