In this case we have the usual list of "1st century witnesses to the life of Jesus". Or are they? Jesus is said to have lived around 1 AD-33 AD (give or take a few years). Now look at the list:
Tacitus in his Annals (c.115 A.D.) NOT contempary. NOT first century.
Pliny the younger and the Roman Emperor Trajan (98-117 A.D.) NOT contempary. Barely even first century.
Flavius Josephus (37-100 A.D.) NOT contempary. And the references to Jesus in his work are suspected to be forgery.
Clement (A.D. c. 30-100) Unlikely to have witness the events(as a three year old?)
Epistle of Barnabas (A.D. c. 70-130) NOT contempary
Polycarp (A.D. 70-155) NOT contempary.
Ignatius (A.D. 35-110) NOT contempary.
Irenaeus (A.D. 130 -200) NOT contempary. NOT first century.
Tertullian (A.D. 160 -220) NOT contempary. NOT first century.
Clement (A.D. 150 -215) NOT contempary. NOT first century.
I looked at the Wiki link and it is the usual stuff about the "evidence" for Jesus outside the bible. Josephus, Tacitus, Sanhedrin 43a, etc. All the good ones.
Of course it is never mentioned, that they are either obviously forged (Josephus and maybe Tacitus) or written about the beliefs of Christians and as accounts of what others said happened. In most cases they only show that at a certain time groups of Christians existed but not that their beliefs had a foundation in reality.
Here's a little bit about those supposed non-biblical accounts mentioning Jesus.
See also: http://www.jesusneverexisted.com/james.html
There are two very important things about this passage in Tacitus' Annals:
1) This passage in the Annals is about the persecution of Christians by Nero. It is strange however, that this is the only passage in all of Tacitus' numerous works, where he mentions this. Nowhere else in all his writings does he write so much as a single sentence about this.
It is even stranger, that early Christians, who did have access to his works, never mention this. Clement of Alexandria or Tertullian, two of the great early apologists, simply don't know about this passage or any persecution of Christians by Nero despite having access to Tacitus' works (including the Annals).
The earliest point in history, that this passage in the Annals is mentioned is in the fifteenth century. Strangely nobody ever noticed it before...
2)Assuming the passage is genuine and written by Tacitus himself, his sources are likely of christian origin instead of any official records, because there are a number of flaws in the passage in question:
a)Pilate was a prefect and not a procurator. (and if he had been a procurator then Tacitus would have written his title as “procurator of XYZ” and not just called him “procurator”)
b) Tacitus does not use Jesus' name but writes “a man called Christ was executed.” “Christ” is a title, not a name. Why should the Roman records say that “the Messiah” was executed?
The whole passage mentioning Jesus in the "Antiquities of the Jews" is nothing other than a forgery. There are A LOT of things wrong and dubious with this passage. I will name a few for good measure.
a) The passage does not fit in with the surrounding text.
b) The whole passage is extremely pro-Christian in writing. That should make you wonder, as Josephus was a pharisaic Jew, who did not hide his dislike for the new Christian cult in his other works. It even makes Josephus seem Christian, given how highly he speaks of Jesus, even going so far to wonder if he can actually be called a man.
c) In this passage Josephus calls Jesus “Messiah”, yet according to the church father Origen Josephus did not recognize Jesus as a messiah nor did he believe in any other Christian claim of miracles of Jesus.
d) Josephus writes about this period of time in some of his other works too, but this passage or any passage mentioning this is nowhere to be found in those.
e) None of the early apologists picked this up and you have to keep in mind that they had access to the Antiquities and were actively searching for passages and quotes like that. The earliest point in time, where this passage is mentioned is in 324 AD.
f) As late as 891 AD this passage still does not appear in most works concerning the “Antiquities of the Jews.”
g) Even several centuries later there are versions of the "Antiquities of the Jews" that are reported to be missing this particular passage.
The original text of Thallus is lost, so there's no way to say, what he originally said. All we have of Thallus about Jesus is an account of Julius Africanus, who quotes Thallus as he mentions a darkness following the Crucifixion of Jesus.
BUT it should be telling, that there was not one other writer, historian or astronomer of that time who noted anything about a darkness several hours long accompanied by earthquakes. It's hard to believe, that neither historians nor astronomers found such an event noteworthy, given the impact it should have had on the people and given that there was no total eclipse scheduled in that region and time period. All we have is one single account quoting someone who said it happened.
Pliny the Younger and Roman Caesars Hadrian and Trajan
These are actually completely irrelevant, because in their letters they only say that Christian cults exist and what the Christians believe in. But obviously this is no evidence that those beliefs are actually true.
Lucian of Samosata
Lucian of Samosata was a second century Greek satirist.
The important part is “second century Greek.” Lucian is only giving evidence, that Christians existed in the second century (a fact which no-one denies) but can contribute nothing, when it comes to providing evidence for a historical Jesus.
A Syrian named Mara Bar-Serapion
Is not considered a reliable source by the majority of all scholars and is also not an eyewitness. The letter in which Jesus is mentioned was composed sometime between 73 AD and the 3rd century and thus only describes what Christians of that time believed, not if it is true.
The Talmud (Sanhedrin 43a)
The Babylonian Talmud is assumed to have been written some time between the 3rd and the 6th century AD. It does not even refer to the Jesus of the bible, but to two different men; Yeshu the sorcerer (stoned and hanged around 100 BC (!) at Jerusalem along with his 5 disciples Matai, Nekai, Netzer, Buni, and Toda) and Yeshu ben Stada (stoned and hanged at Lydda at the eve of passover but in the second century AD).
Several gnostic writings
The copies of the gnostic gospels, which have been found are dated to around 350 - 400 AD and consensus among scholars is, that the originals have been written around 140 AD (when the gospel of Mark had already been around for 70 years, if we assume it has actually been written at 70 AD, the earliest estimate).
It's also worth noting, that the Gnostic gospels differ in key aspects from the biblical gospels (Gospel of Judas just being the prime example here).
As such the existence of the Gnostic gospels will not help to support the claim of a historical Jesus.