I recently wrote on New Mathematics.
Now I expand a bit.
Mathematics is a cultural product that allows brain connections to the external world, through the scientific method.
Mathematics exists in my brain, other people's brains, and in libraries. The only mathematics we will ever know is human mathematics, whatever is found in recorded human history. If the books are lost, and nobody remembers them. we have to look for the books, or redo the mathematics.
Fahrenheit 451, by Ray Bradbury, tells us about this phenomenon.
What distinguishes Homo sapiens from other primates, is the social part of culture. I imagine something like this. Gases in our brains, exhaled through our mouths go through the air, and get through their senses, into other people's brains. We can talk, other primates cannot talk with so many words.
This is is the quid. This is so powerful, that sometimes we believe mathematics is real, like a chair or a table.
As Bradbury reminded us, the moment all copies of One Hundred Years of Solitude disappear, and all of us that read the book die. Macondo ceases to exist.
Whatever new "One Hundred ..." is ever written, won't be the same.
Thus with mathematics.
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