sympy is good enough for typical uses. the user interface is worse but that doesn't matter to Claude. I imagine if you have some really weird symbolic or numeric integrals, Mathematica may have some highly sophisticated algorithms where it would have an edge.

however, even this advantage is eaten away somewhat because the models themselves are decent at solving hard integrals.

I don't think we should pick a winner. When it comes to mathematical answers the best would to pose the same query to all of them and if they all give the same result then our space-rocket is probably going in the right direction.

For numeric stuff, I've been playing recently with chebpy (a python implementation of matlab's chebfun), and am really impressed with it so far - https://github.com/chebpy/chebpy

I like to think of Claude as enjoying himself more when working with good tools rather than bad ones. But metaphysics aside, tools that have the functions you would expect, by the names you would expect, with the behavior you would expect, do seem to be just as important when the users are LLMs.

I've always sort of assumed the models were just making sympy scripts behind the scenes.