Did Jesus really exist?
First and foremost, there are no contemporaneous accounts of Jesus' existence that are not legitimately argued as being inaccurate or downright forgeries.
If Jesus was so powerful and influential, the obvious dearth of contemporary accounts of him is a sign that perhaps he didn't exist, or at the least, was not as important nor powerful, much less capable of supernatural power, as later reports suggest.
Many theists cite Roman historian Flavius Josephus as a source for verifying the existence of Jesus. The problem is, Josephus was born in 37 AD/CE. Jesus supposedly died 30-33 AD/CE. So Jesus was dead before Josephus was even born. The same thing goes for Roman historian Tacitus, who was born in 56 CE.
There are no surviving Roman records of the First Century that refer to, nor are there any Jewish records that support the accounts in the Christian gospels --- except one.
In Rome, in the year 93, Josephus published his lengthy history of the Jews. While discussing the period in which the Jews of Judaea were governed by the Roman procurator Pontius Pilate, Josephus included the following account:
About this time there lived Jesus, a wise man, if indeed one ought to call him a man. For he was one who performed surprising deeds and was a teacher of such people as accept the truth gladly. He won over many Jews and many of the Greeks. He was the Messiah. And when, upon the accusation of the principal men among us, Pilate had condemned him to a cross, those who had first come to love him did not cease. He appeared to them spending a third day restored to life, for the prophets of God had foretold these things and a thousand other marvels about him. And the tribe of the Christians, so called after him, has still to this day not disappeared. - Jewish Antiquities, 18.3.3 §63 (Based on the translation of Louis H. Feldman, The Loeb Classical Library.)
The legitimacy of this tiny statement in Josephus' writing has been embroiled in controversy since the 17th century. It could not have been written by a Jewish man, because it sounds too Christian, and it interrupts the flow of writing before and after. Josephus was a Jew. He would never therefore claim that He [Jesus] was the Messiah. Therefore the statement is blasphemous to his own personal beliefs and an obvious sign that his writing was later doctored.
It's widely regarded that this paragraph is not authentic. It was inserted into Josephus' book by a later Christian copyist, probably in the Third or Fourth Century. Yet this citation is the single-most referenced source of evidence by Christians to defend the claim that Jesus was a real person that existed and was the Messiah.
Josephus Flavius, the Jewish historian, lived as the earliest non-Christian who mentions a Jesus. Although many scholars think that Josephus' short accounts of Jesus (in Antiquities) came from interpolations perpetrated by a later Church father (most likely, Eusebius), Josephus' birth in 37 C.E., well after the alleged crucifixion of Jesus, puts him out of range of an eyewitness account. Moreover, he wrote Antiquities in 93 C.E., after the first gospels got written! Therefore, even if his accounts about Jesus came from his hand, his information could only serve as hearsay.
Tacitus, the Roman historian's birth year at 64 C.E., puts him well after the alleged life of Jesus. He gives a brief mention of a "Christus" in his Annals (Book XV, Sec. 44), which he wrote around 109 C.E. He gives no source for his material. Although many have disputed the authenticity of Tacitus' mention of Jesus, the very fact that his birth happened after the alleged Jesus and wrote the Annals during the formation of Christianity, shows that his writing can only provide us with hearsay accounts.
- Socrates vs Jesus - An analysis of the evidence for the existence of a historical Socrates verses historical Jesus
- A Silence That Screams - A detailed analysis of the known knowledge about Jesus in history.
- Historicity of Jesus - a FAQ on this common issue
- Lee Strobel - author of The Case For Christ, a well-known Christian apologetic tome claiming to provide evidence for Jesus' existence, unfortunately this publication is extremely one-sided and fallacious and ignores commonly-known evidence that is in dispute of his findings.
- Answers to scholars' questions about Josephus' Jesus Account 
- Historicity of Jesus FAQ
- Constantine invented (Jesus and) Christianity  - Three new ideas in the field of ancient history
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