Mathematics as what mathematicians study is not itself a representation (of, well, itself), so that's obviously false in that sense, and I'm not sure how representation of it is relevant to its own nature. And, of course, math itself isn't dependent on what is studied in thermodynamics.
As far as I understand it math is the symbolic representation of formal logic which is itself a reflection of thermodynamic principles.
Mathematics as what mathematicians study is not itself a representation (of, well, itself), so that's obviously false in that sense, and I'm not sure how representation of it is relevant to its own nature. And, of course, math itself isn't dependent on what is studied in thermodynamics.