[MINI] Theorem Provers

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Theorem Provers

Fake news attempts to lead readers/listeners/viewers to conclusions that are not descriptions of reality. They do this most often by presenting false premises, but sometimes by presenting flawed logic.

An argument is only sound and valid if the conclusions are drawn directly from all the state premises, and if there exists a path of logical reasoning leading from those premises to the conclusion.

While creating a theorem does feel to most mathematicians as a creative act of discovery, some theorems have been proven using nothing more than search. All the "rules" of logic (like modus ponens) can be encoded into a computer program. That program can start from the premises, applying various combinations of rules to inference new information, and check to see if the program has inferenced the desired conclusion or its negation. This does seem like a mechanical process when painted in this light. However, several challenges exist preventing any theorem prover from instantly solving all the open problems in mathematics. In this episode, we discuss a bit about what those challenges are.