Conflicts with Vienna Summer of Logic, but very interesting:
We have already witnessed the moment where chess-playing computers have surpassed humans. It might seem to be only a matter of time that computers will also surpass humans in mathematical theorem proving. In fact, the traditional notion of mathematical proof faces in the beginning 21st century what we will call “the computer challenge”. Three different aspects are worth separating:
- proof search;
- proof check;
- proof representation.
Proof search has its known limitations due to undecidability and complexity results. However, special areas, such as semigroup theory, already enjoy considerable support from computer-generated proofs. Proof check is recently the “hottest” area, in no small part due to the attempt to formally verify the proof of the Kepler conjecture by its author Hales. Proof representation seem currently be the stumbling block for convincing the mathematical community to accept computer aided theorem proving as a viable alternative.
In our workshop we solicit contributions for discussions the current state of the art of computer aided theorem proving (ATP), approaching the topic from the mathematical (or even philosophical) side, as well as from computer science. Special focus is put on the last two items mentioned above, addressing the more concrete question:
- How, and to what extent, can (or will) proof checking convince the mathematical community from the correctness of a proof?
- Does computer generated proof representations match with our intuitive notion of mathematical proof?
The answers to both question should give us a deeper insight in the challenges and tasks for mathematical proofs and computer-aided theorem proving in the 21st century.
- Jesse Alama, Theory and Logic Group, Technical University of Vienna, firstname.lastname@example.org
- Reinhard Kahle, Center for Artificial Intelligence / Department of Mathematics, New University of Lisbon, email@example.com