I would like one word for "proud by thinking that one cannot be surprised by what others know".
Arrogant is explained as "having or revealing an exaggerated sense of one's own importance or abilities." So the word I am looking for could be explained by "having or revealing an exaggerated sense of one's own knowledge and understanding."
TecBrat is correct. Know it all
It's not an adjective, it's a noun. But it is the most common idiom for such a person. And it acts as one word (usually hyphenated):
"He's such a know-it-all; you can't tell him anything!"
Such people are usually described as condescending:
showing that you think you are more important or more intelligent than other people
Related, though not exactly what you describe, a pedant is someone who is overly concerned with minutiae and loves to show off their (not always useful) knowledge. Pedants would rarely admit to surprise or wonder at new information, because they believe they already know things that are more worth knowing.
Pedant is more related to intelligence than condescending, as people can be condescending about things other than intelligence.
The condescending gym employee took a look at me and recommended I start with five pound weights.
Be aware that the adjective form pedantic in everyday usage holds connotations associated more with being long-winded and making use of complex words and jargon when not always appropriate to show off your vocabulary.
