In the middle and late 19th century, members of the then small mathematical community began the search for a rigorous foundation of Mathematics. In accordance with the Euclidean model of reasoning, the ideal foundation ought to consist of a few simple, clear principles, so-called axioms, on which the rest of knowledge can be built via firm and reliable thoughts free of contradiction. However, at the time it was not clear what assumptions should be made and what operations should be allowed in mathematical reasoning.