Pyotr Kuznetsov never knew his biological parents: when he was 9 months old, he was adopted by the Dubensky family. After her husband's death, his foster mother Matilda Dubenskaya moved from Kharkov to Moscow. In 1902, she placed Pyotr in the care of her old friend, Vera Kolmogorova, Andrei's aunt.

Later, Pyotr moved to the Kolmogorov estate in Tunoshna, where he lived for three years. In his childhood memoirs, he described Vera Kolmogorova's arrival at the estate with baby Andrei. In the years that followed, Pyotr spent his summers in Tunoshna, where together with Andrei he attended an improvised school run by their foster mothers. In Tunoshna, the adults and children created a handwritten magazine titled "Spring Swallows", which featured math problems invented by the children.

Pyotr and Andrei went to the private Repman Gymnasium in Moscow, graduating in 1918. Andrei's father, Nikolai Kataev, was present at their graduation exams.

In 1919, Pyotr volunteered to serve in the Red Army. When he came back, he stayed at the Kolmogorovs' and studied at Moscow University. As a student, Andrei Kolmogorov went on dialectological expeditions to the North with his childhood friend.

In 1948, Pyotr defended his doctoral thesis and became a professor at the Department of Philology at Moscow State University and worked at the Institute of the Russian Language. One of the founding fathers of the Moscow School of Phonology, he supported research in the fields of structural and mathematical linguistics. Also, he participated in the seminar "Some Applications of Mathematical Methods in Linguistics", which Andrei Kolmogorov organized at Moscow State University.