Kill Math
What we have here is a failure to define our terms.<p>Math <i>is</i> the manipulation of abstract symbols according to abstract rules. If you don't like symbols, you don't like math. If you are illiterate in symbols you are illiterate in math.<p>The word is often used imprecisely, though. Because so many real-world problems can be translated into math, there is a temptation to equate "math" with "any problem that can be expressed in math". Thus you frequently see poetic statements like "my cat is great at solving differential equations", or "music is math because it's all about harmonic series and Fourier analysis". But these things aren't literally true. You can put a bucket under a flowing faucet, and it will collect all the water, but that isn't really integration. The bucket isn't doing math.<p>And being ignorant of math isn't the same as being stupid. As the OP points out, you can get a lot of quantitative reasoning done without using math. A classic Fun Fact About Math is that it took thousands of years to invent the number zero. And it's true. But that doesn't mean that the ancient Egyptians used to waste hours staring into newly-emptied buckets and baskets in stunned amazement, murmuring "what on earth is that" to themselves in Coptic. People understood what "having no objects" meant long before there was a <i>symbol</i> for "the number of objects in an empty basket". It was the <i>highly abstract symbol</i> "zero", and the highly abstract operations involving zero, that had to be invented. [1]<p>It's worthwhile to recognize that interpreting the real world in terms of abstract symbols, and vice versa, is a terribly difficult skill that requires lots of practice. (In my case, I was well through grad school before many bits of physics clicked.) And it's worthwhile to recognize that you can often do without math: You can reason quantitatively without it. Birds do it! Bees do it! But don't pretend that you're doing math unless you are actually doing math. The abstractions <i>are</i> the math.<p>---<p>[1] Or, rather, discovered. Although we'd better stop there, because I won't be able to cope with the ensuing philosophical back-and-forth.