Who was Theudas? Acts 5 vs Josephus

The passages

For before these days rose up Theudas, boasting himself to be somebody; to whom a number of men, about four hundred, joined themselves: who was slain; and all, as many as obeyed him, were scattered, and brought to nought.

Acts 5:36

After this man rose up Judas of Galilee in the days of the taxing, and drew away much people after him: he also perished; and all, even as many as obeyed him, were dispersed.

Acts 5:37

The problem

Acts has Gamaliel speaking in the early 30s AD. He mentions Theudas, then Judas of Galilee, who rose "after this man" at the census of AD 6. Josephus describes a Theudas who led a crowd to the Jordan around AD 44–46, under the procurator Fadus, and was killed. That is about a decade after Gamaliel's speech and long after Judas. So either Luke put a later event into an earlier speech and reversed the order, or he is referring to someone else.

What believers and scholars say

A different Theudas. Theudas was a common abbreviation of several Greek names. Josephus tells of a number of rebels at the death of Herod in 4 BC and does not name them all. Another leader named Theudas could have been one of them. It is plausible and cannot be shown.

Luke relied on Josephus and got it wrong. Some scholars argue that Luke knew Josephus's work and misremembered the order. That requires Acts to be written after the 90s, and many think the case for dependence is weak.

An error in a speech. A third view is that Luke composed Gamaliel's speech from memory of things he half-knew. Ancient historians were open about writing speeches that suited the occasion. If so, the mistake belongs to Luke and not to Gamaliel.

Where this leaves it

The simplest explanation, a second Theudas, is untestable. The next simplest, an error of order by Luke, would be a small one in a long book. Neither affects the point of the speech, which is a case for caution about opposing a movement that may be of God.