Re:There’s more to mathematics than rigour and proofs (2007)
by ravi-delia on Tuesday April 19, 2022 @10:36PM
(#31092160)
Math is at it's broadest the study of formal systems. Computer science is the study of a particular formal system. While it is a powerful enough system to contain all of math within it, there are many such systems nested within each other. Is the Turing machine formalism more powerful? No. Is it more efficient or intuitive? Also no. It requires axiomatic reasoning to construct, and then reproduces it internally. Math and CS are set equal, but one predefines an entry point and the other does not. From the human perspective math gives rise to CS, which is just one of math's many children.
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Re:There’s more to mathematics than rigour and proofs (2007)
by l33t2328 on Tuesday April 19, 2022 @11:18PM
(#31092437)
I’d argue that logic is a subfield of computability theory, and so by extension we (in CS) absorb math.
Re:There’s more to mathematics than rigour and proofs (2007)
by ravi-delia on Wednesday April 20, 2022 @08:31PM
(#31104796)
Like I said, you can indeed construct logic through CS! But you can also obviously construct CS from logic. You can also construct logic through the natural numbers, so number theory absorbs math and by extension CS? Fact is anything reasonably complex can replicate everything else. Exactly one of these fields, however, is specifically carved out as the study of any formal system, and it isn't CS.