Try reading the evidence.
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To be fair to the Historical Jesus article, it does say that that was likely subject to alteration by later Christians. To be honest, though, it says it contained some truth originally, which is entirely unverifiable because, as you are about to see, none of that appears to have been written by Josephus himself. This means, amusingly enough, that some of the strongest evidence for Jesus as a real person may have been destroyed by his own followers... I'm not sure if that speaks more about Christians or humanity in general (probably the latter though).
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That is apparently considered good proof, although I don't know if the second part is referring to the biblical Jesus... probably not. If you can't tell, I find it unconvincing at best.
Make of that what you will, I find it too boring to read, hence my earlier comment about none of the fawning praise heavily edited by later Christians being written by Josephus himself. The man just seems to have been exceptionally boring, probably why he was a good historian.
Jesus was a rather common name in the priesthood it seems, so... how can anyone claim that there is historical evidence of a specific Jesus? It's all very surface level at best, including Tacitus's work, which only references a "Christus"*, which doesn't necessarily refer to anyone called Jesus. It was also written somewhere in the region of half a century after Jesus likely (if he existed, of course
) died, which also took place around the time Tacitus was born.
*According to Wikipedia, I'd heard that it was Chrestus (unless I'm mistaken, sorry if I am, although this little aside isn't that important either way). Not sure if that changes anything, although it implies that there are different versions of it, so it's possible somebody's not playing fair. Not sure who or for what purpose, though. Considering Rome's... let's say interesting history with Christianity, it could be either.