Is math discovered or invented

Answer 1

You can't 'invent' 1 + 1 = 2; it

just does.

On the contrary,

1 + 1 = 0 in mod(2) arithmetic

1 + 1 = 10 in base(2) arithmetic

1 + 1 = 1 in Boolean arithmetic

1 + 1 = [an arbitrary value] in group theory, depending on

your choice of group.

In fact, '1 + 1 = 2' is a consequence of selecting one particular set

of rules to define one particular formal system. But there are lots of

other systems that can be defined, and confusing 'Peano arithmetic'

with 'mathematics' is like confusing 'Chess' with 'games'.