foundational crisis in mathematics

The foundational crisis in mathematics refers to a period in the early 20th century when mathematicians began questioning the basic principles and assumptions underlying the entire field. Concerns arose about the consistency, completeness, and rigor of mathematical theories, particularly following discoveries such as Gödel's incompleteness theorems, which showed that in any sufficiently complex mathematical system, there are true statements that cannot be proven within that system. This upheaval prompted a re-evaluation of the foundations of mathematics, leading to the development of various schools of thought, including logicism, formalism, and intuitionism, each offering different perspectives on what constitutes mathematical truth.