I’m a mathematician and not a computer scientist. The first order PA axioms are recursively enumerable. Hence it’s clearly something of interest to computer scientists. The second order PA axioms aren’t so…are they part of computer science? What do computer scientists think about proofs in second order PA? There are no computable models of ZFC so wouldn’t it be the case that while computer scientists deal with ZFC that ZFC isn’t part of computer science? what is your definition of computer science? Physicists deal with a vast amount of mathematics but math isn’t physics. In the same way mathematics isn’t computer science.
Overall I think most mathematicians would not consider mathematics as part of computer science.
The lines between (academic) fields are blurry -- academic fields do not form a set theoretic partitioning over areas of study.
More generally, I think that computer scientists (in particular PL theorists and type theorists) are much more likely to use powerful logics than mathematicians, with the obvious exception of set theorists.
https://mathoverflow.net/questions/97077/z-2-versus-second-o...
In the following mathoverflow answer Nik says,
These are fundamental questions. We know that any computable set of axioms which holds of the natural numbers must also have nonstandard models.
The second order Peano Axioms are not computable since those axioms are categorical.
https://mathoverflow.net/questions/332247/defining-the-stand...
Are you of the opinion that mathematics is computer science? I have a hard time believing that the Jacobian Conjecture is computer science.
Computer science ought to be about computation, right? There are non-computable objects that mathematicians study. Is that part of computer science?
Why is this a barometer for whether to answer a question or unpack assumptions?
