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Essay text:
Some heuristics are fairly general, for example, in a proof that is about t break into several cases do as much as possible that will be of broad applicability before the division into cases occurs. But many heuristics are area-specific; for instance, heuristics appropriate for plane geometry will probably not be appropriate for group theory. The development of good heuristics is a major area of research and requires much experience and insight.
Brief History
In 1930 Kurt Godel and Jaques Herbrand proved the first version of what is now the completeness of predicate calculus. Godel and Herbrand both demonstrated that the proof machinery of the predicate calculus can provide a formal proof for every logically true proposition, while also giving a constructive method for finding the proof, given the proposition...
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