The Pentateuch is the name for the first five books of the Old Testament: Genesis, Exodus, Leviticus, Numbers and Deuteronomy. According to tradition, the Pentateuch was written by Moses, though almost all serious Biblical scholars dispute this claim. Christians and Jews claim that Moses wrote them  though this is unlikely.In the 18th Century Thomas Paine understood it.
In the first place, there is no affirmative evidence that Moses is the author of those books; and that he is the author, is altogether an unfounded opinion, got abroad nobody knows how. The style and manner in which those books are written give no room to believe, or even to suppose, they were written by Moses; for it is altogether the style and manner of another person speaking of Moses. In Exodus, Leviticus and Numbers, (for every thing in Genesis is prior to the times of Moses and not the least allusion is made to him therein,) the whole, I say, of these books is in the third person; it is always, the Lord said unto Moses, or Moses said unto the Lord; or Moses said unto the people, or the people said unto Moses; and this is the style and manner that historians use in speaking of the person whose lives and actions they are writing. It may be said, that a man may speak of himself in the third person, and, therefore, it may be supposed that Moses did; but supposition proves nothing; and if the advocates for the belief that Moses wrote those books himself have nothing better to advance than supposition, they may as well be silent. 
In the book of Numbers Moses is described as the meekest of men, which would be arrogant if he wrote that himself.
Defense of Mosaic Authorship in the Face of Common Rebuttals
Moses was a man educated in Egypt in the court of Pharaoh. He would have no doubt learned exceptional writing skills as well as styles common to the day. Great leaders were known to have written stories about themselves from the third person in order to give it a better narrative quality. It fits with the literature style of the day for him to write in the third person, especially if he was the meekest of men. Now on this note, it is not heretical, nor is it compromising to the 'inspired-ness' of the Jewish text to say that a scribe of perhaps even Moses' successor Joshua, was tasked with adding such details as the account of Moses' death and meeting with God in Deuteronomy 34. As a tribute to a leader he had known, respected, and been mentored by, it is not too far off to say he would add such a note as this.