Nah, euclidean geometry was not complete. Tarski didn’t come up with a complete version until the 20th century. I’m not sure how famous Tarski geometry is, but it doesn’t seem very famous in USA outside of math depts.
this doesn’t mean that “it’s impossible to create any consistent set of math statements that completely describes everything,”
It says far less than that: “It’s impossible for a mathematical system containing the natural numbers to be both complete and consistent.”
In itself it has very little to do with physical reality. I think it’s more about how we think about math and then its applications.
reality itself could be a complete system, understandable from both the outside and inside if only viewed at the right angle…
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Nah, euclidean geometry was not complete. Tarski didn’t come up with a complete version until the 20th century. I’m not sure how famous Tarski geometry is, but it doesn’t seem very famous in USA outside of math depts.
It says far less than that: “It’s impossible for a mathematical system containing the natural numbers to be both complete and consistent.”
In itself it has very little to do with physical reality. I think it’s more about how we think about math and then its applications.
This has been largely debunked.
I dunno what his dream was, but Hilbert’s program is very much dead.