Described as the most important logician since Aristotle. He was known for his two incompleteness theorems.
He grew up in the Czech Republic, which was then Austria-Hungary, during World War I. He was proficient at college-level mathematics by the time he enrolled in the University of Vienna.
He posited influential ideas on the axioms of set theory, proof theory, classical logic, intuitionistic logic, and modal logic.
His father Rudolf managed a textile factory. He married Adele Nimbursky.
He was good friends with Albert Einstein during their time at Princeton.