Logic is Like Abstract Art

Modern logic unleashed new areas of mathematics. Even when language and intuition fail, conclusive theories can be constructed with the help of logic. When little children share chocolates, they already have to deal with numbers. Even complicated mathematical objects can often be grasped intuitively. We draw vectors as little arrows of a sheet of paper. But how can we draw a non-commutative algebra? How can we understand quaternions and tensor products, if we cannot make them out of chocolate? When one tries to deal with completely abstract mathematical objects without getting caught in contradictions, or when one wants to analyse mathematics itself with mathematical methods, logic is indispensable. A Language for Talking about Math - "The question, what exactly constitutes a proof, is not really part of mathematics", says Professor Matthias Baaz (Vienna University of Technology).