Short answers, pulled from the story.
Ptolemy's three most significant works were the Almagest, an astronomical treatise that was the only surviving comprehensive ancient account of astronomy; the Geography, a handbook for drawing maps of the Greco-Roman world using geographic coordinates; and the Tetrabiblos, a four-part astrological treatise. All three were important to later Byzantine, Islamic, and Western European science.
Ptolemy lived in or around Alexandria, in the Roman province of Egypt. His exact year of death is not recorded by primary sources and must be inferred; suggested dates include around 165, 168, 170, and 175 AD. His birthplace is also unknown, though a 14th-century source claimed it was Ptolemais Hermiou in Egypt.
Robert R. Newton, in his 1977 book The Crime of Claudius Ptolemy, accused Ptolemy of fabricating observations to fit his theories and called him "the most successful fraud in the history of science." Newton pointed to a specific error: an autumn equinox Ptolemy claimed to have observed at 2pm on the 25th of September 132 AD, when it should have occurred around 9:55am the day before. Other scholars, including Owen Gingerich and Bernard Goldstein, disputed Newton's conclusions, and a 2022 discovery of Hipparchus' lost star catalogue further complicated the accusations.
Ptolemy's Geography, titled Geographike Hyphegesis in Greek, was a handbook for drawing maps of the known world using geographic coordinates. Its most notable feature was a catalogue of 8,000 localities drawn from the work of Marinus of Tyre and other sources, the largest such database from antiquity. His mapped world spanned 180 degrees of longitude and about 80 degrees of latitude.
Ptolemy argued in his Harmonics that musical scales should be based on multiple different ratios arranged into tetrachords, rejecting the Pythagorean view that the single ratio of 3:2 was sufficient. He tested tuning systems using a device called the harmonic canon, or monochord, measuring relative pitches along a single string. His synthesis of empirically derived ratios developed into what is now called just intonation.
Ptolemy's geocentric model was the only mathematically rigorous account of the solar system available, and the Catholic Church promoted it on that basis. The Almagest served as the authoritative text on astronomy across Europe, the Middle East, and North Africa for over a thousand years. His planetary models were only displaced during the Scientific Revolution, when heliocentric models reappeared.