I have to disagree with you on language and cognition. If you went around asking famous mathematicians how they think the last thing they would tell you would be "words".

Creative and inventive thought is very picturesque and non-linear: https://www.amazon.com/Psychology-Invention-Mathematical-Fie...

I would add to your references Hadamard's book[0], where he talks about how ideas form in various mathematicians' heads.

I don't really disagree with you, it's just that Victor seems to be claiming too much for his new interfaces, and selling symbolic manipulation short. Of course all kinds of things need to be happening inside our heads before we start manipulating symbols. But Feynman's papers and books are full of equations and derivations, not just answers. Most of Victor's examples are actually counter-examples, because they are examples of problems where a little algebra would not only be faster and easier but would yield a simple formula that you could use later, the next time the problem comes up.

Take the book design example. What happens the next time you need to fit a similar graph on the page? If you had used algebra you could have written a little calculator in Python in which you could plug in the new numbers and which would return the solution. Victor's way requires you to treat each graph-fitting problem as a special case, even if they're all the same.

[0]http://www.amazon.com/The-Psychology-Invention-Mathematical-...