Volokh was born to a Jewish family residing in Kyiv, Ukraine, then part of the Soviet Union. He emigrated with his family to the United States at the age of seven. Volokh exhibited extraordinary mathematical abilities from an early age. At the age of 9, he was attending university-level mathematics and calculus courses after he was found studying differential equations on his own. When only 10 years 1 month old, he earned a 780 out of a possible 800 on the math portion of what is now called the SAT-I. He is one of the youngest children to have achieved this feat.