And that’s there we disagree. I am in one of the most selective math PhD programs in the country, and most of my classmates aren’t sure that they want to do math research for a career. There is no way to be sure until you’re at least half-way through your PhD. We spend 2 or 3 years in graduate school taking courses and reading papers before we can even begin to think about research problems.</p>
<p>MOST math grad students started their PhD program simply because they liked math. They can decide if they want a research career while they’re in graduate school. If not, they are well trained for a range of quantitative and analytical careers outside of academia.</p>
<p>I mean every person has to make their own choices and people will have differences in opinions. IMO, it’s a waste of time to go to get a PhD if you aren’t relatively sure that you want to do research. Of course, you don’t know what research is really like until you really get deep into the program, but I feel like you can be reasonably sure ahead of time by doing some research with professors and perhaps an independent study or senior thesis. And it’s a lot harder, psychologically speaking, to leave a PhD than most people think.</p>
<p>Of course, an MA/MS in mathematics is a pretty useful degree and if you can extricate yourself after 2-3 years with that in hand if you decide you hate it, then no harm done.</p>
<p>Again, difference of opinion here. Personally, I don’t think you should go to a PhD program thinking that there are a wide variety of careers in which a PhD would be useful, because the truth is a lot of employers (willing to bet most) would prefer an MA/MS with experience to a PhD, especially in fields like finance and operations research. You should go…if you want to do research…because that’s what a PhD is preparation for.</p>
This may work in the sciences. It won’t work in mathematics. 99% of all senior theses are reading courses and students cannot easily “do research with a professor.” What would that even mean? There are two main steps in mathematical research:
knowing the literature well enough to form a hypothesis extending current knowledge
knowing the techniques to prove this hypothesis</p>
<p>Most undergraduates are not in a position to do either. (Keep in mind that the undergraduate math curriculum ends in the 19th century. The first half of a graduate program is dedicated to learning some subset of 20th century mathematics…) Unlike in the sciences, there’s no lab work or easy tasks that an ambitious-but-untrained undergraduate could do. If you are not doing the theoretical work, you are not doing research.</p>
<p>Ialso think the situation is somewhat more similar in engineering or CS or whatever than one may be inclined to believe initially, where you might enjoy doing a few serious projects as an undergraduate and be good at it, get admission to some solid PhD programs, but realize after 6 years that your steam to do it is not the same. The relationship with an adviser and doing several years’ worth of making mistakes and slowly learning to make a contribution is generally not possible to replace in terms of realizing if the path is for you. People leave academia even after some not-at-all-unsuccessful postdocs. People, actually, rework their careers a lot in various settings (doesn’t have to be academia).</p>
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<p>Now “relatively sure” can mean a lot of different things. I think basically, the best definition I can think of is knowing the pitfalls of leaving a PhD, knowing that one could have spent that time a different way, knowing that you don’t have to do a PhD to learn and appreciate mathematics all your life, etc etc … and still having a strong feeling it’s worth it and that one might very well end up happy doing mathematics research at the end. </p>
<p>I’d say that my stance would be to try to avoid a PhD pretty hard, inform oneself, break down biases both toward and against the path, etc etc, and then if it still seems the best way to go, just go for it and give it a very good shot. </p>
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<p>Now this varies. EVEN in mathematics, sometimes students do relatively a fair amount of research as undergraduates. They are certainly in the minority, and I myself was too all over the place to be one of them. But even so, I claim that given the length of an undergraduate degree as compared with the amount of time it takes to really get to one’s best work, it’s often hard to tell if a career in research is something the individual wants. Doing what it takes to be successful in a research career is, in my view, still quite distinct from knowing what research is (and even liking it a fair bit). I have come to believe this after seeing people with plenty of talent, at the very strongest programs, doing very nice work, still deciding that doing what it would take to not flop (well, by their definition, this means do pretty well as opposed to barely scrape by with something not quite acceptable to them) at the career is not really in line with their goals.</p>