The difference between one and three

Thoroughly enjoying the great JND Kelly's Early Christian Doctrines.
Just reached that exciting part where the Romans start to get into Monarchianism while the East start to flirt with extreme trinitarianism - trying not to topple over the edge into tritheism.
Trifling hair splitting?  Or something really important?

Monotheism - the belief there is one God.  A belief that if you had more than one god, one must surely have been there first, so the other could be created.

Trinity - belief that God comes in three Persons.  Not totally independent persons like a human "person" - not the atomized, community-less "persons" of modernism, the captains of their own souls and correspondingly shoddy, lonely and isolated.  But three Persons in community, self-giving, eternally sharing, forever loving.

Somewhere between those two in tension is where the Church (mostly) drew its line.  Not one God with Jesus the unlucky bloke and the Spirit a nice feeling or inspirational miasma.  Not three gods squabbling, fighting and challenging for priority - and begging why not four, or five, or three thousand.

Three persons - one God.  Mathematical nightmare,basis of being, challenge to our world.