Darpa May Be Hilbert
August 28, 2012
are a set of (originally) unsolved problems in mathematics proposed by Hilbert. Of the 23 total appearing in the printed address, ten were actually presented at the Second International Congress in Paris on August 8, 1900. In particular, the problems presented by Hilbert were 1, 2, 6, 7, 8, 13, 16, 19, 21, and 22 (Derbyshire 2004, p. 377). Furthermore, the final list of 23 problems omitted one additional problem on proof theory (Thiele 2001). Hilbert’s problems were designed to serve as examples for the kinds of problems whose solutions would lead to the furthering of disciplines in mathematics. As such, some were areas for investigation and therefore not strictly “problems.”
This blog post is not the appropriate forum for a review of the status of research regarding the PhD carnival these problems have created. You may recall that one of the problems, “the cardinal number of the continuum” can drive some people crazy.
I noted the story “23 Mathematical Challenges.” DARPA, a US government research agency, has rolled out its own set of 23 problems. Presumably PhD candidates and grant writers will hop to them. Here’s a sample problem if you think you are pretty good at solving USA Today sudoku puzzles:
Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?
Once you have that nailed, what about:
Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability, and variability.
My question, “Is Darpa the new David Hilbert?” Hilbert fedoras would be a wonderful addition to the Darpa authorized clothing regulations.
Stephen E Arnold, August 28, 2012
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