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Year 433 (CDXXXIII) was a common year starting on Sunday (link will display the full calendar) of the Julian calendar. At the time, it was known as the Year of the Consulship of Theodosius and Maximus (or, less frequently, year 1186 Ab urbe condita). The denomination 433 for this year has been used since the early medieval period, when the Anno Domini calendar era became the prevalent method in Europe for naming years.
- Flavius Aetius returns, with the support of the Huns, back to Italy. He gains control over emperor Valentinian III, age 14, and becomes his "protector".
- Petronius Maximus is appointed consul of the Western Roman Empire.
- Pope Sixtus III helps to settle a Christological dispute between the patriarchs Cyril of Alexandria and John of Antioch, that has continued since the First Council of Ephesus, two years ago. They sign the "Formula of Reunion", thus ending their conflict over Nestorianism.
- Liu Bing, high official of the Liu Song Dynasty (d. 477)
- Odoacer, first "barbarian" king of Italy (d. 493)
- Juqu Mengxun, prince of the Xiongnu state Northern Liang (b. 368)
- Xie Lingyun, Chinese poet of the Southern and Northern Dynasties (b. 385)