FOM: techniques & problems

Martin Davis martind at
Thu Aug 13 13:35:18 EDT 1998

I believe this happens regularly and expectedly in mathematics:

1. A difficult longstanding problem succumbs to a new technique.
2. The technique is quickly learned and applied to a bunch of problems.
3. Harder problems require the technique be refined. Virtuosity develops.
4. Virtuosos naturally go where their hard-won expertise is effective.
Others may wonder whether it is all worthwhile.

This is as natural as the tides. Telling talented people who have devoted
enormous effort to becoming virtuosos that they should do something else is
as pointless as telling a violinist to become a pianist. 

In a social setting where enough resources are found to permit talented
people to do what they find interesting and worthwhile all of this is a


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