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I have completed masters in Pure Mathematics a year back. I was preparing for an exam for pursuing a PhD program in the same. The results came out in this year in the month of April and found that I have failed to clear it.

Most of my friends have cleared the exam and have got enrolled in it. I feel left out. Now I am simply sitting in my home and preparing for next year's program.

Since the results came out, I have hardly made any progress in Mathematics, as I don't find it interesting as it used to be. As a remedy I bought many books to bring back my old interest in Mathematics, but failed to do so. I talked to my teachers on this issue but instead they start telling success stories of my friends who have qualified the exam letting me disgusted.

Earlier I used to spend hours solving many problems both from my books as well as on Math Stack Exchange but I don't find the urge to do it anymore. Though I open this site I feel that none of the problems posted are suitable for me to solve.

I do read books but the problems seem a distant dream. Asked many people what to do; they advised me to take decisions on your own in your life.

Really don't know if it is a good place to ask but cant find better place. Do share your thoughts if you were in a similar situation or so.

Should I change the subject or look for jobs or do something else? Any alternatives you can chalk out for me.

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Two things:

  1. A single exam is a high-variance way to measure the ability and potential of a complicated and multifaceted being called a human. In other words, I wouldn't take a single failure too seriously. Sometimes you have a bad day; some people simply don't perform well on tests even if they perform well "in real life." And even if it turns out that you are less qualified than your peers according to the traditional standards of the field, that doesn't mean you don't have something unique and valuable to contribute.
  2. Is there anything in your life right now that you're excited about? If not, you might consider external factors. Some days I'm fed up with my problem, and my research, and my career. But after going for a run, eating well, spending time with friends, seeing a thought-provoking movie, and getting a good night's sleep, I often find (much to my surprise) that I am excited about my life and my work again. In other words: don't underestimate the value of external factors. (Especially exercise. I cannot stress that one enough!)
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    Great answer -- also, you may benefit from talking to a trained counselor or psychologist. – aparente001 Jul 29 '15 at 5:43
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    Also, you might want to take some time off and do something else, maybe visit friends or go on some short vacation to get your energy back. Since the test is in next year, taking off 1-3 weeks to recuperate shouldn't be a big issue. – Olorun Jul 29 '15 at 14:06
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    Excellent answer (and name, Ups Ground backwards) from @Dnuorg Spu, and other commenters! I encourage you to take a break and talk to a counselor, if you choose, before making decisions about what to do next. Whatever you do next, you'll be refreshed. – wdb Jul 29 '15 at 15:59
  • thank you very much for the comments!I will definitely try that – Learnmore Jul 30 '15 at 2:34
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In my view the real problem is that you are not interested in mathematics, not that you failed an exam. You don't say where you're studying, but it is probably not in the United States because here PhD programs do not have their own entry exams. In fact, most US math PhD programs would give you several chances to pass all sufficiently important exams. So if you were interested you could certainly apply for programs elsewhere.

For whatever it's worth, I believe you that you are not very interested in mathematics. You don't sound very interested. I looked over some of the questions that you asked on math.SE and you seem to be a bit locked out of mathematics beyond the undergraduate level of solving problems. Note that I am not speaking of talent but really literally of interest. I noticed that you don't mention anything in mathematics beyond solving textbook problems. For someone to have completed a master's degree and not gotten any farther than "I read these books and do these problems" signifies a lack of engagement with the material (again, not necessarily mastery but engagement) at the level that would merit further pursuing it.

This lack of interest in mathematics is not a bad thing. Mathematics is not your spouse or your child, to whom you probably owe something even if your ardor has cooled. Pure mathematics is only for the interested; it has almost nothing to offer anyone else, and it doesn't need anyone else. I think you should find what you're interested in. Maybe it will be close to mathematics; maybe it won't. Maybe you should take some time off school entirely and concentrate on purely non-academic interests: getting a master's degree is literally more than a lifetime's worth of schooling for most people. I can't tell you what to do with your life, but I can tell you what you don't have to do.

Good luck.

  • Just curious: is an undergraduate who's interested in math one who has done some sort of research, or what kind of going-beyond-the-textbooks are you referring to? Or is it about the kinds of questions? – coldnumber Jul 29 '15 at 10:51
  • @coldnumber That's a seriously large question in its own right. However, yes, doing research (preferably with a professor), trying to further your understanding of deeper problems, and/or working on larger projects either in-class or preferably during an internship show that you are one who's interested in math. – NoseKnowsAll Jul 29 '15 at 14:38
  • @coldnumber: I agree that this is a hard question to answer, and I should make clear that my impression that the OP is not so interested in mathematics is an impression, not a definitive judgment. (In part I am taking him at his own word...) Doing research in the sense of writing a paper is certainly not necessary, but at least asking some questions and seeking answers beyond the textbook level is what I had in mind. – Pete L. Clark Jul 29 '15 at 15:22
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Qualifier exams are a reality of Ph. D. programs, but they are not good predictors of academic success. They are better at eliminating those that will not do well than predicting those that will do well. I did not pass my written qualifier exams, so I had an oral exam, which I did pass, and then I finished my Ph.D. A Ph.D. program and the world of academia beyond it have many setbacks. What you do in response to the setbacks is just as important as your successes.

Also, remember that you can continue doing math for fun if you want. When you do it for fun, you can solve whichever problems you choose, and you don't have anything riding on it. If you continue on the Ph. D. path, there will be constraints on what you do and pressures that can limit your enjoyment. I was sick of my dissertation research, but I couldn't start over, so I finished it. I'm glad that I did, but I was not doing math that I enjoyed at the time.

  • Good advice. A change of focus could be a good way to apply what the op has learned to a new and interesting area. Switching to a area like bioinformatics where there is a need for people with a working knowledge of statistics might be appropriate. – cs_alumnus Jul 29 '15 at 20:25
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Of my many friends with doctoral (and masters) degrees in math, physics and computer science, I can think of only one who has gone on to a career as an academic professional. The rest have happily gone to different pursuits.

Chances are, even if you were to get a PhD, the same would be true for you. In my opinion, you've just been given an opening to go find out what your "different pursuit" is going to be -- a few years early.

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I realise that you specified pure mathematics, so this may not work for you, but one option is to think about other fields where your background in mathematics may provide a different research path. Close allies (applied mathematics, physics, economics) are the obvious possibilities, but I originally trained in mathematics and then later in social sciences. The context for my research is social science (for example, how does the social structure influence transmission of ideas) but I rely on a mathematical approach to do the research. Since you also said that you enjoy solving problems (or used to), maybe you could think about what type of problems interest you and work in an interdisciplinary area.

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You may want to take a look at "Think Like a Freak" by the authors of "Freakonomics", especially chapter 9: "The Upside of Quitting". Quitting is sometimes a necessary step for your progress.

You may also consider a lateral move. Mathematics...is a gigantic galaxy. What type of math are you focusing on? Perhaps moving from pure math into applied math might bring a whole new perspective? And fun? Probability, Statistics, Machine Learning...these are very hot topics nowadays. And well paid! (Finance & Big Data employers, to name a couple).

If really no good option stands out, then look at that chapter 9 again ("would you consider let us toss a coin for you?").

Good luck.

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