Math is good, math is right. Almost as good as greed
Take the centerpiece of my early career, the work on increasing returns and trade. The models I and others used were, in a way, typical of economics: clearly untrue assumptions (symmetric constant elasticity of substitution preferences; symmetric costs across products!), and involved a fair bit of work to arrive at what sounds in retrospect like a fairly obvious point: even similar countries will end up specializing in different products, and because there are increasing returns in many sectors, this will produce gains from specialization and trade. But this point was only obvious in retrospect. People in trade were not saying anything like this until the New Trade Theory models came along and clarified our thinking and language. Trust me, I was there, and went through a number of seminar experiences in which I had to bring an uncomprehending audience through until they saw the light.
The same is true for the liquidity trap. The basics of what happens at the zero lower bound aren't complicated, but people who haven't worked through small mathematical models -- of both the IS-LM and New Keynesian type -- generally get all tied up in verbal and conceptual knots.
-- Paul Krugman
Noah Smith has a fairly caustic meditation on the role of math in economics, in which he says that it's nothing like the role of math in physics -- and suggests that it's mainly about doing hard stuff to prove that you're smart.
I share much of his cynicism about the profession, but I think he's missing the main way (in my experience) that mathematical models are useful in economics: used properly, they help you think clearly, in a way that unaided words can't.
What is true is that all too many economists have lost sight of this purpose; they treat their models as The Truth, and/or judge each others' work by how hard the math is. It sounds as if Smith was taught macro by people like that. And there are a lot of people in macro, some of them fairly prominent, who are what my old teacher Rudi Dornbusch used to call "fearful plumbers" -- people who can push equations around, but have no sense of what they mean, and as a result say quite remarkably stupid things when confronted with real-world economic issues.
But math is good, used right.