Example setting: You are discussing a certain topic/problem with a math professor who is good at that certain topic/field. On this occasion he is wrong but cannot see the point because he is too confident of himself. My choice is overconfident; is there a better single word?
This might possibly have negative connotation where you don't mean to imply such, but the word that comes to mind is obstinate.
Obstinate: refusing to change your behavior or your ideas
I might even say "He was confidently obstinate" to clarify the source of the obstinance, but I believe over-confidence is the default assumption in these cases.
too confident especially in a way that is rude : done or made without permission, right, or good reason
A class of presumptuous men, whom age has not made cautious, nor adversity wise. --Buckminster
Your professor seems to have superiority complex
- an inflated estimate of one's own merit, usually manifested in arrogance (Collins via TFD)
You could also call him self-opinionated
Having an arrogantly high regard for oneself or one’s own opinions (Oxford)
Or even conceited
Excessively proud of oneself; vain (Oxford)
When someone refuses to acknowledge the value of another person's opinion, you could call them narrow-minded.
On another note: I've found that the best way to break through the wall of arrogance, is to look the perpetrator directly in the eye; say, "You're not as smart as you think you are,"... and walk away. (Don't expect to pass the course.)