Can Mathematics Be Proved Consistent?

Kurt Gödel's groundbreaking work in 1931 revealed profound limitations in formal mathematical systems through his first incompleteness theorem. He demonstrated that within any system capable of expressing elementary arithmetic, there exist true statements that cannot be proven within that system. This pivotal finding challenged the quest for absolute rigor in mathematics and led to further inquiries about the consistency of mathematical proofs, establishing Gödel as a key figure in 20th-century science.