First some comments from A.W. Pink on the writer of the book of Hebrews.
That this Epistle was written by Paul is clear from 2 Peter 3:15. Peter was writing to saved Jews as the opening verses of his first Epistle intimates; 2 Peter 3:1 informs us that this letter was addressed to the same people as his former one had been. Then, in Hebrews 10:15, he declares that his beloved brother Paul "also according to the wisdom given unto him hath written unto you." If the Epistle to the Hebrews be not that writing, where is it?I fully believe it was the Apostle Paul that wrote Hebrews because the writing styles are similar, and he uses much of the same phrases and ideas.
Before taking up the study of the opening verses of our Epistle, let us adduce further evidence that the apostle Paul was the writer of it. To begin with, note its Pauline characteristics. First, a numerical one. There is a striking parallel between his enumeration in Romans 8:35-39 and in Hebrews 12:18-24. In the former he draws up a list of the things which shall not separate the saint from the love of God which is in Christ Jesus. If the reader will count them, he will find they are seventeen in number, but divided into a seven and a ten. The first seven are given in verse 35, the second ten in Romans 10:38, 39. In Hebrews 12:18-24 he draws a contrast between Mount Sinai and Mount Sion, and he mentions seventeen details, and again the seventeen is divided into a seven and a ten. In Hebrews 12:18, 19, he names seven things which the saints are not "come unto"; while in Hebrews 10:22-24 he mentions ten things they have "come unto," viz., to Mount Sion, the City of the living God, the heavenly Jerusalem, an innumerable company of angels, the general Assembly, the Church of the Firstborn, to God the Judge of all, to the spirits of just men made perfect, to Jesus the Mediator, to the Blood of sprinkling. Compare also Galatians 5:19-21, where the apostle, when describing the "works of the flesh," enumerates seventeen. So far as we are aware, no other Epistle writer of the New Testament used this number seventeen in such a manner.
Again; the terms which he used. We single out one only. In Hebrews 2:10 he speaks of the many sons which Christ is bringing to glory. Now Paul is the only New Testament writer that employs the term "sons." The others used a different Greek word meaning "children."
For doctrinal parallelisms compare Romans 8:16, with Hebrews 10:15, and 1 Corinthians 3:13 with Hebrews 5:12-14, and who can doubt that the Holy Spirit used the same penman in both cases?
Note a devotional correspondency. In Hebrews 13:18, the writer of this Epistle says, "Pray for us." In his other Epistles we find Paul, more than once, making a similar request; but no other Epistle-writer is placed on record as soliciting prayer!
Finally, it is to be noted that Timothy was the companion of the writer of this Epistle, see Hebrews 13:23. We know of no hint anywhere that Timothy was the fellow-worker of anyone else but the apostle Paul: that he companied with him is clear from 2 Corinthians 1:1, Colossians 1:1, 1 Thessalonians 3:1, 2.
In addition to the many Pauline characteristics stamped on this Epistle, we may further observe that it was written by one who had been in "bonds" (see Hebrews 10:34); by one who was now sundered from Jewish believers (Heb. 13:19) — would not this indicate that Paul wrote this Epistle while in his hired house in Rome (Acts 28:30)? Again; here is a striking fact, which will have more force with some readers than others: if the Epistle to the Hebrews was not written by the apostle Paul, then the New Testament contains only thirteen Epistles from his pen — a number which, in Scripture, is ever associated with evil! But if Hebrews was also written by him, this brings the total number of his Epistles to fourteen, i.e., 7 x 2 — seven being the number of perfection and two of witness. Thus, a perfect witness was given by this beloved servant of the Lord to Jew and Gentile!
In the last place, there is one other evidence that the apostle Paul penned the Hebrews’ Epistle which is still more conclusive. In 2 Thessalonians 3:17, 18 we read, "The salutation of Paul with mine own hand, which is the token in every Epistle, so I write, the grace of our Lord Jesus Christ be with you all." Now, if the reader will turn to the closing verse of each of the first thirteen Epistles of this apostle, it will be found that this "token" is given in each one. Then, if he will refer to the close of the Epistles of James, Peter, John and Jude, he will discover a noticeable absence of it. Thus it was a distinctive "token" of the apostle Paul. It served to identify his writings. When, then at the close of Hebrews we read "grace be with you all" the proof is conclusive and complete that none other than Paul’s hand originally wrote this Epistle. (Exposition of Hebrews by A. W. Pink)
Colossians 2:2 That their hearts might be comforted, being knit together in love, and unto all riches of the full assurance of understanding, to the acknowledgement of the mystery of God, and of the Father, and of Christ;
Hebrews 6:11 And we desire that every one of you do shew the same diligence to the full assurance of hope unto the end:
Hebrews 10:22 Let us draw near with a true heart in full assurance of faith, having our hearts sprinkled from an evil conscience, and our bodies washed with pure water.
In the OT, we find this passage: Habakkuk 2:4 Behold, his soul which is lifted up is not upright in him: but the just shall live by his faith.
It is quoted three times in the NT, and each time the surrounding chapters deal with an aspect of the phrase - the just shall live by faith.
Romans 1:17 For therein is the righteousness of God revealed from faith to faith: as it is written, The just shall live by faith. Paul explains how to be just before God.
Galatians 3:11 But that no man is justified by the law in the sight of God, it is evident: for, The just shall live by faith. Here Paul explains how the just are to live.
Hebrews 10:38 Now the just shall live by faith: but if any man draw back, my soul shall have no pleasure in him. Here Paul goes on to show examples of how believers have lived by faith - Chapter 11 is referred to by many as the Hall Of Faith Chapter.
Paul has a certain characteristic way of ending his letters, which he makes mention of in the following passage:
2 Thessalonians 3:17-18 The salutation of Paul with mine own hand, which is the token in every epistle: so I write. The grace of our Lord Jesus Christ be with you all. Amen.
Romans 16:24 The grace of our Lord Jesus Christ be with you all. Amen.
1 Corinthians 16:23-24 The grace of our Lord Jesus Christ be with you... Amen
2 Corinthians 13:14 The grace of the Lord Jesus Christ, and the love of God, and the communion of the Holy Ghost, be with you all. Amen.
Galatians 6:18 Brethren, the grace of our Lord Jesus Christ be with your spirit. Amen.
Ephesians 6:24 Grace be with all them that love our Lord Jesus Christ in sincerity. Amen.
Philippians 4:23 The grace of our Lord Jesus Christ be with you all. Amen.
Colossians 4:18 ...Grace be with you. Amen.
1 Thessalonians 5:28 The grace of our Lord Jesus Christ be with you. Amen.
2 Thessalonians 3:18 The grace of our Lord Jesus Christ be with you all. Amen.
1 Timothy 6:21 ...Grace be with thee. Amen.
2 Timothy 4:22 ...Grace be with you. Amen.
Titus 3:15 ...Grace be with you all. Amen.
Philemon 1:25 The grace of our Lord Jesus Christ be with your spirit. Amen.
And Hebrews 13:25 Grace be with you all. Amen.
Timothy was Paul's representative. In 1 and 2 Timothy, Paul exhorts his son in the faith to be faithful and to endure hardship, etc. In Hebrews, we see this:
Hebrews 13:23 Know ye that our brother Timothy is set at liberty; with whom, if he come shortly, I will see you.
A fitting end to what may well be the last epistle the Apostle Paul wrote before being martyred for his faith - showing that his beloved disciple had endured and persevered in the faith. Paul's exhortations had borne fruit, and he was sure to let his brethren know of Timothy's faithfulness, despite his possible fear and lack of boldness in his younger days.