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I am a 31 years old software engineer at a big technology company in Silicon Valley. I have a master's degree in computer science and moved into working full time right at the time of my graduation. During those ~6 years in industry, I always tried to work a few hours during the day on my personal passion which is studying mathematics. Ultimately, every time I want to study a specific topic, I made so little progress because of my full-time job that I got frustrated. I figured just a few weeks ago that something needed to change and I should pursue my passion, which is research, and then got into my head that I must do a PhD. Now, the principal reason of doing a PhD for me is to be able to work full-time on maths. Something I am dreaming about, just thinking about it makes me very happy. On the other hand, at the same time, I know that I am taking a major pay cut (from 6 to 5 figures), and my lifestyle will dramatically change.

EDIT : Question has been put on hold so I will try to narrow down my questioning to a specific concern.

Considering that I have no demonstrable research experience, no real recommendations by academia people ( 7 years out of college, my teachers will likely had forgot about me ), no good grades in my masters ( average ), and a degree in computer science vs a math one, is it really possible to get accepted in a pure math phD program ?

Note : the only math experience I had is high school ( grade 18/20 ) and my personal experience ( which is not demonstrable )

  • This is too many questions to ask all at once. – aeismail Jan 24 '18 at 0:28
  • Should I split it into multiple threads ? – user149705 Jan 24 '18 at 0:29
  • Yes, but #3 is off-topic (except for the general question of can "older" students get admission, which has probably already been answered), and #4 is probably too broad. – aeismail Jan 24 '18 at 0:33
  • Thanks for your input. I will be more considerate next time around – user149705 Jan 24 '18 at 4:13
  • I think that the gap between somewhat undergrad level and research is huge in pure mathematics. The good news: there is an easy test. If you can read up-to-date research papers in your field without much trouble, you are good. – Oleg Lobachev Jan 24 '18 at 23:33
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I did my PhD in my fifties, after a computer science industry career. I am also a permanent resident alien. I can see two problems you are going to have that I avoided:

  1. I didn't start my PhD until after I had my retirement fund saved up, so my standard of living did not change.
  2. I continued in computer science, so my industry experience helped. I could read current computer science papers without too much difficulty.

One approach to the standard of living issue is to rehearse by trying to live for a year at a graduate student spending rate. That will let you find out if you can do it, and build up your investments with the money you are not spending.

The biggest problem I see is the transition to Mathematics. You could perhaps use the Mathematics GRE subject test to evaluate where you are relative to what you will be expected to know. You might do better doing a computer science PhD but specializing in theory. There are some fine open problems, including the great P=NP question.

  • Thank you for your answer ! I have a little saved already in my savings, 401k and I hold some stocks that I plan to sell to buy the house if I were to relocate to study. I think I need to pass a GRE test to apply in the phD programs as well, so this is on my list. The issue with CS phD is that it is not really my passion, I work more in probability/machine learning and use my CS skills to program. On the other hand the subjects I am passionate about relate to mathematics as you can see from my original post. – user149705 Jan 23 '18 at 22:54
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    Let me just reinforce Patricia's point here: if you want to study mathematics, but still enjoy programming, and like probability, there are probably people who might be researching something you'd like. But they may not be in mathematics departments! Also check computer science, applied mathematics, statistics, finance (some very hard probability work there). I know of a few mathematicians who are even in engineering departments. You may need to decide whether your priority is to learn pure math broadly, or do research in a field you'd enjoy and where you can find a job. – AJK Jan 24 '18 at 1:24
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    ...industrial engineering, operations research, electrical engineering, ... – JeffE Jan 24 '18 at 2:22
  • the rehearse recommendation is a really great approach I think... – nmz787 Jan 28 at 8:49
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As to question 5, which is closely related to the title question, there are some very practical things to consider here.

Your time spent as a graduate student in math may actually be the most satisfying period of your life when it comes to pursuing math as a passion. This is true for almost all the people I know from grad school (and for me too, so far in my career). The academic job market is such that most people I know who pursued a career as an academic mathematician have wound up at mainly teaching-oriented colleges. Teaching 3 classes per term is very time consuming. Added to this is service to the department and the college, and professional development as an educator. There is simply not a lot of time in these jobs to sit around thinking about math and working on (research) problems. In contrast, I could do this for 6 hours a day in grad school! If you happen to wind up working at a teaching college, you may feel that once again your passion is something you must pursue on your own time.

As another anecdotal point, I have many friends from grad school that went to work as software engineers after getting their Ph.D. in (very pure) math. In fact, every single Ph.D. I know from my (50th-ish ranked) program is either at a teaching school or in some kind of industry.

Your salary as an academic mathematician is also likely to be lower than as a person working in the computer science industry. The American Mathematical Society collects data on that and other things each year: http://ams.org/profession/data/annual-survey/annual-survey

This answer reads as more pessimistic than I really wanted. My personal opinion is that you should go for it if it makes you happy and you have no life obstructions to the pursuit of a Ph.D. in math. But since you asked what your future will look like, and there is no way for anyone to actually know that, I figured a description of what I have seen may be useful information.

  • I really appreciate your comment. I have overlooked the fact that as a busy teacher, I might face the same situation as I am right now. The difference I can see also is that as a teacher I would be more prone to stay up to the latest research in my field, here in my industry I spend long time doing development and the overall climate doesn't allow me to fully study whenever I have free time. I understand the vagueness of my questions I just need some kind of general guidance. Thank you ! – user149705 Jan 24 '18 at 17:08
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Here are some things to think about. Have you considered a PhD program that is in applied mathematics? This might not be as sexy as theoretical, but it might be a good way to combine your passion and a reasonable way to make an income.

If you work in academia as a researcher or academic it might leave you time between semesters to make extra income consulting.

The data mining/science industry is hot right now. Yes, knowing the software is good in that industry, but it is the math and statistics that is the root of most things in data mining. This would be another way of supplementing your income.

Best of luck!!

  • Thank you for your answer !, Yes I am already in the world of data mining machine learning. But ultimately this is not my true passion. I always dreaming of working in pure mathematics. The financial aspect can be dealt with I think following your suggestion, consulting, teaching that could be done I guess. – user149705 Jan 23 '18 at 22:57
  • That makes sense. I have been studying data mining lately too and have found myself drawn more towards the statistics and probability side of things. – drsnark Jan 23 '18 at 23:01
  • Do you have any input on the other questions I had ? If not I want to thank you once again. – user149705 Jan 23 '18 at 23:03
  • Yes, I experienced something similar as to what you are going through about 15 years ago. I knew what I loved doing (academics), and knew that I, at best, felt mediocre about my job (programming). I did not have the money to go back for a ms/phd and knew that it was risky to take out a loan to do so, but I did. For me, it was worth it. I met people and gained experiences that I never would have had if I did not take the risk. I do work in academia now as a programmer, not a researcher, and feel that it is a happy compromise. – drsnark Jan 23 '18 at 23:06
  • Awesome ! May I ask why you didn't go through the route of scholarships ? and what was the theme of your phD ? And after how many years in industry did you decide to go back for academia ? – user149705 Jan 23 '18 at 23:09
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Here is a successful story. Similar to you, this guy also worked 6 years in industry (at Google, as Tech Lead). He then quite his job for an extremely successful PhD, then started a company with his PhD supervisor, based on the ideas in his PhD thesis (code mining).

Back to your questions.

  1. Instead of determining which area to choose, perhaps determine which school you can admission first.
  2. That's not uncommon. After starting PhD, you will often have several months to do literature review.
  3. Of course, of course.
  4. Yes, academic positions are very competitive. You need to be at least as good as the guy I mentioned above to stay at Silicon Valley as an assistant professor.
  5. I do think you are making a really bad choice. As you don't have a clear goal in mind, and don't know what a PhD can bring to you. Did you have kids? kids cost a lot, a lot of money.
  • Thank you for you comment ! I should probably iron out a few things. I have a few schools in mind, University of Pennsylvania, Carnegie Mellon are my top 2 ( I really want to move out of the silicon valley to be able to afford a house and PA seems like a good choice ). So I will move out In any case. I have no kids which is an other factor in my decision. It's true that I don't have a clear goal in mind, the only thing I want is to be able to do my passion which is research in maths full time, the phD certificate is a big + for me as I will consider it as an achievement. – user149705 Jan 24 '18 at 20:46

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