(March 23, 2022 at 10:04 am)HappySkeptic Wrote:(March 23, 2022 at 9:59 am)polymath257 Wrote: Such mathematical knowledge is *permanently* beyond anything we can ever know.
On a side note - would an alien species with different senses and ways of thinking coming up with mathematics which is analogous (mappable) to ours?
Is mathematics truly universal, or are some of the assumptions built into it human-centric?
There's an old line that says 'the positive integers are given by God. All the rest is the work of man'.
In other words, the positive integers are universal, but calculus (for example) may not be.
I'm not sure how much I agree with that sentiment, but there is an argument for it.
That said, modern mathematics is ultimately the study of formal axiom systems. If aliens use anything close to that, there would be 'mappable' pieces in each direction. But I would be very surprised if the specifics of, say, bounded operators on Hilbert space, were independently discovered by aliens.
