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Zusammenfassung:
We don't know whether it is fundamentally easier to check the solution to a problem than it is to find the solution in the first place; this is the famous P versus NP problem, one of the seven Millennium Problems in mathematics. In defiance of this, there exists software that can in practice solve many problems faster than it should be able to. I'll discuss these so-called SAT solvers and applications to pure mathematics.
Dies Academicus