The epistle doesn't claim to have been written by anyone. The question of the authorship of Hebrews has been around since at least the 2nd century. Although Irenaeus placed Paul as the author, and tradition ever since then grew that he had written it, the question is far from settled. Already Clement of Alexandria and Origen noticed that the letter's style diverged from that of Paul's. Raymond Brown summarizes the main reasons why the epistle isn't accepted as Pauline today:
The elaborate, studied Greek style is very different from Paul's. Common Pauline expressions ("Christ Jesus", some ninety times) never appear in Heb. More important, the outlook is not Paul's. Whereas the resurrection is a major factor in Paul's theology, in Heb it is mentioned only once (13:20, in a subordinate clause); and conversely the major Heb theme of Christ as high priest does not appear in Paul. Paul denied that he received his gospel from other human beings; God revealed the Son to him (Gal 1:11-12). How could he have written that the message was declared first by the Lord "and attested to us by those who heard" (Heb 2:3)?
Naturally, the place to start with the question of Pauline authorship is why Paul did not identify himself as the author in the address if he wrote the letter. Jerome speculates, or relates about some who speculate, that the reason Paul omitted his name from the greeting was because he was "in disrepute" among the Hebrews. But the letter was clearly written to a Christian congregation (6:7ff., etc). The other hypothesis was that it was written to the churches in Judea and they would have been persecuted if the unbelieving Jews knew they had received a letter from Paul. But how would they keep it a secret, and even more, why would Paul write a letter knowing such problems might arise as opposed to going in person, which he was more than willing to do (Acts 21:13-14), being apparently much safer as well as avoiding rumours as to who wrote this. So this obstacle has to be admitted to remain.
On the other hand, the arguments by Raymond Brown are not entirely conclusive. We can immediately say that the absense of Christ as high priest in other Pauline letters means almost nothing. It's a bit odd, but it can be attributed to the occasion, and one can postulate that the example was freshly formed to meet it (therefore no occasional references to Christ as high priest in other Pauline letters). Also, Hebrews 2:3 can be understood as the same "witnessing of the faith" as 1 Cor. 15:1-11. The lack of emphasis and almost no mention of the resurrection certainly does seem to weigh against Paul, but again this is weakened since it might be due to the occasion. Missing common expressions also weighs heavily against Pauline authorship, as does the style. There is nothing in the occasion or audience that could eliminate these last two problems. Jerome again noting the difference in style attributes this to Paul having written it in Hebrew, which he could write more "eloquently" and which was translated into equally eloquent Greek. The problem with this is that Hebrews was not translated, it does not share Semitic "eloquency" but instead Hellenistic "eloquency" of philosophical traditions similar to Philo and quotes the Septuagint. No amanuensis is hinted. Summing up the arguments, the factors seem to tilt Hebrews away from Paul.
Of the many other authors posited (Barnabbas, Apollos, Luke, Clement of Rome, etc), all of them are as Kümmel says, mere suppositions, although Apollos is a very possible candidate (Apollos was knowledgeable in the Scriptures, was from Alexandria like Philo whose works are similar in their allegorical and metaphorical methods of interpretation, was a good speaker, and probably possessed Hellenistic schooling, similarly to the author of Hebrews).
Date of composition and overall authenticity
Although the letter is anonymous, it could still be pseudonymous because it presumes authority over a congregation (whether fictional or not) as well as an equal footing with Timothy, making it unlikely for the author to post-date having worked in the time of Paul, likely with Paul, if the letter is authentic and not from a forgerer. But this cannot be a consciouss forgery because it would have claimed someone important in apostolic, or even sub-apostolic, Christianity as its author as can be seen from the countless examples of forgery in ancient (and modern!) literature. But we cannot really rely on this, perhaps the forgerer did not feel comfortable writing down a name and preferred more passive personal notes (e.g. 13:18-19, 23-24, etc), and in any case one has to wonder why the letter has no address as to who it's from if it is addressed to a genuine congregation. However, the lack of stress on the authenticity of Christian beliefs (2:3) dispose of the theory of "passive personalia". The absense of an address means the author was well-known to his audience, as the internal evidence confirms, and that his letter carrier knew the location of the church, making it unnecessary to address to whom the letter is sent, and this is similar to the address of 2 and 3 John (2 John 1:1, 3 John 1:1); the author may simply not have had a formal/honorary title such as in 2 and 3 John. As far as the equal footing with Timothy, this is so vague that no forgerer would have written it like this if he wished to solidify the letter's authority. The author's authority over the congregation does not point toward pseudonymity or authenticity since either way it could/would have existed, and especially not when this is the only factor that stressed the letter's authority, and is probably to be discarded as an objection in view of the above mentioned unstressed authenticity of teachings (2:3) as well as the overall absense of stress on authority; the author simply presumes it is there, and this hardly points toward a forgerer. The letter carrier would have in all likelihood been known to the church and/or would have informed them as to the author. The absense of the letter carrier's greeting in the address and closing does not argue against authenticity, but if anything only against Pauline authorship; he simply may have been omitted because the author was sending him to that church anyway, but whatever the reason, see the somewhat hurried greeting in 13:24. The fact is, the author notes that he is sending them a letter via someone else (13:22 - he is clearly not giving it himself), and personal references are not forgotten seeing 13:23, so clearly this cannot be attributed to a forgerer who forgot to be specific, and the oddity of not including further personal references in 13:22, 24 therefore cannot be explained, unless the letter is authentic.
As far as the date goes, the question mainly revolves around whether Hebrews was written before or after 70 AD. There are several factors that have been pointed to as indicating one way or another.
1. The letter speaks of the Temple in the present tense, indicating it's still there. Brown answers that Josephus similarly speaks of the Temple in the present tense, yet his works were written after its destruction. However, Josephus speaks of it only when looking at the Temple through the point of view of the past. Furthermore, Hebrews doesn't speak of the Temple as standing only in its text; the letter is very intent on proving that it is unnecessary and that the Christian's true Temple and temple services are in Heaven. This is difficult to understand if there was no Temple or temple services in existence to compare.
The other counter-objection is that it is not known how, or if at all, the destruction of the Temple would have affected the author's argumentation. But see Hebrews 8:13! I am not persuaded with Kümmel that Hebrews 8:13 doesn't mean that the old order of the Temple sacrifices is still in place. Even if it refers to the whole Law of the Talmud, it could have in no way neglected the destruction of the Temple to support its argument. Therefore, these factors by themselves are sufficient to establish a date before 70, and probably before the Jewish war started in 66 (but the latter fact is not nearly as certain as the former).
2. The references to persecution (10:32-34, 12:4) are taken to be indicators of Domitian or later. But the persecutions in 10:32-34 are those of confiscation of property and other such punishments, seeing no one has yet shed their blood for the faith (12:4), and such expectation was certainly not impossible for the 60's (James' death, etc). Whether the letter presupposes the possibility of a Neronian persecution cannot be determined, but certainly hinted as not having happened by the somewhat mild punishments in 10:32-34 held as somewhat the highest point that would probably be reached, even though he is certainly aware of the possibility of death (12:4). But overall there is no hint of a state-wide persecution as under Nero, Domitian, or anyone later.
3. Kümmel sees a literary relationship in the "high", developed style of literary Greek between Hebrews and Luke-Acts. Since he sees Luke-Acts written in 80-90, he places Hebrews in that time period as well. But aside from the assumption about the date of Luke-Acts, if we have forgeries with "low" Greek such as 2 Peter as late as 100-150, assuming it is a forgery, why couldn't there be an equally "high" Greek in the 60's? Philo has an even more developed literary Greek, and wrote in the 40's. It is certainly an argument from an intuition that New Testament writings are either authentic and "primitive" or late and "developed". But the closeness of the developed language has nothing to do with the date of another piece of writing. It is not theology, which at any rate is not developed to require a date after 70/80.
4. It cannot be inferred from 2:3 and 13:7 that the apostolic age (30-70) is over. Hebrews 2:3 could have been said by any Christian who was not a disciple or witness of Christ's teachings on earth and resurrection, of whom there were many even in the 30's. Notably, Apollos was one of them. Hebrews 13:7 does not necessitate a date after 80 or so. Even in Paul's day some of the witnesses of the original 500 had died (1 Cor. 15:6), who wrote in 55 AD. In any case, if one wants to posit that all the leaders had died out, then the congregation must be made up of very old men. This can hardly be squared with both the exhortation to remember their teachings (how would the younger members?) as well as 5:11-14, even though in verse 12 he tells them they need to be teachers (but in that case who are the presbyters if they are all old men and women needing to be reinstructed?). On the whole 13:7 seems to be a mixture of remembering the lifestyles of both past and present leaders, not necessarily that all of them died out.
5. Some say the author has Judaism separated from Christianity far further than Paul by maintaining the Old Covenant was flawed and obsolete. But the author does not go any further than Paul did. Paul also considered the Old Covenant to be obsolete (Galatians 3:2), flawed (Galatians 3:9, 21-25), and described the Old Covenant as having been replaced (Galatians 3:15-20). However, the fullness of separation from Judaism and language suggests a date not before the 60's, but certainly does not necessitate one after the 60's. It is certainly a step before the Epistle of Barnabbas (70-100) which describes the Law as evil, unnecessary, and having been misunderstood by the Jews as literal instead of symbollic.
On the whole, the letter seems to presuppose a Christianity established with leaders, but this wasn't anything new for even the 40's and 50's. The theology seems to presuppose a date in the 60's, since it presumes for one the dispute of the Law is somewhat over. Despite the fact that the author stresses the uselessness of the Temple's regulations especially now that Christ had come, his arguments could hardly be understood if he didn't assume the controversy of the Law versus faith to be over, since his arguments do not appeal on any solid basis but on that of the Christian's acceptance that Christ replaced the Law. The occasional verses from the Old Testament he gives only support the above, not the other way around (i.e. they prove the insignificance of the Temple's regulations by supporting the Christian understanding of Christ replacing the Law, not proving it), and does not reiterate his arguments in a connected emphasizing manner, but has them spread out, supporting on occasion, and has nothing about why the law does not need to be followed to be saved. His symbollisms presuppose the era after Paul's imagery, since they unlike Paul's are not explained and connected through reasoning and argumentation but on the basis of the tradition of such, and the overall theology seems the product of post-Pauline tradition, combined with the fact that the salvation of the Gentiles is not even a question. Overall, a date before 60 based on this is unlikely, and so 60-65 is the likeliest time of composition.
- Brown, Raymond, An Introduction to the New Testament, p.694
- Jerome, On Illustrious Men, 5
- Jerome, ibid.