Doing multiplication in your head isn't the point though, you can externalise language and use it to do things you can't do in your head by writing it down.
Mathematics was born out of very careful reasoning that we do through language, we only use formalisms as they allow us to avoid the massive ambiguities that exist in natural language. Formal symbolic manipulation came out of our already existing abilities of symbolic manipulation through language.
Mathematics was born out of very careful reasoning that we do through language, we only use formalisms as they allow us to avoid the massive ambiguities that exist in natural language. Formal symbolic manipulation came out of our already existing abilities of symbolic manipulation through language.