Who wrote Matthew:

The book of Matthew does not identify its author. However, its title “The Gospel According to Matthew” leads many scholars to believe the book was generally considered early on to have been written by Matthew. The name was not applied until the second century A.D. Therefore, it cannot be used as definitive evidence for Matthew as the author.

Matthew the tax collector was a known author and referred to as an author by Papias, bishop of Hierapolis, as early as 130 A.D. However, the material Papias is referring to as being written by Matthew is not necessarily the Gospel account. Many scholars believe Matthew probably wrote a collection of Jesus’ sayings prior to writing the Gospel, and this may be what Papias is referencing.

The best evidence for Matthew being the author of the book of Matthew is found within the text. The book of Matthew is the only Gospel account which identifies Levi the tax collector as Matthew:

As he walked along, he saw Levi son of Alphaeus sitting at the tax collector’s booth.

Mark 2:14

After this, Jesus went out and saw a tax collector by the name of Levi sitting at his tax booth. “Follow me,” Jesus said to him,

Luke 5:27

As Jesus went on from there, he saw a man named Matthew sitting at the tax collector’s booth. “Follow me,” he told him, and Matthew got up and followed him.

Matthew 9:9

In its original Greek, Matthew is the only Gospel account to refer to the money used to pay taxes as a nomisma. The Gospels of Mark and Luke refer to the money as a denarion. This word choice strongly suggests the book of Matthew was written by someone very familiar with money, specifically tax collection.

Identifying Levi the tax collector as Matthew and usage of the proper name for the coin used to pay taxes, strongly suggest the author of Matthew, at the very least, used the witness account of Matthew when writing the Gospel. However, it is more likely Matthew himself, a known author, wrote the account himself.