Any rigorous study of unpredicted applications of pure math?

September 30, 2011 4:29 PM

It is often said that pure math research finds unpredictable applications long after it is done. Has anyone tried to investigate this phenomenon rigorously?

An example of this bit of conventional wisdom:

Trying to solve real-world problems, researchers often discover that the tools they need were developed years, decades or even centuries earlier by mathematicians with no prospect, or care for, applicability.
Peter Rowlett, "The unplanned impact of mathematics". Nature 475, 166–169. 2011 July 14. doi:10.1038/475166a (paywalled, I think)

Has anybody has tried to make a serious academic study of this phenomenon? For example, to try to determine whether math is actually unusual in this respect by any measure, or to try to do a cost/benefit analysis on doing research this way.

I am not asking whether pure math research is worthwhile, nor whether applications are the right measure of worth for such research. I am asking narrowly about this particular claim about applications.

(I was reminded of my interest in this question by one of wierdo's comments in today's Tevatron post to the blue.)

posted by stebulus to Science & Nature (5 answers total)

One of the things that stuck in my mind from reading Andrew Hodges's biography of Turing was that the idea of a mathematician is a relatively recent one. People like Christoffel, Ricci-Cubastro and Levi-Civita (the last two mentioned in the article) were all working with the understanding that what they were doing might have some application. They all had physics-y backgrounds. Of course, Ricci-Cubastro and Levi-Civita are given as an example in that Nature article. Go back 150 years or so and you have an awful lot of people working on things that they knew were liable to have applications, even if those precise applications were as yet unspecified. I suppose I'm trying to argue that perhaps these things are far more organic than the article makes it seem, which makes it unsurprising that I don't know of the sort of article you're looking for.
posted by hoyland at 6:09 PM on September 30, 2011

I don't have an answer to your question, but here's a related thread you might find interesting.
posted by epimorph at 6:14 PM on September 30, 2011

This is not a rigorous study, but this, which links to this and this, I found very interesting. Cool question!
posted by xiaolongbao at 10:48 PM on September 30, 2011

Doron Zeilberger's book A=B is a highly readable discussion of computer-generated proofs for certain types of identities or relations. The second chapter remarks on your question, perhaps tangentially:

Computers not only find proofs of known identities, they also find completely new identities. Lots of them. Some very pretty. Some not so pretty but very useful. Some neither pretty nor useful, in which case we humans can ignore them.

There is then a brief listing of publications, describing work derived from this approach.
posted by Blazecock Pileon at 6:38 AM on October 1, 2011

You will love this paper.

the mathematical universe

or to try to do a cost/benefit analysis on doing research this way.


The suggestion that research in pure math may actually be the most efficient way to new insights in physics.
posted by yoyo_nyc at 10:12 AM on October 1, 2011