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At the beginning of my undergraduate career, I was almost sure I would want to apply to graduate programs in pure mathematics. Is it common to make such drastic change at the end of one's undergraduate career?

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    I've seen it happen, though it definitely is not common. It sounds like you are letting two bad experiences really color your opinion of graduate school and, more generally, research. What was bad about those experiences that turned you off? – Cameron Williams Jul 16 '15 at 00:41
  • I think it's not very uncommon. Plenty of extremely talented people choose not to get a phd. There are other awesome things you can do. – littleO Jul 16 '15 at 00:43
  • @CameronWilliams In the first experience, my group was domineered by one student. He ended up solving a project, which our mentor thought would take at least two summers to solve, on his own in one night. We were left the task of translating his work into four papers for publication. In the second experience, we made really good progress for four weeks. Then, halfway through the program we realized the problem had been solved. –  Jul 16 '15 at 00:46
  • Would the question of whether it happens often have some bearing on your deciding what to do? ${}\qquad{}$ – Michael Hardy Jul 16 '15 at 00:48
  • @MichaelHardy Perhaps not. But it would be nice to clarify the purpose of undergraduate research. Is it meant to prepare undergrads for research in grad school; or, is it to help undergrads decide whether they would like to go to grad school? –  Jul 16 '15 at 00:51
  • Given the way mathematicians design curricula, I suspect the first purpose has greater influence. But the way mathematicians design curricula has lots of irrationalities in it. ${}\qquad{}$ – Michael Hardy Jul 16 '15 at 00:54
  • I think you need to have a real talent for mathematics before you decide to go to a grad school. It is difficult to define the talent, but it should be obvious for everyone including yourself. –  Jul 16 '15 at 00:56
  • There is a quote: "Advice is what we ask for when we already know the answer but wish we didn't." I don't know if your answer is 'go to graduate school' or 'change course now' but, I'm sure it's the former. – Eoin Jul 16 '15 at 00:59
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    It is all too easy for those "undergrad research experience" things to go wrong, and in many different ways. The ways that graduate school can go wrong are different. :) But the issues you describe in your comment should have been avoided by the faculty sponsor/mentor... to fail to do so is a failure on their part, not yours... and/but, yes, other failings occur at a graduate level. Still, those REU things are almost completely unrelated, or are anti-related, to genuine research, despite what people like to say. Problems solved overnight or in a few weeks are not usually genuine... – paul garrett Jul 16 '15 at 01:02
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    Also, if we grant that your bad experiences with REUs were due to incompetents or jerks, one should note that there are incompetents and jerks everywhere, so "not going to grad school" is not a way to avoid them. Also, just as grad school can be dreary, other jobs, etc., can be, too. – paul garrett Jul 16 '15 at 01:04
  • You may find advice also on academia.stackexchange.com – zahbaz Jul 16 '15 at 01:06
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    Your bad experiences have nothing to do with yourself and it sounds like you're reeling from them. You could be dragging around some self-esteem issues as a result which can cloud your judgement. I was not very good at research as an undergrad and hopped from project to project until I landed a really good one my senior year. Now I'm more or less leading my whole research group. Bad experiences can help build character and make you stronger. I wouldn't give in so easily if you still love mathematics. – Cameron Williams Jul 16 '15 at 01:10
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    By the way, six years is not the high end of the length of time graduate school will take. At my school, 6 years was the average. – Matt Samuel Jul 16 '15 at 03:22

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I think it's very common. Oxford and Cambridge produce about 400 mathematics graduates a year, only a small fraction do PhDs.

The whole point of undergraduate research opportunities is to give you a feel for what research is. This then allows you to make a more informed choice of whether it's for you. Realizing now that it's not right for you is much better than deciding that three years down the track.

Many math PhD students are disappointed that it's not more like undergraduates maths where nice well-developed closed theories are studied. Instead a lot of it is trying to understand and make sense of strange examples in order to build a theory.

In terms of your experiences, these things happen. Sometimes only after it's written up does a student discover it's already been done. Research is very hard to plan and progression rate is generally very unclear.

Do a PhD if you love maths and can't imagine doing anything else.

Mark Joshi
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