>Mathematics describe rules of reasoning which preserve truths about the world.
I'd disagree even with this, and state something even weaker. Mathematics describes rules of reasoning. A sound mathemathical theory of the something in the real world is a (partial) correspondence between statements about the real world and mathematical statements, such that the mathematical manipulation of statements preserves correspondence to truths about the world, or produces statements that don't correspond to the world.
I think this distinction is important because it emphasizes that it is the scientists' responsibility to pick an appropriate mathemathical model.
I'd disagree even with this, and state something even weaker. Mathematics describes rules of reasoning. A sound mathemathical theory of the something in the real world is a (partial) correspondence between statements about the real world and mathematical statements, such that the mathematical manipulation of statements preserves correspondence to truths about the world, or produces statements that don't correspond to the world.
I think this distinction is important because it emphasizes that it is the scientists' responsibility to pick an appropriate mathemathical model.