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There's equivocation in that statement, though, whether you meant there to be or not. There is clearly a difference in how we manipulate English words for normal human activities and the symbolic manipulation with very strict rules we today associate with mathematics and computer science. Human language goes back thousands of years, into the indefinite past we can't track past. Symbolic manipulation is a much, much more recent development, starting only ~2300 years ago around Euclid and not really coming into full development until much later... you can argue about exactly when it is but I'd personally put it as late as the 19th century for it to be recognized in the modern sense. It must be something different if separated by that many centuries.

To disprove my point, please generate a list of 5 random 5-digit numbers and demonstrate multiplying them in your head as quickly as you can read them. Since you can't, clearly there is something about that that is hard for you, despite the fact that the act of reading this text, maintaining physical homeostasis while you do it, and all the other things your brain is doing as you do this represents a staggering amount of raw computation that is vastly, vastly in excess of what is nominally needed to achieve that computation.



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.




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