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I read "The Man Who Loved Only Numbers," a great book about Paul Erdős, last summer. The book describes Ronald Graham, a super interesting character who worked on discrete math and graph theory at AT&T Bell Labs, and often collaborated and baby sat Erdős for many years.

Yesterday, I went to talk to my professor who is at the top of her field. She introduced me to a retired mathematician who had been her mentor. He had worked in IBM's dynamical systems team, now defunct. Obviously, he had been doing cutting edge stuff in the field of dynamical systems.

Am I correct to extrapolate from these two events that serious "pure" mathematics used to be done in the private sector but isn't anymore? If so, what happened? Has computer science or physics subsumed math in the private sector, or did companies already suck the most they could out of basic research in most applicable fields we consider pure math?

This is important to me as I love math, but am not sure a future professorship in math academia is in the cards for me.

Thanks in advance for the responses!

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    $\begingroup$ The situation around Bell Labs changed, and they weren't able to do what they used to do. I think they were a pretty exceptional case. $\endgroup$ – Qiaochu Yuan May 12 '16 at 0:32
  • $\begingroup$ @Qiaochu Yuan Do you know what happened? $\endgroup$ – qbert May 12 '16 at 0:47
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    $\begingroup$ It's a long story, and I'm not sure I can summarize it well. You can read about it here: amazon.com/Idea-Factory-Great-American-Innovation/dp/0143122797 $\endgroup$ – Qiaochu Yuan May 12 '16 at 1:03
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Well, first, a professorship in academia is always a long shot. Tenured positions are gold and about as hard to find without help and a massive amount of talent.

That aside, I can speak for my own field of operations research/data science: obviously, this area is booming in the private sector. A big part of this is graph theory and numerical analysis, where you need to prove convergence of algorithms. Machine learning theory requires a ton of mathematics to prove theorems (just look up Latent Dirichlet Allocation for topic modeling).

Not sure if this is what you are after, but I think that it is not true that the golden age of industrial mathematics has passed: it has merely transformed. When you think back to Bell Labs and 1950-1970's era industrial math, you are talking about a time before widespread availability of computers. Had computers been available, I don't know how that era would have looked, but it will likely have looked less "academic" then it actually was.

If you equate "industrial math" with private sector researchers scribbling on chalkboards, then yes, that era is gone...they now scribble on smart boards, program simulations, mine massive datasets from sensors and internet servers, and hack the heck out of tools like MATLAB, Mathematica, and R.

Is this stuff "pure" math...well, even in the "golden era", you can be sure that if the private sector is paying for it, there's an economic motive, not just a love of learning (although the two are not mutually exclusive). One of your examples, dynamical systems, is actually very applied, especially when compared to fields like number theory (although it also has a lot of applications) or category theory. However, I would be hard pressed to find an area of math "unsullied" by an actual use in the world.

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  • $\begingroup$ This is a great answer, thank you. Do people working in your field publish academically? I am thinking this might be a good barometer for how linked they still are to important and new research. Also, do you think there is still a bit of a lag for companies still trying to figure out how to best apply human capital with all this computing power? $\endgroup$ – qbert May 12 '16 at 2:11
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    $\begingroup$ @qbert absolutely! Take a look at informs.org/Find-Research-Publications/INFORMS-Journals. Also, there is the Society of Industrial and Applied Mathematics, with most contributors from private sector:siam.org/journals. Not only are these folks "connected" they ARE making the important and new research. Academics often read their research! Anyway, opportunities abound if you are wiling to forgo the, increasingly Quixotic, quest for traditional tenured academic positions. $\endgroup$ – user237392 May 12 '16 at 2:18
  • $\begingroup$ This is great to hear. Thank you for your response and the resources $\endgroup$ – qbert May 12 '16 at 2:19

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