He later received his B.S. in mathematics ( summa cum laude ) from Duke University in 2000 .
He later obtained his Ph. D. from Carnegie Mellon University in 2005 under the supervision of professor Manuel Blum .
He later received his B.S. in mathematics ( summa cum laude ) from Duke University in 2000 , and obtained his Ph. D. from Carnegie Mellon University in 2005 under the supervision of professor Manuel Blum .