 Thus a contradiction in a formal axiomatic system is disastrous; since any theorem can be proven true, it destroys the conventional meaning of truth and falsity.The discovery of contradictions at the foundations of mathematics at the beginning of the 20th century, such as Russell's paradox, threatened the entire structure of mathematics due to the principle of explosion.This motivated a great deal of work during the 20th century to create consistent axiomatic systems to provide a logical underpinning for mathematics.