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Note: This question is about pure math PhDs and not applied, and I mean pure as in an area of math which has no current applications outside of mathematics. It could also be broadened to theoretical PhDs, but I will focus it.

I'm a recently graduated mathematics major with CS skills and working in software engineering and set to enroll in a good math PhD program this Fall. Since I can either continue working or go to a PhD program, I am naturally asking the question:

What value does a pure math PhD hold in a job application to an applied industry, and why? Admittedly, I cannot see why anyone involved in hiring employees would choose a job applicant with a pure math PhD and zero relevant skills/experience over a job applicant with years of relevant skills/experience or with a degree in a more relevant field.

If this question needs to be more specific I would like to focus on software engineering in the U.S. (still broad, let me know if I must focus it more). But I would welcome answers from any other industries too. This answers a larger question of mine that I have on whether a math PhD is a practical ideal these days, which I started here on Math Overflow.

(Why this is an important question:

  1. Most (somewhere near 90%, see here, here) math PhD students will end up industry. Many aim unrealistically for academia, struggle financially with postdocs for a few years, and then eventually switch to industry, usually in finance or software engineering.
  2. A pure math PhD (or any theoretical PhD) requires years of intense focus on books and papers, and there is not much time for developing industry skills in case they must go to industry. In one case, I saw that a pure math PhD graduate had to get a masters in computer science after their math PhD. Overall, it seems like such students will be in a suboptimal position after graduation in the 90% chance they must go to industry, and that this is all glossed over in academia. Hence, this question could help.)
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    I feel like you answered your own question: "I cannot see why anyone involved in hiring employees would choose a job applicant with a pure math PhD and zero relevant skills/experience over a job applicant with years of relevant skills/experience or with a degree in a more relevant field". What more do you want than this?
    – Ertai87
    Jul 5 at 19:00
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    if you can work in a quant, you're all set.
    – Fattie
    Jul 5 at 22:37
  • @Fattie, I agree with you that the "quantitative field" is opened widely to many smart Ph.D people with some basic computer programming skills. I have seen that many times. Jul 6 at 2:46
  • There are certainly some places that value mathematical ability and PhD-level thinking. But for the majority of industry positions, a PhD on your resume will signal "overqualified and probably slightly out of touch with the real world".
    – B. Ithica
    Jul 6 at 9:50
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    Buddy of mine ended up as a quant for some investment fund. Pay is top notch but you need to write code too sometimes. Had pure math degree followed by CS degree, followed by CS master and a bunch of coding experience in between. The coding was enough to get him through the door, but his math skills landed him the job. The guy is really passionate about math tho.
    – BoboDarph
    Jul 7 at 7:19
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A PhD in the UK now has strong emphasis on employability outside academia, as we have so many PhDs and nowhere near as many faculty positions. What you, and your potential future employers will be wanting are "transferable skills". For example, giving presentations, independent working, teaching others, writing, ability to learn quickly, networking. Maybe investigate the training available as part of the PhD programs you are interested in, to see how much of an emphasis there is on transferable skills.

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Admittedly, I cannot see why anyone involved in hiring employees would choose a job applicant with a pure math PhD and zero relevant skills/experience over a job applicant with years of relevant skills/experience or with a degree in a more relevant field.

Industry won't consider a PhD as equivalent to years of experience. So far as they are concerned, it's a higher degree. So you would be treated as a new graduate with a better degree.

They hire new grads, rather than people with years of experience because they are cheaper.

Industry is also not obsessed with exactly what degree you have. Just make sure you aren't either. Instead, they are looking for the right person for the job they have. Which is a lot more than what degree you have.

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  • This is true: I'm a pharmacist and I work in a completely unrelated field (precision machining). They absolutely didn't care that I have no degree in Engineering - btw it comes pretty handy sometimes as part of my job is coaching Problem Solving - making experts explain the issue to a layperson helps them figure out the solution Jul 8 at 9:25
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What I would recommend is looking at the websites of the programs, and seeing where their grads end up. Find out how many graduated each year, and how many got what sort of job.

As you do this, you should assume that anybody they don't mention did not get a decent job, or the program would be happy to list them.

Also, get a count of entries into the program. Somebody once said that there are two types of Ph.D programs, those which admit a few people each year, and graduate a fiew, and those which admit a lot of people and graduate a few. In my experience (and that of a friend who was successful in geting a Ph.D.), you'll have a 30% chance of getting your Ph.D.

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You seem to be implicitly assuming that 'industy experience' is a single monolithic thing and if you gained it in any company it will be just as useful in any company. This is certainly not the case. No new hire ever has all the skills a company needs right from the start.

So if a company compares different candidates for a given position they need to look at two components: first how much of the skills needed does the candidate already have and second how fast can they learn the skills they don't yet have. Pure math PhDs tend to do very good on the second component. That is you hire a pure math PhD if you need someone who can learn (and then apply) anything, especially anything vaguely math related, very quickly.

If you job description requires applying the same skills over and over again and do it very well, a math PhD who doesn't have this skill is probably a poor choice. If your job requires finding the needed skills and then learning them over and over again, a math PhD might be a very good choice.

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I dare saying this question is so broad there is only one answer: yes. Sometimes.

You assume a pure math PHD has zero application in pretty much every aspect. I am not sure I would buy that given that data analysis and ai work are getting more dominant in many industries, and i.e. a very statistical phd may be quite relevant. There is such a thing as insurance math, which is heavily statistics based. Risk management in the financial field is another area - the necessary domain knowledge may be faster to get than the mathematical knowledge, which the PHD proves.

So, while a "no" is a likely answer for most positions - there are some that are quite specific and extremely math heavy.

That said, as a career - those positions are quite rare, so, "beware what you wish for".

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    those are all applied math/stat positions. A Ph.D. in those would be great, but the question is about applied math Ph.D.'s Jul 5 at 19:37
  • I think you limit that too much. Those are all applied positions, right - but who do you expect to hire anyone and pay him without any application at all? That would literally be a grant. Maybe some billionaire having a "pet mathematician" on staff. Anything else - a pure math PHD may be it, but the position will have applicability or it has no value generated. And you did not ask for pure math jobs, but about HIRING a pure math PHD. In the positions I see, someone would be hired - for a junior/trainee program.
    – TomTom
    Jul 5 at 19:53
  • And especially the statistical field has quite some applications where people actually do publish research papers about things like risk management. So, I could see someone having exposure to this application of statistics in university, then doing a PHD, then doing some move into the industry and being preferred to someone with experience BECAUSE OF HIS PUBLISHED WORK.
    – TomTom
    Jul 5 at 19:55
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    " In the positions I see, someone would be hired - for a junior/trainee program." I agree, which makes getting a pure math Ph.D. less worthwhile, especially since an employer could always go after people with applied BS degrees. As for your original post, I'm reasonably aware of the situation; I was in a biostat Ph.D. program for a while, and talked with many stat people (we were taking the same courses). A pure math Ph.D. is not a statistics degree. Jul 5 at 22:22
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    It's interesting how everyone here seems to think that PhD is essentially trade school.
    – ojs
    Jul 6 at 9:14

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