[Koshkin]

> The effectiveness of mathematics then is more about its conciseness

Indeed! Ultimately, this is expressed in mathematical notation - which is necessary if you want math to "just work" for you (almost automagically).

> If math and language were built from only relations our brain and body could sense

Which they, of course, are; hence the whole mystery of the "unreasonable effectiveness" of our "everyday" mathematics (such as linear algebra or complex analysis) in areas unreachable to our senses or to our ability even to imagine things (e.g., the quantum world).