I need and request some advice on selecting the area for my research. In particular, I want to know the about job prospects of Applied Mathematics Versus Pure Mathematics in Academia. I understand that Applied Mathematics would give an edge for industrial jobs. But is this a disadvantage for getting academic jobs. Ideally one should select the research area based on ones interest. My first preference is to get an academic job after Phd and do research in Pure Mathematics. And this was my plan when I joined this Phd Program (Turning down an offer of Phd in Computer Science). However, now I find, most of my seniors, who are about to graduate, are struggling to get an academic job.Therefore my reasoning is that if with applied maths I have almost similar kind of job prospects in landing an academic job then I should go for it. Once, if I am fortunate enough to get an academic job, then I could work on whatever area that interests me. And in the worst case scenario, I would have more options in getting an Industrial Job. Do you find this logic OK or naive? Please advice.

I am providing some more information about my circumstances.

I am a first year international student pursuing PhD from a Public University(Group II -Old AMS Classification) in USA. I am already 32 years old. I am married and I have a kid. After obtaining my undergraduate degree in Electrical Engineering I have worked for about 10 years in my home country and then I left my well settled job and comfortable life to pursue mathematics. I know programming and have experience of working in Big IT companies. I am hard working, motivated and reasonably good at maths (GPA - 4.0) but of course by no means an exceptionally intelligent/ genius as is evident from my profile. I am also not from a Top 20 maths department in USA. Although many past students of my University got academic jobs,I understand that getting academic job in USA is difficult (especially for International Students).

Some probable broad research areas that come to my mind are - 1) Algebraic Topology 2) Algebra and Number theory 3) Graph Theory / Combinatorics 4) Algorithms 5) Mathematical Optimization 6) Fluid Mechanics / Aerodynamics. 7) Control System

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    $\begingroup$ Why the downvote? $\endgroup$
    – Git Gud
    Mar 17, 2013 at 22:14
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    $\begingroup$ academia.stackexchange.com would be a more appropriate SE for this question, IMO. $\endgroup$
    – JB King
    Mar 17, 2013 at 22:18
  • $\begingroup$ Computer Science and Algorithms are synonyms, sez D.E.Knuth... and your range of topics of interest sounds awfully wide (to me, a complete outsider). $\endgroup$
    – vonbrand
    Mar 18, 2013 at 3:24

4 Answers 4


I'll be the cynical response. Give it up. You have very low probability of gaining a full time research position in pure simply because online education is going to be making radical changes with how education is administered. Realistically you should aim to industry. A PhD can train you to be quite excellent in areas outside research math.

Research positions come from folks with lots of publications, so say you finish at 33, you will need to publish great works, each work takes 1-2 years. So 3 publications puts you around 6 years of work; now that is around 40 years of age. In the mean time you will live frugally. That is a tough shot there. I argue to aim more well-balanced, and aim more realistically by questioning your expectations and responsibilities and work/life balance.
If you deny my cynicism and pursue your advanced research, but then start to notice 1)marriage tension 2) neglecting time with child 3) inner / emotional tension

then it is time to refocus on a balanced life.

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    $\begingroup$ Hi. I just received some down votes for giving a bit of realistic advice. First I would like to point out three facts. 1) Read terence tao's blog to where he says that mathematics is such a wide field, that many great mathematician's should pursue careers out of academia. 2) Tenure positions in academia are very scarce 3) he is already a father, and is responsible for his family, which means that he will be eligible for assistant professorships, which is merely contract hire (not stable). Which implies that it is less risky to pursue industry as a highly skilled mathematician. thank you! $\endgroup$ Oct 1, 2014 at 15:27
  • $\begingroup$ I am not saying he should not pursue a phd, but should explore interests outside academia. $\endgroup$ Oct 8, 2014 at 23:06
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    $\begingroup$ Glad to see I'm not the only one who's disturbed by all the "follow your dream" euphoria. The man has a family to support, and that should be the first priority. He may have to give up some dreams and work at a boring job in order to do this. That's reality; that's what millions of people do. Number Theory is a nice hobby, but relying on it as a source of income is naive and irresponsible. $\endgroup$
    – bubba
    Jan 25, 2016 at 14:09
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    $\begingroup$ Maybe "irresponsible" was too strong, but my 5 minutes of editing time expired. Let's just say that he ought to have a backup plan, for safety. $\endgroup$
    – bubba
    Jan 25, 2016 at 14:16
  • $\begingroup$ While not denying anything said in this answer, I'll just point out that 8 years later, after 2 years of distance and mixed learning during the pandemic, universities still hire teaching and research staff. $\endgroup$ May 12 at 17:08

Do what you like best, anything else is just self-torture. If you are good at it, you'll succeed. As Manos' answer says, just make sure you have work near the area of ultimate interest. Look for a position not only in the US, there are plenty of good universities elsewhere.

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    $\begingroup$ This is quite late but still to show my thankfulness I am accepting you answer.It has helped me in reaching a decision.I also benefited from other thoughtful answers.Thank you everyone for your answers!Just to update you about my decision - I have decided to pursue Number theory, I have already passed my Quals, got my masters degree on way to PhD., and most importantly got a great advisor. I don't know about the future but certainly I am loving every moment of my journey thus far. $\endgroup$
    – Samal
    May 21, 2014 at 23:49
  • $\begingroup$ @Samal, good luck! And I'm happy to have helped a bit. $\endgroup$
    – vonbrand
    May 22, 2014 at 1:47
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    $\begingroup$ @Samal Four years has passed... Do you wanna share any updates with us? Have you got a postdoc/tenure-track position? $\endgroup$
    – No One
    Nov 20, 2018 at 22:39
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    $\begingroup$ @NoOne Now $6$ years has passed .samal was not active ,I think she leave the phd without completing.it...Her Last seen Jun 17 '14 at 18:30 $\endgroup$
    – jasmine
    Sep 22, 2020 at 19:37

Here is what I believe:

First of all, do not abandon your dream of doing research in pure math. This is a long road and you can build it slowly and consistently. For this reason, and since you have a family to support, I recommend you solve first the survival problem, i.e., get a well-paying job e.g. in an applied math department or in an electrical engineering department. This will provide you with the psychological strength to pursue research directions you wish, without having much pressure. Note that pressure might turn your love for math into a nightmare. Finally, since you are only 32, you could achieve a position in a pure math department later in your career. I think Weierstrass did not become a professor until his forties :)

  • $\begingroup$ Thanks for your reply and encouragement.I am a graduate teaching assistant. Although we have to live very frugally but I have a very supportive family and survival is not an issue right now. This is about what would be a wise choice considering future job prospects. $\endgroup$
    – Samal
    Mar 17, 2013 at 22:26

I think that you should follow your plan to get a PhD in pure math and work in academia. Not because the chances are particularly high that you will end up doing this, but rather because it is much easier to gracefully switch from this plan to another plan than vice versa. As long as you work fairly hard and maintain a reasonable outlook, the worst that will happen is that you might decide after some small number of years that math research isn't for you, at which point you might choose to graduate with a master's degree and look for work in industry. That would still not be a bad position to be in.

That being said, I think you should also make sure to ask some PhD students who left academia, in order to get more balanced advice.


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