I don’t think you can easily separate mathematics into either invention or discovery. It’s both. It’s a form of pseudo-play.
You made great points about the human nature of math, designating it an invention. But math implies more unknown math, as theorems exist within the mathematical structure we have built, so we are in a sense, discovering parts of an invention.
Think of it like legos. Simple build system, which generates enormous complexity. We created something infinitely complex and we’ve been playing with it, finding new tricks along the way, for the last 44,000 years. But lets actually investigate this claim:
Scholarpedia lays out 5 pillars of play:
Play Is Self-Chosen and Self-Directed
Play is intrinsically motivated, means are more valued than ends.
Play is guided by mental rules, but the rules leave room for creativity.
Play is imaginative.
Play is conducted in an alert, active, but relatively non-stressed frame of mind.
I would say 2,3, and 4 all fit trivially, Thus it’s not play, (unless you like math like me) but rather almost play.
Let me know if you think I’m wrong or I’m not making any sense.
I think there’s a significant difference of scale between a fridge and Mathematics.
Math is a set of rules and concepts we apply to itself in order to perpetually generate new rules and concepts.
A fridge is just an icebox.
Now if you created a series of rules and concepts around the fridge, then yes I would grant you they are similar.
The difference is is the social relationship humans have to the object. Math has a social relationship consisting of specific formalisms. A fridge has no such social relationship. It’s just where we humans like to keep the ice-cream.