Kurt Gödel Biography

Kurt Gödel was an Austrian-American logician, mathematician, and philosopher who profoundly impacted 20th-century scientific and philosophical thought. He is most celebrated for his two incompleteness theorems, which demonstrated that within any consistent axiomatic system powerful enough to describe natural number arithmetic, there exist true statements that cannot be proven from the axioms. To establish these theorems, Gödel pioneered a technique known as Gödel numbering, which encodes formal expressions as natural numbers. His work also clarified connections between various logical systems and showed that the continuum hypothesis is not disprovable from the accepted axioms of set theory.