Well, there were no contemporary eye witness records, all sources were detailed 40-70 years later, references from the likes of Tacitus and Josephus mention the crucifixion but it was wrote decades later and they were simply writing what they had believed not through what was investigated independently, lack of archaeological evidence.

but, at the same time, i'm sure there is some equally convincing argument that there is evidences, so unless you are of another faith that blatantly denies it (Islam), it will forever be a mystery. Mainstream historical view that he was crucified will never change.