Were Muḥammad ibn Musa al-Khwarizmi and Ādi Shankara alive at the same time?
Yes. Muḥammad ibn Musa al-Khwarizmi and Ādi Shankara were alive at the same time, from c. AD 788 to AD 817–823.
Muḥammad ibn Musa al-Khwarizmi
9th-century Persian mathematician and astronomer
Born c. AD 780 · died c. AD 850
Ādi Shankara
An Indian philosopher and theologian who consolidated the doctrine of Advaita Vedanta and revitalized Sanskrit scholasticism.
Born c. AD 788 · died AD 817–823