This is more an expanded comment on Eli's answer than an answer in itself. Eli wrote:
The intention of the list is to cover all of the possible wisdom professions and to show that none of them can compete with the word of God as given to Daniel.
This is an astute observation when taking into account the style of the whole book. Long lists occur in many places in the book, and are clearly to give an exhaustive, expansive, totalizing feel.
In the next chapter (3:2),
King Nebuchadnezzar sent to gather the satraps, the prefects, the governors, and the counselors, the treasurers, the justices, the magistrates, and all the officials of the provinces...
Then the music instruments are also listed at length, and there is another expansive expression about who was present (3:7):
As soon as all the people heard the sound of the horn, pipe, lyre, trigon, harp, bagpipe, and every kind of music, all the people, nations, and languages fell down and worshiped...
Then in 4:1:
King Nebuchadnezzar to all peoples, nations, and languages, that dwell in all the earth...
Two lists in 5:3-4:
...that the king and his lords, his wives and his concubines might drink from them. They drank wine and praised the gods of gold and silver, bronze, iron, wood and stone.
And another in 6:7:
All the presidents o the kingdom, the prefects and the satraps, the counselors and the governors are agreed...
These are only some of the examples. It is interesting to note that these lists most often concern groups of pagans, and often those who are in some sort of authority and are set up in contrast or opposition to Daniel.
Since this is such a repeated pattern in Daniel, to miss that "none of [the wisdom professions] can compete with the word of God as given to Daniel" would be to miss the point of the passage.