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I am in the second year of a three-year PhD in algebraic topology — though not in topological data analysis or anything practical — and I am beginning to think about job prospects and life after my PhD.

I have been fortunate in that my PhD has gone well so far — I've written a few preprints — and I (hopefully!) won't have much difficulty finding a postdoc. However, I am not sure if I want to go down that route. I love research but I hate teaching, and, more than that, I am really tired of being poor and having no job (or even geographical) stability. I have a partner with a non-academic job and I don't want to abandon her and to go to Canada or something in a year's time. Continuing in academia would seem to prolong the problem for another ten years at least (and that's assuming I don't fail as a postdoc which is a big if). Thus, I am wondering what jobs are available for those who earned a PhD in algebraic topology, or, indeed, in pure maths generally?

I spoke with my advisor, but he never seriously considered a career outside academia himself and doesn't really see the point in not "trying a postdoc." The other questions I could find on Stack Exchange mainly address people who only realise they don't want to be academics just before their PhD defence. Is there any way I can spend my final year as a PhD student to make myself more employable?

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    your question is general, but since you mention you do not want to move to Canada it woul be helpful if you state where you want to reside.
    – EarlGrey
    Jan 18, 2023 at 10:02
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    There are very many jobs in industry that someone with a PhD in algebraic topology could get and do well at, but there are very few that actually involve algebraic topology, or even general pure math research. There are research jobs in industry, but they're dissimilar to academic math research.
    – anomaly
    Jan 18, 2023 at 21:51
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    If it's a good/decent school, the top consulting firms will look at you. Some quantitative hedge funds, like D.E. Shaw, like people who didn't focus on finance before joining them. There are other groups in investment banks that would have a look at you if you can get in touch (e.g., I know people who came from CERN or with a Ph.D. in algebra). You'd have to be willing to code for them as well. There are specialized recruiters (head hunters) who represent Ph.D.s. Try to get in touch with one (friends at your B-School? ...?). Sneak into a recruiting event at your B-School? Jan 19, 2023 at 0:49
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    Depending on where you want to be located, quantitative finance jobs generally consider anyone with a technical PhD and can be quite lucrative. Many of them offer graduate internships. One of the strange things about getting a PhD is that jobs that specifically require your PhD expertise don't pay much, and jobs that pay a lot don't want you for any specific thing you know, but just want you because you're numerate. Jan 19, 2023 at 1:01
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    Related: Are there any research careers except professorship for a person holding PhD in pure mathematics? Not a duplicate, though, because that other thread explicitly asks for opportunities with a research component. Jan 19, 2023 at 8:33

6 Answers 6

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A brief report from the front, from a postdoc who does topological data analysis and is on the job market:

  • Computation of some sort is the only obvious route to a non-academic job that uses math skills. I'd urge you to pick up some type of coding basics, naturally I'm biased towards data analysis. My friends who don't have these have struggled on the job market.

  • I don't know of any employers outside the academy that are interested in pure algebraic topology. Even the people I know who do TDA at receptive National Labs are more focused on useful computations than extensive theoretical work. Geometric and topological reasoning about data otherwise seems to land you largely at tech companies. Graphs are topical.

  • Rumor has it that the NSA has some demand for theory. But who knows? And historically the theory part of their objectives aligns with number theory, by reputation.

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    Perhaps link to this? nsa.gov/careers Jan 18, 2023 at 15:12
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    "some type of coding basics [...] who don't have these have struggled on the job market" Let's remember that the entrance in the pool of candidates considered for an interview is given by some sort of HR tool (either a computer program or an intern in psychology) that could not differentiate between astrology and astronomy, but is very good at doing comparison between a given checklist and what is in written in your CV/motivation letter ...
    – EarlGrey
    Jan 18, 2023 at 15:20
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    @RichardErickson Very reasonable suggestion...I think I'm going to leave it out, but only because it's Google-able and I didn't want to make a list more generally.
    – user137975
    Jan 18, 2023 at 17:39
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    @EarlGrey: Not to prompt extensive discussion, but if you've never done any computational work at all, most places that want it have more competitive candidates in their pools even w/o PhD's.
    – user137975
    Jan 18, 2023 at 17:39
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    @davidbak I know of at least one company who blacklisted anybody who did that (it was a company that was putting in a lot of effort to be fair in their hiring, so they had fairly strict processes of which initial stages were 'blind' (and bypassing the processes removed the blindness)). As someone who has had to make hiring decisions I can also say with confidence that it's always been the 'bullshitters' (smooth talkers who lack skills) who got forwarded from the CEO. Jan 20, 2023 at 9:06
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What jobs are available for PhD in algebraic topology or indeed in pure maths generally?

I suggested Are there any research careers except professorship for a person holding PhD in pure mathematics? in the comments. On the one hand, there are careers like management consulting, where being highly intelligent and articulate is more important than having specific knowledge. On the other hand, there is anything IT-related, where there is a presumption that anyone who understands algebraic topology can pick up whatever they need. I personally do think that formal education in software engineering is usually better than educating someone on the job - but math Ph.D.s are capable of being trained on the job for most-if-not-all IT-related jobs, so our job prospects in this sector are quite good. On the third hand, there is insurance, but that has been a bit eclipsed by the other two options.

Is there any way I can spend my final year as a PhD student to make myself more employable?

First off, it's great that you are making plans now! Since your final year is going to be busy, you need to focus here. Three very specific recommendations:

  1. Learn Python if you don't know it yet. This is the most common programming language out there, and will thus open the most doors for your time investment. No need to become deeply proficient - just understand enough to be able to tick the box (many application forms are nowadays processed automatically), and master some simple coding challenges in the interview, like FizzBuzz. If you are already comfortable with Python, attend a Data Science bootcamp or similar. Data Science is still hot.

    Both suggestions are actually not (only) about the sheer knowledge you will gain. They are in large part about signaling: by investing time in these areas, you show potential employers that you are thinking ahead and doing things to make you more employable. Talking about this is a great conversation to have with a recruiter.

  2. When you do talk to a recruiter, they will ask you what you did in your Ph.D., as a way to break the ice, and to see whether you can explain complex topics to a non-expert - which is a skill you will need in any job you might get that goes beyond flipping burgers. Thus, develop and practice an elevator pitch. Test it on non-experts. This is typically not easy for pure math Ph.D.s.

  3. Once you have that elevator pitch, start networking and talking to people. Attend job fairs. Does your university have any kind of assistance? This can be invaluable. Use these opportunities to perfect your elevator pitch, to ask what people in industry are looking for in candidates, what else you could do to make yourself more employable. Do more listening and less talking at the beginning, and leave a good impression. (Which is why you should get that elevator pitch down first, and start on Python or Data Science.)

A bit of encouragement: I am working with a couple of math and physics Ph.D.s, and most of them are doing something completely different than when they studied, mostly software development and data science. And I recently was involved in peer reviewing my old math department as an "industry representative". The industry job market for mathematicians is definitely quite good, and if you do invest in yourself, there will almost certainly be a job for you out there.

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    Very nice answer. Anything that requires deep thought, analysis, modeling, and solid evidence is a good fit for a mathematician, though you might not get to apply algebraic topology a lot. Interesting if you do, of course.
    – Buffy
    Jan 19, 2023 at 14:29
  • Would the downvoter be interested in leaving a comment as to what about my answer is not useful? I would like to learn. Thank you! Jan 20, 2023 at 9:22
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    "formal education in software engineering is better than educating someone on the job [...] math Ph.D.s may just be the best there is for someone hiring for industry" - as someone who works in business computing, I'd caution that most computation here is not especially difficult from a mathematical perspective. The problem is largely about managing a large variety of simple computation. Formal education does not usually touch the sides. And the OP said he "doesn't like teaching" - if that means a general aversion to communicating and explaining, that's another black mark.
    – Steve
    Jan 20, 2023 at 9:53
  • @Steve: I do not exactly know what business computing is, but I was looking at true software engineering, backend full-stack development of large business critical systems within a legacy codebase and architecture, in teams distributed across multiple continents, with implications from database optimization to security. We do have a number of on-the-job trained math Ph.D.s, and I would still maintain that someone who has learned about code modularization in a formal way would likely be better. YMMV. Jan 21, 2023 at 6:17
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    Second, on-the-job experience remains an irreducible requirement for a competent developer, because (a) academia reproduces their full range of craft skills poorly, and (b) there is a large variation in industrial practices and facilities around software which makes it difficult to tailor one general academic curriculum with any one employer's needs and circumstances. (2/3)
    – Steve
    Jan 22, 2023 at 10:44
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"what jobs are available for PhD in algebraic topology or indeed in pure maths generally?"

First, recommend you look at these questions, that refer to real-life applications of algebraic topology.

Short Summary of Fields where they hire topology folks in industry:

  • Sensor network design (ex: global sensor integration)
  • Computer vision & pattern recognition
  • Robotics for motion planning and behavioral algorithms
  • Logistics and factory operations movement
  • Protein folding and analysis of DNA function
  • Game theory for economics (thru Brouwer's fixed point theorem)
  • Nuclear power risk management
  • Nuclear instability modeling (fusion attempts ex: DOE)
  • Actuarial science modeling
  • Asynchronous computation and concurrency issues for parallel computing
  • Topological data analysis (mostly simplification of "big data" sets)
  • Hydrodynamic instability modeling
  • Design of topological insulator materials for computers
  • Mesh processing for 3D modeling and printing
  • Neurology to understand the functionality of brain parts
  • Agriculture (mostly sensors and logistics - also spherical cows)
  • Geographic Information Systems (GIS)

A quick search of Jobs Topology finds that in 2023:

  • Amazon is hiring quite a bit in this area for logistics, factory, and delivery optimization
  • Los Alamos (although Post-Doc) is hiring for topology of quantum materials
  • National Institutes of Health (NIH) is hiring for DNA topology
  • Lawrence Livermore is hiring for topology optimization of HPC computation systems
  • Mitsubishi is hiring for topology optimization of electric machines
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If you managed to survive for a PhD, you can take any advanced qualification cetificate that is expendable in the place where you reside now. Every university offers them, they are your paid entrance to the workforce. Find one that fits your profile and interest

However, yes, there is a way to spend your time to be more employable, you should look at what people are doing in the private world. Like your PhD topic, which is an open research question looking for someone to tackle it, a job opportunity arise because there is a need in a company for a profile like "yours". But no one is looking for your profile, there is simply a need for your skills. Now you are deep in your PhD trench, thinking that you can do and can fulfill your working life only in the very specific topic of the holomorphism of biquadratic asymmetric complex tensor, therefore either you find a job dealing with holomorphism of biquadratic asymmetric complex tensor (or at least holomrophism of biquadratic symmetric complex tensor) or your life will be devoid of meaning and you will suffer for your choice.

This is not how the human mind works, and especially this is not how the market for the workforce works. If you have a PhD in Mathematics, or in Physics, or even in Chemistry, in general it is equally relevant to the potential employer: they care, but they do not really vouche for the content, they hire you for the method you applied to tackling problems.

Or, if everything is unsatisfactory, you start your own company and you enjoy the ride in providing algebraic topology services. I know nothing of them, but there must be a market. Check what others did (5 secs google search brought me to https://www.johndcook.com/blog/2016/01/27/next-areas-of-math-to-be-applied/ ) and then good luck!

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You could possibly find a research institute that does not have a teaching aspect. There are some around. Here is one.

https://perimeterinstitute.ca/

You have to be pretty stellar to get a job there. And it is in Canada. There are other such institutes. Google for them.

Industry is going to want some kind of thing that can, in some way at some level, however indirectly, be sold to a customer.

Computers of some kind is the obvious one. Programming in nearly any language is a good start, especially if you have done some significant software project. Database development is possible. Signal processing is big. Artificial intelligence is huge right now.

I recall a story about a large auto industry company that hired an astrophysics guy. His job was to teach the car engineers about various things such as cosmology and stellar dynamics and so forth. Not to get them doing research, but to broaden them and give them ideas about various methods of solving problems. But then, you mention you don't like teaching.

Maybe you have some kind of hands-on technical hobby? One of the techs at this company got his start learning to "cherry out" his racing car. He does everything on the car from electrical to fuel injection to body work. Then he personally races it. So when he's putting together some equipment in the lab it's a breeze.

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  • what does “And it is in Canada” mean or what is it meant to imply? Plus, PI is for theoretical physics (as the full name states) so not that clear that someone with algebraic topology would be hired Jan 19, 2023 at 4:06
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    @ZeroTheHero I think it was a bit tongue in cheek, but OP did mention not wanting to move to Canada.
    – Dan Romik
    Jan 19, 2023 at 5:02
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If you want a job as a mathematician outside of academia, possibilities might include anything in high tech that really depends on math, e.g., machine learning and robotics, or perhaps Wall Street, where they do a lot of modeling and can afford to pay piles of money.

But it may also be helpful (or not) to know that the largest single employer of mathematicians in the US is the NSA. Is government service a possibility?

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  • yes, finance is good. Actuarial work used to be. I don't know if that is still true.
    – Buffy
    Jan 19, 2023 at 14:28
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    Actuarial work has very little actual mathematics. Due to factors such as regulations and limited/unclean data, most of the models they make are quite simple. And even then, most of the modelling is automated by software that does most of the work for you. I would say actuarial work requires more business knowledge rather than any mathematical knowledge.
    – Nanoputian
    Jan 19, 2023 at 19:35

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