Is there a word to describe curiosity in a positive way?

I'm looking for a word that describes a curious, interested state of mind- open minded, exploring, wondering, but without being nosy.

"inquisitiveness" and "inquiringness."

inquisitive: given to inquiry, research, or asking questions; eager for knowledge; intellectually curious: an inquisitive mind.

inquiring: seeking facts, information, or knowledge: an inquiring mind.

Alternately, consider "thirst," "craving," "appetency,"appetite" (for learning, knowledge, etc.), and "intellectual acquisitiveness."

acquisitiveness: having a strong desire to acquire things, as ideas and information: an acquisitive mind.

I would also offer interested, since it is still very positive and has almost the same meaning as curious.

• showing curiosity or concern about something or someone; having a feeling of interest.