Mosaic authorship of the first 5 books of the Old Testament known as the Pentateuch was generally excepted before Christ and a couple centuries after for the exception of a few verses at the end of when talking about Moses death. Biblical Scholars Wood and Marshall write, “For centuries both Judaism and Christianity accepted without question the biblical tradition that Moses wrote the Pentateuch. Ben-Sira (Ecclus. 24:23), Philo (Life of Moses 3. 39), Josephus (Ant. 4.326), the Mishnah (Pirqê Abôth 1. 1), and the Talmud (Baba Bathra 14b) are unanimous in their acceptance of the Mosaic authorship.”
However, in 2 Esdras 14:21-22 it is suggested that the scrolls that contained the Pentateuch were destroyed during the siege of Nebuchnrazzar was excepted by early Church Fathers such as Irenaeus and Clement of Alexandria though they acknowledged Mosaic authorship of the original law. The centuries following the Church Father scholars were continuing to call into question if Moses did pen the Pentateuch. Wood and Marshall also note that, “During the mediaeval era, Jewish and Muslim scholars began to point out supposed contradictions and anachronisms in the Pentateuch.” Moreover, scholar such as Julius Wellhausen came up with documentary theories that denied Mosaic authorship all together. Despite some of these objections I think Moses at least wrote most of the Pentateuch for the following reasons.
- Paul affirms that Moses was the author of some of the law, writing in Romans (which is part of the Pauline corpus excepted by most scholars) 10:5, “For Moses writes about the righteousness that is based on the law, that the person who does the commandments shall live by them.”
- Luke affirms his authorship in gospel of Luke (16:31; 20:37; 24:26, 27, 44) and in Acts (3:22, 15:21). Luke is known for being a great historian and detailed as he interviewed many to compose his writings (Luke 1:1-4) which he connects both Acts and the gospel of Luke together (Acts 1:1).
- The internal evidence seems to suggest Mosaic authorship((Ex 17:14; 24:4, 7; 34:27; Nm 33:1, 2; Dt 31:9, 11)
- Jesus himself affirms Mosaic authorship of some kind. In the John 5:46-47 he says, “There is one who accuses you: Moses, on whom you have set your hope. 46 For if you believed Moses; you would believe me; for he wrote of me. 47 But if you do not believe his writings, how will you believe my words?”  (my emphasis) Moreover, in Mark 12:26 he says, “And as for the dead being raised, have you not read in the book of Moses, in the passage about the bush, how God spoke to him, saying, ‘I am the God of Abraham, and the God of Isaac, and the God of Jacob’? (my emphasis)
Some may ask why I concentrated mainly on what the NT has to say about Mosaic authorship vs. the Old Testament. The main reason I did this was due to that the NT is our most recent documents that are canonized (for Christians anyway), Paul and Luke are known as at least decent historians (not to say the OT writers were not), and I wanted to highlight what Jesus had to say on the manner within the gospels. The NT seems to give a stamp of approval to Moses penning most of the Pentateuch which is the position early Christians took at before and right at the beginning of the Church.
 D. R. W. Wood and I. Howard Marshall, New Bible Dictionary, 3rd ed. (Leicester, England; Downers Grove, Ill.: InterVarsity Press, 1996), 893.
 2 Esdras 14:21-22 reads as follows, “For thy law is burnt, therefore no man knoweth the things that are done of thee, or the works that shall begin. 22 But if I have found grace before thee, send the Holy Ghost into me, and I shall write all that hath been done in the world since the beginning, which were written in thy law, that men may find thy path, and that they which will live in the latter days may live.” The Cambridge Paragraph Bible: Of the Authorized English Version (Cambridge: Cambridge University Press, 1873), cxix.
 D. R. W. Wood and I. Howard Marshall, New Bible Dictionary, 3rd ed. (Leicester, England; Downers Grove, Ill.: InterVarsity Press, 1996), 894.
 Allen C. Myers, The Eerdmans Bible Dictionary (Grand Rapids, Mich.: Eerdmans, 1987), 810.
 The Holy Bible : English Standard Version. (Wheaton: Standard Bible Society, 2001), Ro 10:5.
 The Holy Bible : English Standard Version. (Wheaton: Standard Bible Society, 2001), Jn 5:45–47.
 The Holy Bible : English Standard Version. (Wheaton: Standard Bible Society, 2001), Mk 12:26.