No reason to keep me, I’m profitless math
You ask me, I’ll teach you to follow a path
Do rotate your head, and you might spot a tent
You will hear a word that reorders events
The same to the ear, if not so to the eye
To say I exist is the same as to lie!
Who am I?
How many letters does the answer have?
You shouldn't be looking for a noun.
I might have used words that confuse puzzle-solvers here and there. One could consider different interpretations for some of the words in the riddle.
You look for more hints? Half the hints are a dead giveaway!