[FOM] Magic Bullet/1

[Harvey Friedman]

MAGIC BULLET

The notion of emulation of a finite subset of Q[-n,n]^k, especially
for small k,n, is so exquisitely fundamental that it will be used
spectacularly in gifted high school math programs. Almost any finite
set immediately creates a delicious gifted high school challenge - to
find a maximal emulation with exquisite invariance. That one can
always do this with the strongest relevant invariance (which is the
exquisite N shift-related invariance) is equivalent to Con(SRP), and
so the kids are going to be verifying massive numbers of exciting
special cases (almost randomly generated) of an exquisite general
state of the art modern theorem. This will consume them in benign
total addiction. So a whole generation of mathematically gifted
people, some of which go into mathematics, others go into math related
fields, and so forth, will have fond memories of getting hands on
experience in serious mathematical struggles for the first time at an
extremely elementary level through special cases of an exquisite
general theorem that requires much more than ZFC to prove.

A relevant question is this: what can compete with such a magic bullet
anywhere in mathematics? We know that the highly successful important
gifted high school math programs have been looking for such a magic
bullet since their inception. I don't think that, even looking around
the whole of current mathematics, they ever came close to this level
of magic bullet. What do you think?

Harvey Friedman