Infinitives

No, it is not an infinity that became inquisitive! It is just the basic way a verb is written when we want to discuss verbs, like so:
to write,
to walk,
to fight, and so on.
There is no tense involved. It is just a simple way of referring to a verb. It is used in sentences:-
e.g. He wants to write about his experiences while travelling.
       She decided to walk to the theatre instead of taking a bus.

Be careful about split infinitives, that is putting a word between 'to' and the 'verb'.
e.g. The pup began to noisily bark at the postman.
     
This is not as elegant as:-
e.g. The pup began to bark noisily at the postman.

No rules of Grammar are broken, but the sentence rolls off the tongue much smoother!