There were plenty of 1st and 2nd century historians or authors who might have mentioned early Christianity or Jesus of Nazareth, but didn't
The emperor Claudius (10bc - 54ad) was noted for writing a lot, such as a treatise on Augustus' religious reforms, and felt himself in a good position to institute some of his own. He had strong opinions about the proper form for state religion.
- Claudius's major works included Tyrrhenica, a twenty book Etruscan history, and Carchedonica, an eight volume history of Carthage, as well as an Etruscan dictionary ... he penned a defense of Cicero against the charges of Asinius Gallus. Modern historians have used this to determine the nature of his politics and of the aborted chapters of his civil war history.
- Seneca the Elder (d. ~39ad), a historian who noted various aspects of Claudius's attitudes to, & activities for & against, various religions
- Suetonius quotes Claudius' autobiography once and must have used it as a source numerous times.
- Tacitus uses Claudius' arguments for the orthographical innovations [the old custom of putting dots between successive words (Classical Latin was written with no spacing)] and may have used him for some of the more antiquarian passages in his Annals.
- Pliny-the-Elder used Claudius as the source for numerous passages in Natural History.
Philo (d ~50ad) mentions mentions Pontius Pilate in the Embassy to Caligula/Gaius 299-305 in relation to Caligula's plan to erect a statue of himself in the temple of Jerusalem when describing the sufferings of the Alexandrian Jews, and Jews more widely, and asking the emperor to secure their rights
- Somewhat separately, some scholars hold that his concept of the Logos as God's creative principle influenced early Christology.
Quintus Asconius Pedianus (c. 9 BC – c. AD 76)
Pliny the Elder (d. 79 AD.), On the German Wars, Annales
Pamphile or Pamphila of Epidaurus, Sth Greece (Greek: Παμφίλη η Επιδαύρια, Pamfíli i Epidávria; Latin: Pamphila; fl. ad 1st century), was a historian who lived in the reign of Nero. Her principle work was the Historical Commentaries, a history of Greece comprising thirty-three books. Photius considers the work as one of great use, and supplying important information on many points in history and literature. The estimation in which it was held in antiquity is shown not only by the judgement of Photius, but also by the references to it in the works of Aulus Gellius and Diogenes Laërtius, who appear to have availed themselves of it to a considerable extent.
Mucianus served as governor of Syria in 69AD and was the author of a memoir, chiefly dealing with the natural history and geography of the East, a text often quoted by Pliny the Elder as the source of 'miraculous occurrences'.
Josephus 37 ad - ~100 ad born in Jerusalem, then part of Roman Judea, son of Matthias, an ethnic Jewish Priest and a mother who claimed royal Hasmonean ancestry. Josephus's paternal grandparents were supposedly direct descendants of Simon Psellus, and he supposedlu descended through his father from the priestly order of the Jehoiarib, which was the first of the 24 orders of priests in the Temple in Jerusalem.
At the outbreak of the First Jewish-Roman War, Josephus was appointed the military Jewish governor of Galilee.
One would think Josephus would have known about early Christianity and to have written about it if it had been a rising religion.
Plutarch (c. AD 46 – AD 120; later named, upon becoming a Roman citizen, Lucius Mestrius Plutarchus, Λούκιος Μέστριος Πλούταρχος) was a Greek biographer and essayist, known primarily for his Parallel Lives and Moralia. He is classified as a Middle Platonist. Plutarch's surviving works were written in Greek.
Tacitus c. 56 AD – c. 120 AD Histories, Annals
- Of course, Annals 15.44 is well-known, but not without doubt. It's a pity parts of Book 5 are missing.
Suetonius (c. 69 - after 122 AD) Lives of the Caesars
Claudius 25 refers to the expulsion of Jews by Claudius. The Ihm's Latin version:
- Iudaeos impulsore Chresto assidue tumultuantis Roma expulit
- "Since the Jews constantly made disturbances at the instigation of Chrestus, he expelled them from Rome."
- "During his reign many abuses were severely punished and put down, and no fewer new laws were made: a limit was set to expenditures; the public banquets were confined to a distribution of food; the sale of any kind of cooked viands in the taverns was forbidden, with the exception of pulse and vegetables, whereas before every sort of dainty was exposed for sale. Punishment was inflicted on the Christians, a class of men given to a new and mischievous superstition. He put an end to the diversions of the chariot drivers, who from immunity of long standing claimed the right of ranging at large and amusing themselves by cheating and robbing the people. The pantomimic actors and their partisans were banished from the city."
Florus (c. 70 - c. 140 ad?) 'Military history of Rome to Augustus' in 2 books
Granius Licinianus (fl. 120 ad?) History of Rome
Appian of Alexandria (c. 95 - c.165ad)
- Roman History in 24 books
- 'Roman wars from the beginnings to Trajan'