Title: Computer Generated Proofs vs. Human-Generated Proofs alias Global Insight vs. Local Insight
Speaker: Doron Zeilberger, Rutgers University
Date: Monday, July 18, 2011 5:00pm
Location: CoRE Bldg, CoRE 301, Rutgers University, Busch Campus, Piscataway, NJ
A traditional proof by a human mathematician surely has its rewards, and when done right, does not only confirm with "absolute" certainty the truth-value of the proved statement, but also explains why it is true, thereby giving "local insight".
While computer-generated (and even computer-assisted) proofs may also yield local insight, they usually don't. But they do something much more important. They give global insight about the nature of mathematics, and meta-insight, that often there is no insight, and the desperate search of humans for insight and understanding is mostly futile. Many theorems are true "just because", and the many human theorems that have "proofs from the book" do so because they are utterly trivial.