Abraham Plessner was a Russian mathematician, born on 13 February 1900 in Lodz, which now is located in Poland. He studied at secondary school where he learned Russian, German, and Polish languages. He studied at the University of Giessen where he studied under Schlesinger and Friedrich Engel. He also studied at the University of Gottingen and Berlin. He completed his doctorate from the University of Giessen in 1922.

After completing his doctorate, Plessner worked in Marburg where he published a paper containing what is now called Plessner's theorem. It is a theorem concerning the boundary behaviour of functions meromorphic in the unit disk. Plessner then submitted his habilitation, the extra post-doctoral qualification needed to lecture at a German university, to the faculty at the University of Giessen. He was denied because he happened to be a Russian citizen. He then moved to Moscow and joined the research group of Nikolai Nikolaevich Luzin at Moscow State University.

In 1939, he became a professor at Moscow State University. He also held a position at the Mathematical Institute of the USSR Academy of Sciences. In 1949, he was dismissed from both posts for unknown reasons.

Plessner is widely viewed as a founder of the Moscow school of functional analysis, and he was widely respected during his residency there. He faced financial and health problems in his later years. He died 18 April 1961 in Moscow.