God is by definition a perfect being. It is more perfect to exist than to not exist. Therefore, God exists. Just given these simple ideas, a few axioms, and a fondness for pushing around abstract ...

We give a constructive proof of McNaughton's theorem stating that every piecewise linear function with integral coefficients is representable by some sentence in the infinite-valued calculus of ...

Some scientific discoveries matter because they reveal something new — the double helical structure of DNA, for example, or the existence of black holes. However, some revelations are profound because ...

Quantified Boolean Formulas (QBF) extend classical Boolean logic by incorporating quantifiers over Boolean variables, thereby enabling the expression of problems in the PSPACE complexity class. The ...

The use of computers means that modern mathematical proofs can run to millions of pages. Such proofs can never be fully verified by humans alone. Does this mean, as some argue, the death of proof? The ...