neugierig
curious
Having the desire or strong interest to discover, learn, or see something new.
Kinder sind von Natur aus neugierig und stellen viele Fragen.
Children are naturally curious and ask many questions.

curious
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curious
Having the desire or strong interest to discover, learn, or see something new.
Kinder sind von Natur aus neugierig und stellen viele Fragen.
Children are naturally curious and ask many questions.

The word is made up of 'neu' (new) and 'Gier' (greed/desire). So it literally describes a 'desire for new things'. This origin helps explain the intense curiosity that the word expresses.
Seine neugierige Art hat ihn schon in viele interessante Situationen gebracht.
His curious nature has already gotten him into many interesting situations.
The preposition 'auf' is a clear signal for the second meaning. Without a preposition, 'neugierig' (curious) usually means that someone is eager to learn. With 'auf', it expresses that you are excited about something in the future.
Der neugierige Nachbar schaute über den Zaun.
The curious neighbor looked over the fence.
In the meaning of 'eager to learn', 'neugierig' (curious) is often used in combinations such as 'neugierige Fragen stellen' (to ask curious questions), 'ein neugieriger Blick' (a curious look), or 'jemanden neugierig machen' (to make someone curious).
Der Trailer hat mich auf den Film neugierig gemacht.
The trailer made me curious about the film.
When you are excited about something in the future, you use the fixed expression 'neugierig sein auf' (to be curious about), followed by the accusative. The preposition 'auf' cannot be replaced here.
Wir sind schon sehr neugierig auf dein neues Haus.
We're already very curious about your new house.
indifferent
'neugierig' and 'gleichgültig' both describe an attitude toward something, but they are opposites. Someone who is 'neugierig' wants to find out, see, or understand something. Someone who is 'gleichgültig' shows no interest and barely reacts to it. 'neugierig' fits when someone asks questions or is eager to know about something. 'gleichgültig' fits when someone does not care about a topic or a person.

Sie ist neugierig, wie der neue Kurs nächste Woche beginnt.
She is curious about how the new course will start next week.
Vor dem Termin wirkt mein Bruder völlig gleichgültig, obwohl es um seine Prüfung geht.
Before the appointment, my brother seems completely indifferent, even though it is about his exam.