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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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undergraduate math vs graduate math

It's really a mild, soft question.

So far, I am an undergrad student, contemplating on several majors.

What will be the major difference if I become a math major and go to a graduate school to study math?

Will a graduate math major generally focus on reading/studying recent research papers? Or will the graduate math major be taught by professors on the things not covered in undergrad programs?

The reason why I am asking this question is that undergrad math programs seem to me at this point so well-covered that after studying the programs, a person will be able to do anything he wants to do, and if one wants to do research, he will be able to catch up with recent progress by reading research papers.

If this is true, why is the graduate school even needed?

By the way, I am a first-year undergraduate student :)

• soft-question
• 10 $\begingroup$ So how exactly do you know what one needs to know to read research papers in all areas? $\endgroup$ –  Michael Greinecker May 22, 2012 at 11:57
• 9 $\begingroup$ When you start your grad level studies you take some courses, learn more on some topics, then you read a lot on your own and study more on selected topics, then you can read papers in those topics, and eventually you should be able to come up with new ideas in the field. $\endgroup$ –  Asaf Karagila ♦ May 22, 2012 at 11:59
• 63 $\begingroup$ Your impression is not very accurate. As a freshman, perhaps when you see the exotic topics that lie ahead of you think that you will learn a vast amount in your next few years, you think surely that must consist of a large portion of mathematics. Alas, it is but a drop in the ocean, and unless your Gaussian abilities allow you to sail the seven seas, in grad school you will probably pick a little island and live there the rest of your life like most people do. $\endgroup$ –  Ragib Zaman May 22, 2012 at 12:32
• 7 $\begingroup$ In hindsight, I wish I had studied fewer subjects deeply, and that I had kept careful notes of my solutions. It doesn't make sense to invest time in a proof/learning something unless you'll be able to use it later. Most of the solutions I wrote down ended up in the waste bin, because I figured "I could just write it down again." True, but at the cost of probably hundreds of additional hours of work. Also, I spent way too much time trying to understand proofs than actually using results to solve problems; I assumed that every proof I came across was well-written and worth remembering (mistake). $\endgroup$ –  vgty6h7uij May 23, 2012 at 12:53

8 Answers 8

Here is what I tell my grad students:

The difference between undergrad mathematics and graduate mathematics is the difference between art history, or art appreciation, and learning to be an artist.

As an undergraduate you see a lot of mathematics, but you don't create new mathematics. The goal of graduate school (and here I am speaking from experience with top fifty U.S. graduate schools, so what I am saying probably applies best in that context) is to learn how to create new mathematics, and then to create that new mathematics.

One specific consequence of this (in my view) is the following: often in undergraduate mathematics classes, proofs and rigor are presented almost as moral imperatives --- as if it is a moral failing to know a statement without knowing why it is true; consequently, people often put a lot of effort into learning arguments just for the sake of having learnt them. (This is exaggerated, perhaps, but I think it reflects something real.) On the other hand, in research, one learns arguments for different reasons: to learn technique, to pick out important ideas --- there is a professional aspect to the way one looks at pieces of mathematics which is not usually present in undergraduate mathematics. One gives proofs in order to be sure that one hasn't blundered; one's interaction with the mathematics and the arguments is much more visceral than in undergraduate courses.

(I am not speaking from any experience now, but I think of the difference between learning how to interact with a block of marble, and bring a new form out of it, however rough it might be, in comparison to looking and learning about a lot of existing beautiful statues, masterpieces that they are.)

• $\begingroup$ Thank you for posting this, by the way. $\endgroup$ –  Akhil Mathew May 26, 2012 at 0:23
• $\begingroup$ To claim that you aren't really doing math until you're doing research belittles legitimate math that undergraduates do. $\endgroup$ –  Andrew Kelley Mar 30, 2014 at 1:33
• $\begingroup$ Dear Andrew, This post is discussing the creation of new mathematics. This is the focus of graduate training in mathematics, and is not the focus of undergraduate training in mathematics, which is instead focused on learning existing mathematics. (At least this is my experience of the two. Perhaps your is different.) Regards, $\endgroup$ –  Matt E Mar 30, 2014 at 4:10

As a graduate student, the most useful skill I learnt as an undergraduate was not the mathematics itself, but how to learn mathematics. The edge of the subject is so wide that it's mostly not practical to get to a lot of current research problems as an undergraduate, even in a particular subfield like geometry or algebra for example.

That's not to say that the mathematics isn't important (and in fact I'm probably underplaying its importance because the parts of it I use all the time have become second nature), but knowing how to learn things efficiently is incredibly useful.

The graduate school experience probably varies quite a lot from university to university (and between countries as well), but my experience is similar to that described by Asaf in the comments - you still do some more formal courses at the start, but more independently than as an undergraduate, and at the same time your supervisor will suggest things you should read and problems you should think about - and these should lead to you discovering more things to read and problems to think about under your own volition.

I should probably also recount what I've always heard said by lecturers as the big difference between begin an undergrad and a grad student - as a grad student, you have to contribute original research. The upshot of this is that while the problems you see as an undergraduate may be difficult, they at least have answers, but this need not remain true when you are a grad student, and learning how to make judgements about which questions are worth persuing is an important aspect of postgraduate study - as mentioned by Eugene, Terence Tao has lots of good advice along these lines.

This also leads to a sound-bite answer to your question "why is graduate school even needed?" - because the process of learning how to do research is distinct from the process of learning how to do mathematics.

Terence Tao has great advice for mathematicians at every stage of their careers.

http://terrytao.wordpress.com/career-advice/

To get an idea of how mathematics graduate school in the United States works I would suggest the book A Mathematicians Survival Guide by Steven Krantz. The books is filled with information about the ins and outs of mathematics graduate school, including advice concerning many of the common pitfalls experienced by graduate students. It also contains advice for recent PhDs about their options after graduate. Overall, a very useful source for those unsure of whether graduate school is for them. The preview on Amazon should give you a good idea about the contents of the book.

From one who failed to realize all the value of his own education... and to provide a wider perspective to @MattPressland's excellent answer.

Although written for high school students, I believe that What You'll Wish You'd Known by Paul Graham resonates deeply with your question. Specifically in wondering "why is the graduate school even needed", I think the following quote sums the essay and answers your question:

Suppose you're a college freshman deciding whether to major in math or economics. Well, math will give you more options: you can go into almost any field from math. If you major in math it will be easy to get into grad school in economics, but if you major in economics it will be hard to get into grad school in math.

This applies to graduate school in that having a Masters in Mathematics will provide you with more options than a bachelors alone. Although theory is often not as applicable in practice, I'd certainly hire the PHD who could show the output of their labor over the BA who could demonstrate the same.

Given that you are just starting as an undergrad in Math, it is highly unlikely that you understand yet what math is. What you have (likely) seen so far probably peaks with calculus. What that means is that you have learned how to apply methods without having learned how to think mathematically and how to prove the theory that underlies subjects like calculus.

It is really not until you take a course in number theory, or a very theoretical initial coverage of linear algebra, that you are exposed to proof methods. (My recommendation, btw, is to take an introductory course in logic as soon as possible. Best course I ever took on my way to a B.S. and eventually a Ph.D. in mathematics.) You may find out that Math is just not for you.

Beyond that, many other subjects that you may be contemplating as a major will require considerable math. So, take as much as you can. I always recommend people double major, with one major being math. Key to success in graduate school in any science or engineering subject (or economics or ...) is mathematics.

Beyond this, it pays to be somewhat practical. It was discussed that there are more opportunities in Statistics. You could also consider Applied Mathematics. Both can be as mathematical as pure mathematics, and the job opportunities (and expected salary) are much better. Some of the best mathematicians I ever encountered with applied mathematicians and engineers.

Finally, realize that computer science is really just applied mathematics, especially if you go on to graduate school.

Whatever you do, pursue a subject that you enjoy. Don't do it because your parents expect you to.

A short, but I hope informative, story from someone with a PhD in Physics, but who also was a professor of Mathematics for a few years.

I was teaching in the physics department at one of America's finest colleges and worked with a brilliant undergraduate math major and published three journal articles with him. He got straight As, and seemed to be able to solve any problem I gave him... including one that I probably could have solved, but it would take me longer than he did. He had such a bright future.

He was accepted to math graduate school at one of America's very top math departments but alas didn't thrive there. There are a few fundamental difference between undergraduate education and graduate education, which he couldn't navigate. (He left school to program computers for a bank.) Speaking in broad terms:

• Undergraduate : You learn math that is already understood by experts, and you solve problems posed by others (professors or books), and are under a fairly strict schedule of classes, exams, paper deadlines, etc.
• Graduate : You create new math that is fully understood by nobody else (yet), you must search and create your own problem, and have very few scheduling commitments, so you must be self-motivated.

This is not to dissuade anyone from attending math graduate school... quite the contrary. I want to alert such prospective students so they know what to expect. Actually, the best preparation at the undergraduate level is to do true research (appropriate to your skill and education) which involves creating your own math problem , and then doing your best to solve it.

One of my criticisms of many undergraduate departments (not just in math or physics) is that they don't teach and encourage students to make their own problems.

So my advice to an undergraduate interested in math graduate school would be to meet with your math advisor and try to arrange a self study (or "independent topics" or whatever is the format at your school) and "test the waters." You may love it (!) in which case graduate school sounds right for you. If not, I think you'll have to decide whether you want to develop such skills (in preparation for graduate school) or instead pursue a career where others will give you problems to solve. There is no shame whatsoever in such a career.

A fun little diversion, which nevertheless illustrates the difference between undergraduate and graduate mathematics education. Consider your favorite discipline in math (number theory, geometry, differential equations, ...) and just start asking questions/problems in that discipline. don't worry that you cannot solve them! (Fermat couldn't solve his Last Theorem, despite what he wrote in his margin.) Just keep asking and asking them. If you find you're stuck, or you can only come up with problems you've already seen, or if you're frustrated by such an effort, stop and think about that. If instead you get energized, excited, and motivated by this little exercise--especially if you come up with a "gem" of a problem--then you may have the temperament and skills for graduate research. (Of course this isn't the only requirement for success.) [You can search for my TEDx talk on "how to ask good questions" where I run through this exercise for sudoku puzzles.]

You want to follow a career path that gives you the greatest personal satisfaction and helps the discipline and society more broadly.

Here's the opinion of someone who majored in math (at a top school in the United States), but was not a genius at it.

This is a condensed, generalized, down-and-dirty opinion, but I stand by it.

Your assumption about being well-covered is more accurate that not. If your intent is to form a mathematical basis of strength that you can apply to applications of math (e.g. finance stat econ) then undergrad is as far as you need to go with it. By the time you take Real Analysis & Complex analysis your mind will have developed in an amazing way. As Matt Pressland said, you learn how to learn Mathematics. Matt also mention the difference between that style of meta-cognition and being able to research. It's impossible to say today that you could or couldn't come up with a unique research idea that would be considered a contribution and that you're passionate about to pursue. However, unless the word research makes your heart throb, you don't need Math graduate school.

I've rewritten the rest of my answer to be a bit more compact.

Do not major in math , minor in it. You will gain a superior analytic mind. However, your employment potential depends on not being a Math major. The Corporate world (Actuarial aside) doesn't know wtf Math is. They will ask if you wanted to Teach High School.

Accounting is boring, and Economics is fluffy. Choose Statistics and augment with Finance. Also, Computer Science requires more hours spent at 1-sitting than Mathematics. Engineering trumps Computer Science as you can learn to be a programmer in your spare time.

First know what you want to do as a career. Do not decide this on your own. Go to your career center for expert help, and shadow professionals and intern . Funny how this is #3.

Conclusion Math can be a minor. Let your possible career path determine your major. At the least you can be earning a salary when you're 22-23 while deciding what new career you want. At the best, you'll save yourself 3-5 years of searching, finding-professional-self, and rebuilding qualifications.

I decided to add some external links that would shed light on why some of my views are as they are. These come fro the Bureau of Labor Statistics... Oh look Statistics is even in the name =)

A small summary is included with the link, but please click and compare. These are just samples, you can find your own BLS data to refute if you want.

Occupations from mostly-pure discipline

Occupations heavy in STAT with Finance Augment

Conclusion for the sample

Stat has way more job positions filled/needed much faster growth than Econ, same entry-level as Math.

Finance augmented, Statistically heavy jobs are quite abundant, pay well, and grow fast. This is what I recommended. I recommended majoring in Stat with a Finance augment. Both examples of this require only a bachelors and are in a job space projected to grow much more than the Mathematician or the Economist. The pure Statistician indeed makes less than those two. So to repeat from previously: Math Masters not needed if you like other things. Don't major in Math in undergrad.

• 8 $\begingroup$ I have to say that my classmates who were taking math as a major and another minor, or worse: taking math as a minor, we're not exposed to enough mathematics and it is incredibly difficult for them to pursue a masters degree in mathematics. If one intends to go to grad school in mathematics, one should learn mathematics -not just see a review of it. $\endgroup$ –  Asaf Karagila ♦ May 23, 2012 at 6:16
• $\begingroup$ Agreed. The masters in Math has to be the goal though. $\endgroup$ –  VISQL May 23, 2012 at 16:46
• 10 $\begingroup$ I really disagree with this answer, but I'm not going to down vote it. Saying a bunch of blanket statements such as "accounting is boring, economics is fluffy, engineering trumps computer science,..." is not well taken. $\endgroup$ –  Samuel Reid May 24, 2012 at 0:39
• $\begingroup$ @Samuel. I understand but there's no time for a lecture. Go to BLS.gov and do a search for Mathematician, Statistician, Economist, Financial Analyst and then look back to what I say. $\endgroup$ –  VISQL May 24, 2012 at 16:40
• $\begingroup$ Please take time to refute my comment with more evidence than I present or to look into yourself before down voting, which is very negative mostly impulsive reaction to the opinion of another based on your own opinion. $\endgroup$ –  VISQL May 24, 2012 at 17:08

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Mathematics

Ph.d in mathematics, exploring new theories at the forefront of mathematics and its applications.

Doctoral studies form our core graduate program.  The faculty in the department excel in numerous areas of applied mathematics and are well versed in many related disciplinary fields, thus they are highly qualified to train graduate students and mentor them in producing high-quality research and dissertations at the intersection of mathematics and the sciences or engineering.  Our Ph.D. training opens doors to research careers in academia, government laboratories, and industry and our department has a strong record of placing Ph.D. students in prestigious postdoctoral positions at top-tier universities and labs, and in industrial positions.

Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office of Graduate Education.

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The Ph.D. degree results from following a program of study in mathematics or in applied mathematics.

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Students working for the doctorate must demonstrate high achievement both in scholarship and in independent research. All programs must follow the general rules of the Office or Graduate Education.

The student’s program of study must include:

• At least six, 4-credit (nonthesis) graduate mathematics courses (i.e., those with numbers MATH 6XXX or MATP 6XXX).
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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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Standardized test preparation platform at an affordable cost. Equipped with  timed practice questions ,  video lessons ,  performance statistics  and  remote assistance . Available in both  desktop  and  mobile. 

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A non-profit, ed-tech initiative founded at Rice University,  OpenStax provides free, peer-reviewed math textbooks in digital forms written by experts in the field. Printed versions of the textbooks are also available for purchase at a low cost as well.

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Department of Mathematics

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See also: The Integrated Ph.D.Degree_Programme

The Department of Mathematics offers excellent opportunities for research in both pure and applied mathematics. Visit the Research Areas page to get a sense of the research interests of the faculty in the department. The written test conducted by IISc for entrance to the Ph.D. programme has been discontinued as of 2013. Students will be selected through the examinations listed below, followed by an interview at IISc.

Eligibility

Minimum second-class or equivalent grade in the qualifying examination/degree (which is relaxed to a “pass class” for SC/ST candidates). See below for degrees that qualify.

Master’s degree in the Mathematical or Physical Sciences, or B.E./B.Tech. (or equivalent degree) in an appropriate field of Engineering or Technology.

The candidate should also have passed one of the following entrance tests: CSIR-UGC NET for JRF, or UGC-NET for JRF, or GATE (all of these to be valid as of August 1, 2018), or the NBHM 2018 Screening Test; or must hold an INSPIRE Ph.D. fellowship.

Concerning candidates who have passed one of the above examinations: only eligible candidates who have been short-listed on the basis of their scores in one of the above examinations will be called for the interview. Note: the short-list for NBHM 2018 will be based only on the NBHM 2018 screening test. Selection to the Ph.D. programme will be based on performance in the interview.

Candidates who are yet to complete their examinations for the eligible degree and expect to complete all the requirements for their degree (including all examinations, project dissertations, viva voce, etc.) before July 31, 2018, are eligible to apply.

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Stanford PhD physicist applies for rural clerk job in central Chinese town

• Su Zhen, with a doctorate from top US university, reportedly appears on civil servant candidate list in Anhui province, sparking speculation

In China, the civil service exam usually consists of a written test, interview and assessment – those listed on the screenshot still have to undergo their “political assessment” before the final decision is made and announced.

As the list has not yet been made public, the Post could not independently verify the original source of the screenshot. However the Post did confirm the authenticity of the case with two insiders, including one from Xiao county, a region of around 1 million people in northern Anhui province, where Su was born and graduated from a local high school.

One of Su’s high school classmates, who goes by the username Hyman, expressed his surprise on Monday on social media site Zhihu, a Quora-like online content platform.

He said when he heard the news from his high school alumni group, his first reaction was, “It’s impossible.”

He said he then turned to other classmates for confirmation, but was told that Su’s WeChat was no longer in use and others had lost contact with him a long time ago.

“I think his intelligence and diligence make him a better academic researcher than me, and there is no doubt that he has a bright future ahead of him,” he said.

Su was one of the school’s top academic performers. According to Hyman, Su was the best student in his class – and the top student in USTC’s physics department.

During his studies at USTC, Su was awarded the Guo Moruo Scholarship, the university’s most prestigious scholarship. According to the university, of the 34 recipients in 2016, 26 went to the world’s most famous universities and research institutes. Su chose to head to Stanford.

Which is why his career choice now is seen by many as inexplicable.

“If he doesn’t want to go into academia and hopes to become a civil servant, a city in China’s economically developed coastal area is also a better choice,” he said.

Others, however, believe Su may have made his decision for personal reasons and his choice should be respected.

In March, there was a similar case in the Yuhang District Education Bureau in the eastern province of Zhejiang when they welcomed a new civil servant who had graduated from Harvard University.

Despite such similar cases, Yuan Lanfeng, a researcher at USTC, believes Su’s case is an anomaly that does not represent the general situation for graduates of prestigious universities.

“It’s not necessary to take such a grass-roots job, even if it’s very hard to find work,” Yuan said, adding that with his CV, the most obvious route for Su is academia, followed by companies, and there must be a personal reason for not going to any of these.

The Post has attempted to contact Su to ask him about his life experiences and career considerations, but has not yet received a reply.

The Post also contacted Mike Dunne, Su’s primary thesis adviser and a professor of photon science at Stanford, for comment, but he also did not respond.

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Do PhD have any value in Finance ?

I will really be glad to hear the perspective of person with a PhD or professionals on this topic.

So I was thinking since yesterday about Starting a PhD after my Master. Right now I am pursuing a master in finance and I was thinking about following up with a Phd. I will try my luck with top universities or more presitigious universities than were I have been until now( UCA in Arkansas, Texas A&M right now). There are many reasons.

I will be 24 at the end of my master so still young to pursue another degree.

-I will work as part-time

-Debt free(Blessed to have parents supporting me until now) so unless exceptional event, I can afford that.

-Many universities provide financial help to students so they can achieve that which represent an precious advantage

-Being able to do research with professionals(increase network, increase my knowledge)

In my case as an international student, I can 5 or 6 years of Visa to focus on my research which represent an advantage

-If I achieved that, it is a guarantee that my starting salary will be around or next to 6 figures(at least from what I have been told by my peers). Even if I am not doing it for money, it is an info to take into account.

I mean these are the few advantages that come to my mind when thinking about it. But the question now is, do PhD hold value in finance ? And if yes Did I have to do PhD in Finance after having a BA in finance and a Msf ? For me it will be quite redundant. Which specialization can make me stand out ? On quora I saw guys speakkng of statistics, strategy, Applied economics And which school will adise me (I intend to enter in touch with the Phd Faculty during the next semester. Right now this is my first semester as graduate student) .

Now with all these things said, I don't know what can be the requirements to be accepted. I don't know how tough is the acceptance rate(if there is one).

In case it is a good idea, I will be glad to hear the requirements I need to have to apply for a Phd.

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Doing a PhD in physics after doing bachelors and masters in mathematics

I have done my bachelors and currently doing masters in pure mathematics. I have done four physics courses during bachelors degree which also includes special relativity. What is the possibility that I may prosper in theoretical physics and earn a PhD in any branch of mathematical physics?

Also, I am going to take the GRE this year but I am little bit confused about choosing subject in subject GRE since scoring in maths is much easier than scoring in physics (if later its possible to change departments then of course I'll choose maths). Any suggestion regarding that is also welcome.

• mathematics
• changing-fields

• You should take up this issue with someone who you would like to be your supervisor –  Maarten van Wesel Mar 30, 2015 at 8:32
• well...not much.....but i am little bit confused about choosing subject in subject gre since scoring in maths is much more easier than scoring in physics (if later its possible to change departments then of course i'll choose maths)......any suggestion regarding that is also welcome. –  SK ASFAQ HOSSAIN Mar 30, 2015 at 9:02
• The first and second part are really two separate questions and should be asked separately (so future users can more easily search for them and so it is clear which answer to accept) –  WetlabStudent Mar 30, 2015 at 14:56

2 Answers 2

First of all, please remember that PhD is not about learning; learning about many different areas/fields/subjects. More specifically, it is not about increasing you knowledge in breadth, i.e., you know Mathematics, you can now learn about physics, then you can learn about computer science and so on.

PhD is about training in research.

Ask your self this question:

How can I contribute to this area (may be theoretical physics or any) in this particular topic by utilizing the knowledge I already have (say, acquired during bachelors and masters) in this specific field (say, in pure mathematics)?

Once you get the answer to this question (it should be in the form of a nice research proposal) you will definitely be able to do your PhD in that area, which you would select and do homework for.

It really depends upon the institute and the department you are targeting to: what actually is the requirement there? And remember, some might not need GRE subject at all.

So, please make a list of the institutes/departments based upon your interests/priorities and mention their requirements. Then you would be in a better position to decide which one should you go for. Maybe, only because it is unavoidable or simply you can perform better in that.

I would suggest you to have a profound focus upon the first part. Chances are that you might end up targeting a Mathematics department only, still being able to contribute in physics. Even, otherwise would give you a clear vision of what should you do and what you don't.

• what about the second part? –  SK ASFAQ HOSSAIN Mar 30, 2015 at 9:16
• 2 @SK - Not every answer on the Stack Exchange will answer both parts of a two-part question. You may have to wait for someone who feels more qualified to talk about the second part. –  J.R. Mar 30, 2015 at 9:37

My understanding of your question is that you want to pursue your PhD in an interdisciplinary field (including both math and physics fields).

It is not uncommon to do such a thing... However, doing PhD level research is different than taking bachelor level courses in that field. Taking those bachelor courses familiarizes you with the basics and fundamentals but that's the beginning of the way to the state of the art knowledge you'll be working with during your PhD.

However, if I'm wrong about my hypothesis and you're changing your field entirely then that's a different thing which requires careful consideration of your interests and circumstances.

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