In Baghdad of al-Ma'mūn's time there appears to have been a degree of intellectual enterprise, especially in the field of natural science, scarcely attained at any other period of Islam. The names of Muḥammad b. Mūsā al-Khwārizmī and Muḥammad b. Mūsā b. Shākir are well known among those which made the Caliphate of al-Ma'mūn, from this point of view, so celebrated in later times. Recently, while investigating the history of the Khazars, I was interested to see that al-Khwārizmī is credited by al-Muqaddasī (ed. de Goeje, p. 362) with a visit to Khazaria, and following this up to find that Suter (“Mathematiker, Nachträge,” p. 159, in Abhandl. zur Gesch. der math. Wissensch., vol. 14, 1902) thought that Muḥammad b. Mūsā b. Shākir must be meant. Elsewhere also Suter found confusion between the two names. It occurred to me that both names stood for one person, and in what follows various considerations are raised and some new material cited bearing on this possibility. It is not claimed that the identification is made out, but that it is worth considering.