> Math, when done well, is based on a logical foundation that makes it understood by its intended audience. NO, they are not just making it up or blowing smoke.

> Math, when done well, is based on a logical foundation that makes it understood by its intended audience. NO, they are not just making it up or blowing smoke. I think you may be misunderstanding what the author is trying to say, or, rather, what part of a mathematician's activity they're trying to discuss. Mathematicians are not making it up, in the sense that we're not engaged in some elaborate game with shifting but meaningless rules. The final product of mathematics is fully as polished and rigorous as its weighty presentation suggests. However, the act of doing mathematics is, or can be, messy, non-rigorous, and nonsensical on the way to discovering that perfect polish and rigor. Much like the old adage that, if you never miss a flight, you're spending too much time at the airport—if every bit of a mathematician's work is up to the full stands of rigor required of a final publication, then that mathematician is not doing the best work that they could do.