Were Omar Khayyám and Peter Abelard alive at the same time?
Yes. Omar Khayyám and Peter Abelard were alive at the same time for 51 or 52 years, from 1079 to 1131.
Peter Abelard was 51 or 52 when Omar Khayyám died.
Peter Abelard
French scholastic philosopher, theologian and preeminent logician
Born 1079 · died 21 April 1142, aged 62 or 63