Mathematicians can cite many other examples of surprising applications. Could the 19th-century founders of mathematical logic have imagined where Alan Turing would take their new field a hundred years later? With the computer science that Turing founded, the once-abstract field of number theory became a foundation of cryptography. The mathematics of origami have contributed to designing solar sails and automotive airbags. In the 1980s, the topological subfield of knot theory became a powerful tool in particle physics. Symposia have already been held on applications of topology to the design of industrial robots. I’ve even read the statement — but haven’t been able to find the reference again — that every significant pure math idea has an application. We just haven’t discovered some yet.
All this is timely, because in some quarters of neo-mercantilist, managerial academia, some mathematics is considered too pure for the national economy, especially in the UK.
In a famous paper on the uncanny way that math describes reality, the physicist Eugene Wigner concluded:
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve. We should be grateful for it and hope that it will remain valid in future research and that it will extend, for better or for worse, to our pleasure, even though perhaps also to our bafflement, to wide branches of learning.
Bill Thurston was one of the great bestowers of that gift.