Moving from Pure Math PhD to Quant Researcher advice

[NoPro]

Hi all,

I'm a 26 year old from the UK but not a US permanent resident, I am a grad student, currently studying in the US, beginning my second year in a top 25 Math grad school (usnews ranking). I have just passed my qualifying exams and so will have earned my second masters in Math, I delayed by about 2 years after graduation during covid and didn't want to go straight into industry so I did a masters and applied for PhD as I believed that to be the direction to find my dream job giving satisfaction, excitement and mental challenge. I earned a 2:1 BA in Math from an oxbridge school, my undergrad courses were mainly pure math and theoretical physics centralized, the few stats courses were intro to probability courses, random variables, measures etc and a course on stochastic processes and random walks. I have no real background in coding, though my friends currently in industry think I should be able to pick it up quick, that I just need to work on python, c++ etc.

I am however, currently in a personal quandry as the advanced grad level math material that I loved and really liked from personal reading and classes is not really available in personal attempts in research, namely that what most researchers and hence PhD students seem tospend their time doing is proving increasingly more abstract (and in my opinion not very beautiful or useful math) in such a way as to keep the paper machine running to keep getting funding. This is true in the projects that have been offered to me, just a further abstraction of a previous result in ways I don't know how it would be useful in the subject area other than for others publishing material on this abstraction of the subject area I like. I have come to the hard decision that I really would hate my life if I were to spend it thinking about and writing about that kind of math, I think it would be an awful existence for me. This hopefully is not the case in some areas of pure math recearch however in speaking with some professors in my area at conferences, they admit to mainly author or coauthor for results like this tenure etc. but seem far more interested in them than I am, questioning whether I really liked the subject areas, which I thought I did based on the fact that I love the material in the books and from class. I have discussed this with my friends in industry and they really think that I would be happier and more successful if I went into industry like them, where they themselves have been successful, being in data analysis and quant analysis jobs.

However, I know that the economy in both europe and the US is not in great shape and industry jobs are becoming increasingly difficult to secure, if I am to make this turn they said that I would get the best advice by posting on a forum, particularly on my next steps if I should go in this direction. Namely, whether or not I should just leave the program and try and step into industry as soon as possible. Or whether I should stick it through and earn the PhD in another 2/3 years, which would perhaps give me a leg up in applications, the current areas of research I would go into would involve heavy analysis mixed with ergodic theory or Stochastic differential equations/markov processes but in an abstract pure math setting, not (at least I havn't asked yet) stochastic calculus which I have been told would be applicable. Also, if I were to continue I would endeavour during this time period to develop additional useful skills, such as perhaps some adeptship in modelling/coding/machine learning/data analysis, via online courses, and courses in programs offered to grad students in many math grad schools and at the most optimistic, working on a project with a friend or in an internship.

Thanks in advance for the helpful responses.

 

[MikeLawrence]

For learning C++, use the first course on this site. The second course is widely spoken of as wonderful, and a rather large jump up from the first (which is itself quite thorough), though I haven't taken the second yet. These two will be most of what you need for industry. The first is honestly most of what you need to get an internship for most roles.

For learning Python, use the course on this site or go to datasim.nl. This second site is the site of the educational vehicle of the creator of the previously mentioned C++ course. Check out the syllabi, or dm me (or @Daniel Duffy, the creator) if you've got questions. I'm in the middle of the Applied Numerical Methods and Applied Numerical Methods with python courses, they are great. But with your level of education the math in them may be mostly covered, so you can peak around and choose between the Quantnet Python course or Dr. Duffy's. for learning striaght python implementation. I think cost is similar.

 

[Daniel Duffy]

What's your PhD topic?

 

[NoPro]

What's your PhD topic?

My current interest is in Operator Algebras, I have just started my second year so am currently in reading courses for research projects. One on the topic of random matrix/free probability/ergodic theory wrt VonNeumann algebras. I am also going to start a reading course with another professor who works in the stochastic diffeq/markov processes over like lie algebras etc. If I stayed I would look to do joint research work with both professors.

The reading course with the second professor hasn't started yet, so I can't speak too much to their research topics, but in general from what I've seen from recent papers in operator theory they involve basically extending identical results from say groups to groupoids or proving topological properties on a family of operators with less strict assumptions. I would be writing papers like this I suspect.

Whilst there are some interesting projects that I've seen in talks that I would try to pursue coauthorship with in addition to the papers for my thesis, they doesn't inspire/reward me enough for the constant learning and thinking alone that I am currently spending on them. Though the math material I use to prove them is great, the subject matter to be proven seems to be more like a hard puzzle that I publish which in my opinion in itself, although good research, is not very interesting though probably fun to work on/prove.

 

[Daniel Duffy]

My 2 cents,

In my experience, people do PhD because they want to. it's hard work. And topic topic is intellectually demanding and rewarding.

Real and Functional Analysis were my favourites in undergrad and I used it in applied research (see my websites)

I feel you should gear up to PDE/SDE, time series etc. for finance. Lots of opportunities?
I did much of my graduate work in Banach and Sobolev spaces (e.g. FEM).

C++ (and Python) is a must in finance.