Has anyone worked out a formal, general-enough definition of what is 'useful', so that it could reflectively be used in mathematics? I am aware of the work in utility theory from economics (but originally from the Bernoullis and improved by von Neumann, so very much 'mathematical'). Such a formalization should be adequate to decide if a particular definition (or theorem) is considered 'useful'.

Note that I fully expect *utility* to be a relative notion, in other words I don't expect anything to be 'universally useful'. I have some tentative definitions, but before I spend too much time working this out, I would like to know if this has already been done mathematically (as the work of economists on this is [expectedly] too biased towards economic utility).

A concrete example: 20 years ago, elliptic curves would have been considered 'not useful' in the context of cryptography, now it is considered 'useful'. **This can be made completely formal**. [In other words, my question is about what has been done before, not a discussion of what this is, which if off-topic for MO].