[also more keen; most keen]
1 : having or showing an ability to think clearly and to understand what is not obvious or simple about something
a keen intellect/intelligence/mind
She's a very keen observer of the political world.
She made some keen [=acute] observations.
a keen wit
2 : very strong and sensitive : highly developed
The dog has a keen sense of smell. = The dog has a keen nose.
keen [=acute] eyesight/hearing
She had a keen awareness of what was happening. [=she knew exactly what was happening]
3 a : very excited about and interested in something
She's a keen tennis player. = She's keen about tennis.
He's a keen student of art history. = He has a keen interest in art history.
b : feeling a strong and impatient desire to do something
He is keen [=eager] to learn more about art history.