At the beginning of the 20th century, the German mathematician David Hilbert (1862–1943) advocated an ambitious program to formulate a system of axioms and rules of inference that would encompass all mathematics, from basic arithmetic to advanced calculus. His dream was to codify the methods of mathematical reasoning and put them within a single framework.
Hilbert insisted that such a formal system of axioms and rules should be consistent, meaning that you can’t prove an assertion and its opposite at the same time.