Often used in formal or written contexts, especially in compounds like 好奇心 (curiosity). As a standalone noun, it can sound somewhat literary.
His curious eyes were directed at me.
Curiosity sometimes invites danger.
He looked at the new transfer student with curious eyes.
好奇 emphasizes an inquisitive urge to know or peek into something, whereas 関心 refers more broadly to concern or attention toward a topic.
好奇 describes an active curiosity about something, while 無関心 describes a total lack of interest or indifference toward it.
curiosity; inquisitiveness
From Middle Chinese 好奇 (xɑuX ɡiᴇ, literally 'good + strange'). The kanji 好 means 'good, fond of' and 奇 means 'strange, unusual'. The combination conveys a fondness for the unusual, i.e., curiosity.