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Anatolii Illarionovich Shirshov (1921–1981) was a prominent Russian mathematician whose work significantly impacted the theories of associative, Lie, Jordan, and alternative rings. Many of his students and their successors enjoyed successful careers in mathematics. Born on August 8, 1921, in Kolyvan near Novosibirsk, he began studying mathematics at Tomsk University before volunteering to fight in World War II. After the war, he resumed his studies at Voroshilovgrad Pedagogical Institute while teaching mathematics at a secondary school. In 1950, he became a graduate student at Moscow State University under A. G. Kurosh and successfully defended his Candidate of Science thesis in 1953 on nonassociative rings and algebras. He joined the Department of Higher Algebra at Moscow State University and earned his Doctor of Science degree in 1958 for his work on nearly associative rings. In 1960, he moved to Novosibirsk to help establish a new mathematical institute of the Academy of Sciences and to contribute to the formation of Novosibirsk State University. From 1960 to 1973, he served as deputy director of the Institute and continued to lead research in algebra theory until his passing.