
Bernard Bolzano
Bolzano is credited for coining the term "heuristic".
The number of circumstances which accompany every event, including the event E which is to be
explained, is infinite. Hence it happens only too frequently that in spite of careful attention we
fail to see just those circumstances which are required to find the true cause. Among the large number
of perceptions it is difficult enough to find those which occured in all or most cases where E took
place. It is even more difficult to remember precisely whether these perceptions have been found
together on other occasions although E did not follow...Given these difficulties, it is desirable
to know some rules which would shorten and facilitate this work somewhat.
 Heuretic, 1837

George Pólya
Pólya elaborated Bolzano's ideas in teaching students how to solve math problems.
If you have to prove a theorem, do not rush. First of all, understand fully what the theorem says,
try to see clearly what it means. Then check the theorem; it could be false. Examine the consequences,
verify as many particular instances as are needed to convince yourself of the truth. When you have
satisfied yourself that the theorem is true, you can start proving it.
 1945

