How did Arend Heyting contribute to intuitionism?

Arend Heyting (1898–1980) was a pivotal figure in the development of intuitionism, a school of thought founded by L.E.J. Brouwer that emphasizes mathematical objects as mental constructions.12

While Brouwer maintained that mathematics was independent of language, Heyting provided the necessary formal structure to the movement. In 1930, he successfully formalized intuitionistic logic, creating a formal language for first-order intuitionistic arithmetic. By doing so, Heyting helped translate the intuitionist goal—which focuses on what can be established constructively and known—into a rigorous logical system. This formalization allowed for a clearer understanding of how intuitionism rejects classical principles, such as the law of excluded middle, particularly when dealing with infinite sets where constructive proof is not always possible.23