He is well known for his work in randomness in computing, algorithmic complexity and intractability, foundations of mathematics and computer science, algorithmic probability, theory of computation, and information theory.
His life is described in a chapter in the book: Out of Their Minds: The Lives and Discoveries of 15 Great Computer Scientists.
He independently discovered a theorem that was also discovered and proven by Stephen Cook. The theorem, which is known as Cook or Cook-Levin theorem, was a breakthrough in computer science and is the foundation of computational complexity. Levin's journal article on this theorem was published in 1973; he reports that he had lectured on it for some years before that time. See , also listed among the external links below.
- Leonid Levin's home page
- A Survey of Russian Approaches to Perebor (Brute-Force Searches) Algorithms, by B.A. Trakhtenbrot, in the Annals of the History of Computing, 6(4):384-400, 1984.