He is a winner of George Sarton Medal by the History of Science Society for a lifetime of scholarly achievement.
His father was Pavel Yushkevich a Sorbonne-educated philosopher and a mathematician, active in politics as a Menshevik who was in "ssylka" (deportation) in Siberia, and later in France.
In 1923, Yushkevich started his studies at the Department of Mathematics of Moscow State University.
From 1930 to 1952 he worked at Bauman Technical University where he rose to professorship in 1940 and head of the department of mathematics in 1941.
Starting 1952, he became a full-time researcher at Vavilov Institute of Natural History, where he worked until retirement.