>>14189284Incorrect.
>P1Mathematics is a science. "science" is derived from the term "scientia" meaning knowledge. What people call "science" colloquially today is what's known as "methodological naturalism." The proper term for a "scientist" is a "naturalist."
Evidence of mathematicians being scientists and not just linguists is in the application of computer science which was developed partly as part of the field of mathematics. There's also the development of methodology to be used in the other sciences such as numerical methods (heavily used in physics and engineering and comes from calculus) and differential geometry (the "Einstein" equation was actually written by Hilbert and much of the theoretical work was done with assistance from Hilbert and Klein in general relativity using tools from geometry; differential geometry was also derived from the need to do calculus on "strangely" shaped surfaces).
>P2Set theory is mostly just a rephrasing of propositional and predicate logic. All argument in general, including the arguments made by naturalists in their conclusions, are founded on logic and can by tested against predicate/propositional logic for their validity. Set theory in mathematics exists primarily to streamline proofs. Traditionally, there was no set theory until Cantor. There was no ZFC/SB until Russel made a mockery of Cantor with his paradox. Set theory is a more contemporary thing that is used because it's very convenient, it was quite useful for certain aspects of analysis and especially topology, and it offers ways to talk about potential examples other than the traditional examples. Likewise, there are many proofs that are not dependent on the notion of a set such as the sum two continuous functions being continuous or the quadratic formula giving the solutions to a quadratic equation for example. You can phrase such proofs in terms of set theory but the proof can be done without appeal to ZFC or SB and nothing is lost.
