He received his Ph.D. from Moscow State Pedagogical Institute in 1959 under the advisorship of Pyotr Novikov. Muchnik's most significant contribution was on the subject of relative computability. He and Richard Friedberg independently introduced the priority method which gave an affirmative answer to Post's problem regarding the existence of recursively enumerable Turing degrees between 0 and 0' . This result, now known as the Friedberg–Muchnik theorem, opened study of the Turing degrees of the recursively enumerable sets which turned out to possess a very complicated and non-trivial structure.
Muchnik also made significant contributions to Medvedev's theory of mass problems, introducing a generalisation of Turing degrees, called "Muchnik degrees", in 1963. Muchnik also elaborated Kolmogorov's proposal of viewing intuitionism as "calculus of problems" and proved that the lattice of Muchnik degrees is Brouwerian.
Muchnik was married to the Russian mathematician Nadezhda Ermolaeva. Their son Andrej, who died in 2007, was also a mathematician working in foundations of mathematics. He died in February 2019.
- A. A. Muchnik, On the unsolvability of the problem of reducibility in the theory of algorithms. (in Russian) Doklady Akademii Nauk SSSR (N.S.), vol. 108 (1956), pp. 194–197
- Albert Abramovich Muchnik, Mathematics Genealogy Project. Accessed January 26, 2010
- Robert I. Soare, Recursively Enumberable Sets and Degrees: A Study of Computable Functions and Computably Generated Sets. Springer-Verlag, 1999, ISBN 3-540-15299-7; p. 118
- Nikolai Vereshchagin, Alexander Shen, Computable functions. American Mathematical Society, 2003, ISBN 0-8218-2732-4; p. 85
- A. A. Muchnik, On strong and weak reducibility of algorithmic problems. (Russian) Siberian Mathematical Journal, vol. 4 (1963), pp. 1328–1341
- S. I. Adian, A. L. Semenov, V. A. Uspenskii, Andrei Albertovich Muchnik,(in Russian) Uspekhi Matematicheskikh Nauk, vol. 62 (2007), no. 4, pp. 140–144