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␈↓ d␈↓Can␈α-the␈α.process␈α-of␈α-scienti≡c␈α.research␈α-be␈α-adequately␈α.modelled␈α-as␈α.a␈α-rule-directed
␈↓ d␈↓search␈α⊂process?␈α⊂As␈α⊃a␈α⊂≡rst␈α⊂step␈α⊃in␈α⊂answering␈α⊂that␈α⊃question,␈α⊂a␈α⊂computer␈α⊃program␈α⊂called␈α⊂"AM"␈α⊃has␈α⊂been
␈↓ d␈↓constructed which performs elementary mathematics research.

␈↓ d␈↓AM␈α∂develops␈α∂new␈α∂math␈α∂concepts␈α∂under␈α∂the␈α∂guidance␈α∞of␈α∂a␈α∂large␈α∂body␈α∂of␈α∂heuristic␈α∂rules.␈α∂ The␈α∂250␈α∞local
␈↓ d␈↓heuristic␈αrules␈αcommunicate␈αvia␈αan␈αagenda␈αmechanism,␈αa␈αglobal␈αlist␈αof␈αtasks␈αfor␈αthe␈αsystem␈αto␈αperform␈αand
␈↓ d␈↓reasons␈α
why␈α
each␈αtask␈α
is␈α
plausible.␈α A␈α
single␈α
task␈αmight␈α
direct␈α
AM␈αto␈α
de≡ne␈α
a␈αnew␈α
concept,␈α
or␈α
to␈αexplore
␈↓ d␈↓some␈α⊃facet␈α∩of␈α⊃an␈α∩existing␈α⊃concept,␈α∩or␈α⊃to␈α⊃examine␈α∩some␈α⊃empirical␈α∩data␈α⊃for␈α∩a␈α⊃recognizable␈α∩pattern,␈α⊃etc.
␈↓ d␈↓Repeatedly,␈α∂the␈α∂program␈α∂selects␈α∂from␈α∂the␈α∂agenda␈α∞the␈α∂task␈α∂having␈α∂the␈α∂best␈α∂supporting␈α∂reasons,␈α∂and␈α∞then
␈↓ d␈↓executes it.

␈↓ d␈↓Each␈αconcept␈αis␈αan␈αactive,␈αstructured␈α
knowledge␈αmodule.␈α A␈αhundred␈αvery␈αincomplete␈αmodules␈α
are␈αinitially
␈↓ d␈↓provided,␈α
each␈α
one␈α
corresponding␈α
to␈α
a␈α
simple␈α
set-theoretic␈α
concept.␈α
 This␈α
provides␈α
a␈α
de≡nite␈α
but␈α
immense
␈↓ d␈↓"space"␈αwhich␈α
AM␈αbegins␈α
to␈αexplore.␈α AM␈α
extends␈αits␈α
knowledge␈αbase,␈α
ultimately␈αrediscovering␈αhundreds␈α
of
␈↓ d␈↓common concepts (e.g., numbers) and theorems (e.g., unique factorization).

␈↓ d␈↓This␈α
paper␈α
will␈α
emphasize␈α
the␈α
control␈α
structure␈α
of␈α
AM,␈α
including␈α
an␈α
analysis␈α
of␈α
its␈α
collection␈α
of␈αheuristic
␈↓ d␈↓rules.␈α A␈αbrief␈αsurvey␈αof␈αexperimental␈αresults␈αwill␈αshow␈αthat␈αthis␈αrule-based␈αapproach␈αto␈αplausible␈αinference
␈↓ d␈↓contains great powers and great limitations.