Name and origin. In the sources he is usually named simply Maximus or Claudius Maximus; the full name is reconstructed fragmentarily (the praenomen is not preserved in reliable forms). In the Greek of Med. 1.15 — Μάξιμος; in Apuleius (Apologia) — Claudius Maximus. Belonging to the gens Claudia does not imply blood connection with the Julio-Claudians (as in the case of Cn. Claudius Severus — the nomen Claudius is widely distributed in the Antonine age and does not indicate dynastic kinship). The specific origo is not established; the general probabilistic profile is an Italian or western-provincial senatorial family.

Senatorial career: consulate and proconsulate.

• Suffect consul — approximately 142 or 144 CE. The precise dating is disputed; it is constrained by the consular fasti and by indirect evidence. Under Antoninus Pius — consistent with the general profile of an Antonine senator-philosopher.
• Proconsul Africae Proconsularis — the most prestigious senatorial provincial office; he held it, by the reconstruction from Apuleius, approximately in 158/159 (the year of Apuleius's trial, see below). The proconsulate of Africa is a position normally awarded to high-ranking consulars after a pause of 15–18 years from the consulate, which agrees well with a consulate of 142/144.

The trial of Apuleius and an extended contemporary testimony. The main non-Marcusian source on Maximus is Apuleius's own defence speech, known as the Apologia (or Pro se de magia — "For Himself, in Reply to the Charge of Magic"). Around 158/159, at Sabratha (a city in the province of Tripolitania, in Roman Africa), Apuleius stood trial on the charge of having used magic to seduce the wealthy widow Pudentilla and seize her property. Maximus presided over the trial as proconsul. Apuleius, having been acquitted, published an extended literary version of his defence — the Apologia — dedicated to Maximus.

In the Apologia Maximus is named many times (Apol. 1, 19, 36, 65, 84, 91, 96, 102 — the precise references should be verified against the edition). The characterisation given by Apuleius is independent of Marcus (Apuleius and Marcus probably did not know each other personally; their connection is through Maximus as the common philosophical environment of Antonine senatorialism). Apuleius emphasises:

• Maximus's learning: deep knowledge of philosophy (Apol. 41 and elsewhere), especially of Stoic doctrine.
• Justice and impartiality as a judicial norm (Apol. 1, 91).
• Seriousness and dignitas combined with openness to reasoning (Apol. 65).
• Maximus as a vir clarissimus — the formula of the highest senatorial rank, consistently applied by Apuleius.

This external characterisation converges with Marcus's internal portrait in Med. 1.15: seriousness + mildness, learning without arrogance, justice, openness of intention. The convergence of two independent testimonies is a rarity for Marcus's teachers (besides Maximus, only Apollonius has independent external testimony — in Lucian Demonax 31).

What does "presided over the trial" mean? A consular proconsul in an Antonine province carried out the judicial-administrative functions of the supreme instance: he heard cases of high rank (cognitio), including charges of magic (the lex Cornelia de sicariis et veneficiis in its Antonine interpretation). The trial of Apuleius is a model of such a cognitio: the proconsul sat on the tribunal, heard the accusers and the accused, pronounced the verdict. That Maximus acquitted Apuleius follows from the very fact of the posthumous publication of the Apologia: Apuleius lived to publish it.

Relations with Marcus. The chronology of the teaching relationship with Marcus is reconstructible in general outline:

• By the time of Marcus's adoption by Hadrian and Antoninus Pius in 138, Maximus was apparently already a mature senator (quaestorship — praetorship behind him), at the start of his consular path.
• His teaching — probably in the 140s (the period of Marcus's intensive philosophical formation), in parallel with Rusticus, Apollonius, and Sextus.
• After the proconsulate of Africa (158/159) Maximus returns to Rome in the 160s, where he may have remained in continuing contact with Marcus the Caesar and afterwards Marcus the emperor (by analogy with Rusticus, for whom continuing contact is attested by Dio Cassius).
• The precise date of his death is not established.

• 01-15 — the principal, developed portrait of Maximus in the Meditations; the third longest in Book I (after 1.16 and 1.7).
• 01-17 — the thanksgiving to the gods; Maximus is implicitly among the "good teachers."
• Med. 8.25 — a separate mention of Maximus's name in connection with the memory of the deaths of acquaintances (a formal reference, not a developed portrait).

• Apuleius, Apologia (= Pro se de magia) — the main contemporary non-Marcusian source on Maximus's character; standard text: Helm, Teubner. English translation: Hunink, Apuleius of Madauros: Pro se de magia (Brill, 1997). NB: precise references to mentions of Maximus in the Apologia should be verified against the edition.
• SHA Marcus (Vita Marci), ch. 3 — Maximus in the catalogue of Marcus's Stoic teachers.
• A. Birley, Marcus Aurelius: A Biography, rev. ed., Routledge, 2000, ch. 3 ("Education") — the reconstruction of Marcus's tutorial environment; for Maximus, also the mention of his connection with the trial of Apuleius.
• A. S. L. Farquharson, The Meditations of the Emperor Marcus Antoninus, Oxford 1944, vol. II, ad 1.15 — the detailed philological commentary, including on the rare vocabulary (προσσεσηρός, ἀδιάστροφος, εὐχαριεντίζεσθαι).
• R. Hard, Marcus Aurelius: Meditations, OWC, Oxford 2011, notes ad 1.15.
• P. Hadot, The Inner Citadel, tr. M. Chase, Harvard 1998 — the general reconstruction of the Stoic programme (consult the index for "Maximus").
• V. Hunink, Apuleius of Madauros: Pro se de magia, 2 vols., Brill, Leiden 1997 — the standard modern commentary on the Apologia, with the prosopographical treatment of Maximus.
• PIR² C 933 (for Claudius Maximus; the exact entry-number should be verified against PIR²).