PhD after industry. Is it reasonable? [closed]

Question

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 )

Answer 1

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.

Answer 2

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.

Answer 3

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!!

Answer 4

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.