Parent comment is way too dogmatic for my taste. It even mentions a mythological entity as an appeal to authority. In my opinion, mathematicians always choose

Parent comment is way too dogmatic for my taste. It even mentions a mythological entity as an appeal to authority. In my opinion, mathematicians always choose the notation that's more convenient for them, at the moment, for a particular problem. If a given problem is easier using another form of sin/cos, etc., they will use it, and it will be used without hesitation. In that sense, mathematicians could not be more pragmatic. However, for many things, as long as the result is correct, they don't care about the operations' computability. Performance is an afterthought because for them (a*п)/п is exactly the same as 'a'. All operations are instantaneous. Taylor series for example are a perfectly fine final answer in calculus, but to a programmer they are an infinite set of partial approximations that can take any arbitrary time to execute. This is what makes computer science fascinating =)