> I can easily see a bright, curious person wasting a lot of time before realizing that the content is merely linguistic, not mathematical. While I rarely find

> I can easily see a bright, curious person wasting a lot of time before realizing that the content is merely linguistic, not mathematical. While I rarely find graphical methods useful for performing calculations, I do appreciate visual interpretations of how mathematical concepts work. I personally find that whenever I have to learn a new topic in math, good visualizations help me form an intuition regarding how things fit together, and can often be useful when reasoning about how to attack a problem (back-of-the-envelope sketch before a more rigorous calculation). For actually solving the problem, on paper or in code, I agree that a symbolic approach is superior. I also think that purely linguistic improvements in math can have a positive effect: a mathematical notation that is easy to learn, understand, and use, will clearly make the math it represents more impactful. I can't find the exact quote at the moment, but I think it was Dirac who said something along the lines that "a good mathematical notation should make correct statements obvious and wrong statements impossible".