

Ask HN: Mathematicians' jobs -- What am I missing? - zhj

Dear HN,<p>having advanced degrees in maths and philosophy (both equivalent to MSc), I wonder what opportunities might be there for me <i>not neglecting maths</i> beside pursuing a PhD.  The problem is, I think, that I'm not specialized or interested in applied math (neither statistics, finance, nor numerical computing) and also not very keen on consulting businesses.<p>So my question is:  What comes to your minds when you think about jobs in, well, "applied pure math"?<p>Any pointers are much appreciated.  Thanks for your time.
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pmtarantino
As swGooF said, you won't be able to find too many places to do math without
apply it to something useful. Academia, in the other hand, is quite
complicated, mainly because the famous "Publish or Perish" [1]. If you don't
want to live your life publishing papers without too much sense, I'd say to
focus on find a good place/subject of applied math and work on it. It should
be as much as fun as do pure math, applied math has a lot of research and math
as pure math, although probably less algebra :)

[1] <http://en.wikipedia.org/wiki/Publish_or_perish>

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swGooF
This is maybe not the answer you want to hear. Outside of academia, there are
not a lot of places that will hire you to do pure math. Most companies need
the math to be applied to some product/strategy for revenue purposes. If your
math has no application, then why would a company pay you for it. That being
said, fields such as data science and machine learning (both applied) are
pretty hot right now.

~~~
zhj
Thanks.

A little further remark, I'm not actually opposed to applying math (or e.g.
some kind of logical modeling), just to the "traditional" _applied math_
subjects, i.e. numerical computing or statistics.

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typhonic
You must have other interests. I suggest you look for a job in one of those
areas. Some things can overlap with pure mathematics, game creation, for
example. Some jobs can simply provide you with enough resources to pursue your
other interests separately, sales, for example.

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ig1
What fields of maths are you interested in ?

~~~
zhj
For example algebraic topology, category theory and (mathematical) logic.

(Functional programming comes to mind, but I really am no programmer, despite
some interest in the languages.)

~~~
ig1
You could possibly find a role working on graph algorithm design ?

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ten_fingers
In the US, long the main sources of employment that use math are efforts in US
national security.

So, at one of the top dozen or so US research universities, about 60% of the
annual budget is from research grants from the US Federal government. The main
sources are NSF and NIH. The main fields are the STEM fields for US national
security and biomedical for medicine.

So, an academic publish or perish job should try to be a job that gets grants
from NSF, etc. In particular, such a job is not just for 'ivory tower', do
what you want, 'generalized abstract nonsense' but is for what the NSF, etc.
want to fund.

Associated with such funded academic groups can be research positions that
just do research and don't teach.

Okay, here is a general view of such work: Generally the most respected work
in a field 'mathematizes' the field. So, fields that got so 'mathematized'
include physics, chemistry, electrical engineering, electronic engineering,
mechanical engineering, chemical engineering, aeronautical engineering,
computer science, operations research, and finance.

Of course for finance, see the career of James Simons.

Now being 'mathematized' is much of genetics aimed at cancer research. There
see the work of mathematician Eric Lander and, in particular, his lecture

[http://www.princeton.edu/WebMedia/flash/lectures/20100419_pu...](http://www.princeton.edu/WebMedia/flash/lectures/20100419_publect_lander.shtml)

April 19, 2010, Eric Lander: "Secrets of the Human Genome".

Notice that it's possible to get a Ph.D. in 'applied math' without setting
foot in a pure math department, especially if you already have a good Master's
in math. So, get your Ph.D. in some part of 'engineering'. E.g., some
departments of electronic engineering have profs interested in whatever in
principle electronics might be used for and, thus, e.g., pursue stochastic
integration and nonlinear filtering and far out directions in 'information
sciences'. See the work of D. Bertsekas at MIT -- he's a terrific applied
mathematician, but I have no idea what department he's in. At Princeton there
is a chemical engineering prof who, really, does nonlinear optimization for
petrochemical plants -- he is popular in Houston. At Stanford notice the
career of D. Luenberger -- again, a terrific applied mathematician but maybe
not in a pure math department. Similarly notice E. Cinlar at Princeton, a
terrific mathematician but not in a math department. Also notice the career of
H. Kushner at Brown's Division of Applied Math -- he worked on a huge range of
topics, sometimes even nurse scheduling. Your Ph.D. might be in 'systems
analysis' or 'engineering/economic systems' or some such.

Notice the broad field of stochastic optimal control, e.g., from E. Dynkin, D.
Bertsekas, and R. Rockafellar. Then notice that Intel has stated that they
already know how to build processors with 1000 cores and have the cores work
together effectively and notice the extreme ability of stochastic optimal
control to make use of millions of threads of conceptually simple parallelism.

Another field, I once did some work in, is multivariate, distribution free
statistics, especially where we can assume a lot of data. There's more to do
in that direction.

Then notice that with a Ph.D. you could get a job as a prof in a B school.
They might need people to teach mathematical finance, operations research,
statistics, 'supply chain optimization', 'constraint logic programming',
'production scheduling', etc.

Also consider mathematizing sociology, and for that notice the work of James
Coleman and Pete Rossi, both past presidents of the American Sociological
Association, and also Leo Goodman.

Don't miss the work on medical research by Persi Diaconis at Stanford, e.g.,

<http://videolectures.net/nips09_diaconis_bamc/>

along with mathematician David Freedman, e.g., as in

David Freedman, 'Brownian Motion and Diffusion', ISBN 0-387-90805-6, Springer-
Verlag, New York, 1983.

No doubt the economists continue to struggle with math; consider moving into
economics where your math background could be a big advantage. Considering
that obviously the economists don't have even a weak little hollow hint of a
tiny clue about either how to avoid a depression or how to get out of one,
there are some good reasons to do good work in economics if that is possible.

If you have some ideas about 'applied math', e.g., maybe something reasonably
respectable mathematically in 'data mining', 'machine learning', 'artificial
intelligence', or, really, nearly anything in engineering or beyond, some math
departments will be interested. Why? Because they want students and some of
the glory of hot fields and applicable work. If you can also get an NSF grant,
so much the better.

Likely you can do applied math in a computer science department. E.g.,
somewhere in California is a prof who specializes in speculative applications
of convex sets and functions. You may have noticed that some computer science
departments are eager to be more mathematical but are struggling with math,
sometimes, even at famous departments, struggling poorly with what is commonly
taught in a junior level course in abstract algebra.

Outside of academics, considering the main source of money, maybe it should be
no surprise that work in US national security has long been a good place to
find a job in applied math. So, consider the various military labs around DC
and, then, the companies who work with them. So consider the whole universe of
US national security work. E.g., computer security is a hot topic, and
monitoring is basically statistical hypothesis tests with false positives and
false negatives. There's plenty of good, new applied math to be done there.

Next, understand that generally there is a problem asking that someone else
create the job you really want. Indeed, if you get very far from academics,
you will have a tough time finding anyone with money enough to hire and also
even able to write a good job description for an applied mathematician. And
they would be terrified to have someone reporting to them doing work they
didn't understand.

So, really, for the job you want, you need to create it for yourself. For
this, the first consideration is, where will the money come from? In
particular, who will your customers be? So, find something to do where
customers are willing to pay for something better, use some math to provide
something better, and deliver the results via computing and the Internet.

~~~
zhj
Thank you very much for your thorough answer and the many starting points to
read into. Much appreciated. Got some "meta-research" to do now...

