⊗5↓_Plans for Future Research_↓⊗*

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The  fascinating  task of  understanding  and  automating  scientific
theory formation  will probably occupy my research  time for the next
few years.    Some of  the projects  I  am contemplating  are  direct
outgrowths of AM,  the "Automated Mathematician" project  which is my
dissertation.

For   example,  attention  should  be   paid  to  those  mathematical
discoveries which ⊗4can't⊗* be  synthesized by the kind  of heuristic
procedure AM follows; that is, what historical inductive leaps remain
when all the "hack" discoveries are discounted?

Another possible direction for my work next year is to take the first
step toward the codification of the heuristics necessary for creative
work in  mathematics.  The AM program can  be used as an experimental
instrument, to help clarify the role of each heuristic.   Ultimately,
such a codification  could lead to a programme  for teaching students
how  to do creative research.  If  AM can do useful theory formation,
then certainly  so  can bright  students who  have  learned the  same
heuristics.

An orthogonal  research interest of mine  is to expand  AM to domains
other than  elementary  number  theory.   Apparently,  the  harder  a
science is, the more  appropriate it is to try  to automate formation
of  its  theories.    So  some  candidate domains  include  geometry,
cryptography, calculus, and  algebra.  Still  plausible are parts  of
chemistry and physics  (e.g., mechanics).  ⊗4Very⊗*  soft fields like
sociology  and psychology have primitive concepts  which are just too
slippery to deal with or even represent adequately using the ideas AM
is based on.

Periodically,  I  will  return  to  the  general  problem  of  theory
formation, and analyze the  information gleaned from my  experimental
systems.  This might result in a  list of general-purpose heuristics,
some notion about  how best to proceed to uncover valuable new ideas,
or some  handles  on  how  to more  effectively  formalize  inductive
heuristics into a program. I believe that we can learn much more from
studying  (and trying to  emulate) problem-⊗4proposing⊗* tasks rather
than from problem-solving tasks.