What does Acts 26:24 mean?

Paul has finished telling how he first persecuted Jesus-followers, then met and started following Jesus. He has also explained that Jesus fulfills the prophecies given in Scripture of the Jewish Messiah (Acts 26:2–23). His audience is Governor Festus, King Agrippa II, Agrippa's sister Bernice, and "the military tribunes and the prominent men of the city" of Caesarea Maritima, the Roman capital in the region (Acts 25:23).

Festus is Roman and has only held the position of governor for a few weeks. He knows little about Jewish religion and culture but wants to have a good relationship with local leaders. Those leaders, however, want Paul charged, convicted, and executed for crimes against the Roman law (Acts 25:1–2, 24). So, Festus is not only politically motivated, but he's also probably an annihilationist and believes the resurrection of Jesus goes against all reason. Only Paul's Roman citizenship and Festus' fair and reasonable nature are in Paul's favor.

It's unclear what Festus is referring to by Paul's "great learning." Paul mentioned how he was trained by the Pharisees (Acts 26:5), and he obviously knows how to address a Roman court, but we don't know how often Festus spoke with Paul before this council. Festus may not know that Paul can quote Greek philosophers easily (Acts 17:28). Felix, the previous governor, spoke with Paul often (Acts 24:24–26). It's possible Festus is merely being sarcastic.