Because of the Antisemitism in the Soviet Union at the time, Reichstein was not accepted to Moscow University, even though he had passed the special math entrance exams.

His family then decided to emigrate, arriving in Vienna, Austria, in August 1979 and New York, United States in the fall of 1980.

Reichstein worked as a delivery boy for a short period of time in New York.

[2] Reichstein received his PhD degree in 1988 from Harvard University under the supervision of Michael Artin.

Parts of his thesis entitled "The Behavior of Stability under Equivariant Maps" were published in the journal Inventiones Mathematicae.