‘Hard’ skills from PhDs remain relevant beyond academia
(1) Financial Math.  Some of the comments here have to do with <i>mathematical finance</i>, e.g., the Black-Scholes model.<p>Mathematical finance done with theorems and proofs has some strong prerequisites of <i>measure theory</i>  with sigma algebras, Markov processes, Brownian motion,  the Radon-Nikodym theorem, conditional expectation, stochastic integration, e.g., 
Ioannis Karatzas, Steven E.
Shreve,
<i>Brownian Motion and Stochastic
Calculus</i>,
Robert M. Blumenthal and
Ronald K. Getoor,
<i>Markov Processes and Potential
Theory</i>.
Can also want parabolic partial differential equations and
stochastic dynamic programming.<p>In my experience, with a pure&#x2F;applied math Ph.D. and as a prof in an MBA program, nearly no MBA students or profs have those prerequisites.  And with my experience in finance, nearly no one in finance has those prerequisites, either.<p>The people in MBA programs, as students or professors, may have gotten such a background from Cinlar, Shreve, or one of a few more.<p>Bluntly, not many people, a tiny fraction even in pure math, and a good background in pure math is a prerequisite, actually study stochastic processes and stochastic optimal control with a measure theory prerequisite.<p>Anyone X with anything like that math background might want to be careful or that background will scare nearly all potential employers, in finance or anything else, and result in X being ostracized and fired or not hired.<p>(2) Math in MBA Programs. When I was a prof in an MBA program, all the math used was undergraduate level, e.g., with hardly even a calculus prerequisite.<p>(3) Advanced STEM Educations for Non-Academic Jobs.  It appears that an advanced education, e.g., in computer science, can help in getting a non-academic job, but the real <i>help</i> is just passing a filter, having <i>proved</i> oneself, and not aiding in doing the job.<p>This situation should not be a surprise:  Having exceptionally good qualifications will make a person X exceptional and rare, that is, one out of 100+.  Then the other 99 can be afraid and resentful and gang up on X, sabotage X with gossip, keep X <i>out of the loop</i>, etc.<p>(4) Jobs and People with Exceptional Qualifications.  It is common for someone X with exceptional qualifications to attempt to use those qualifications to get and do well in a job as an employee.  That would mean that person X has a supervisor Y who created the job.  But as we can anticipate, it is rare for a supervisor Y to have the exceptional qualifications or to create a job that needs such qualifications.  Moreover Y could be uncomfortable, feel threatened by, a subordinate X having and using qualifications Y did not have.  In simple terms, commonly Y hires X to apply routine <i>muscle</i> to work conceived by Y.  To borrow from a James Bond movie, X is not hired to think and, instead, is hired to do what they are told.<p>(5) Potential of Exceptional Qualifications.  For a person with exceptional qualifications that might be powerful and valuable for a career, don&#x27;t look for a corresponding job created by someone else and, instead, create the corresponding job for yourself.  E.g., do a startup.<p>(6) Financial Success.  If person X works as an employee, then the supervisor of X knows to the last penny just how much money X is making and usually will do their best to keep down the amount.  However, if person X owns a business, then for X the customers replace the supervisor, and it&#x27;s common for the customers not to know even roughly how much money X is making.<p>So, net, for X with exceptional qualifications that seem powerful and valuable, start and run a successful business and make use of those qualifications.  There X can be making a nice fortune, with no supervisor at all and with customers who neither know nor much care how much X is making.<p>(7) Academic Research Jobs.  In academic research, the prof is essentially begging a little money from sources with big money, working hard, and then begging journals to let them give away the results of the work for free.  So, we might anticipate that such jobs won&#x27;t pay very well.  I concluded that broadly academic jobs were, for someone who wanted to support a family with financial security, financially irresponsible.