### Challenges for the Future

#### Posted by David Corfield

Benjamin Mann of DARPA has constructed a list of 23 challenges for mathematics over the next century.

Whereas Hilbert notes about his 23 problems

I have generally mentioned problems as definite and special as possible, in the opinion that it is just such definite and special problems that attract us the most and from which the most lasting influence is often exerted upon science,

Mann’s challenges are generally open-ended, resembling Hilbert’s sixth problem:

6. Mathematical treatment of the axioms of physics

The investigations on the foundations of geometry suggest the problem:

To treat in the same manner, by means of axioms, those physical sciences in which mathematics plays an important part; in the first rank are the theory of probabilities and mechanics.

rather than his thirteenth:

13. Impossibility of the solution of the general equation of the 7-th degree by means of functions of only two arguments.

Some motivation accompanies Mann’s list, but it would be good to see experts write a few paragraphs for each challenge on that inviting parchment background.

Posted at December 28, 2007 10:53 AM UTC
## Re: Challenges for the Future

For some inimitable Arnoldian exposition on Hilbert’s thirteenth problem see the first pages of the lecture From Hilbert’s Superposition Problem to Dynamical Systems.