Was Jesus Crucified?

Was it crucifixion?

At least one scholar has said that what happened to Jesus was not technically crucifixion, but suspending from a pole.
https://www.telegraph.co.uk/news/religion/7849852/Jesus-did-not-die-on-cross-says-scholar.html

I do not think the distinction matters so I am not going to address that here. I am going to consider any execution by of Jesus by the Romans to be crucifixion.

There was a crucifixion, but...

Some non-believers think there was a cruxifixtion, but Jesus did not die.

This is the position of Muslims. Islam teaches that it was made to appear that Jesus died on the cross. This is usually taken to mean some made to look like Jesus was crucified, but could include the swoon theory.

This very much is an important distinction, but not one I am concerned with here. This would still imply something happened; some kind of crucifixion was a historical event.

So was Jesus crucified?

Scripture

I do think we have good reason to think it happened. I think the gospels are evidence, even if they cannot be considered reliable. I will note that they probably all draw on a single source, so are, in effect, a single witness to what happened, but that is at least some kind of witness.

A better source is 1 Cor 15 which includes an early creed of what they believed happened. It is quite brief, but does clearly include the crucifixion. I believe the early Christians were honest and pious - they really did believe. We cannot be sure exactly what they believed - surely quite different to modern Christianity - but they certainly did believe Jesus was crucified, and I think by far the most likely reason for that is that he really was crucified.

We also have Josephus and Tacitus. Neither is conclusive, but both are good supporting evidence of the crucifixion.

Tacitus

Christus, from whom the name had its origin, suffered the extreme penalty during the reign of Tiberius at the hands of one of our procurators, Pontius Pilatus, and a most mischievous superstition, thus checked for the moment, again broke out not only in Judæa, the first source of the evil, but even in Rome, where all things hideous and shameful from every part of the world find their centre and become popular.

The text does no favours to Christianity, which gives it an authentic feel. Of course, all it really makes clear is that Tacitus believed that Christians believed Jesus (or someone) as crucified, but the most likely reason for that is that it happened.

Josephus

Josephus mentions Jesus three times, but only the Testimonium Flavianum mentions the crucifixion, and - perhaps not coincidentally - is the most dubious. It is generally accepted that it has been subsequently modified, and the debate revolves around what is original and what in interpolation. There does seem to be consensus that the original kernel included the crucifixion.

Why would it be made up?

I think it also worth mentioning that the crucifixion is not something you would make up. It was the most humiliating of deaths, and quite the opposite of what we would expect to be made up. I base that on the later attempts to try to give Jesus as much honour in death as possible, with the invention of the burial in a stone tomb in Mark, which later becomes an elaborate burial by the time of John. Also consider the ascension of Elijah - that is what we would expect if it had been made up.

I think when you strip away the fantasy that Christianity later wove around the account, what we end up with is a belief in a man thought to be the messiah (in the Jewish sense; a man of the seed of David, appointed by God), and crucified for just that reason.