"The thermodynamicist Wilson taught a seminar on mathematical economics that autumn of 1935, an outgrowth of his attempt to reform the field. Only four students enrolled - Abram Bergson, Sidney Alexander, Joseph Schumpeter, and Samuelson. Samuelson immediately began translating into math the economics he had brought with him from Chicago. "A student who studied only one science would be less likely to recognize what belonged to logic rather than to the nature of things," he recalled later. "One of the most joyful moments of my life was when I was led by E.B. Wilson's exposition of Gibbsonian thermodynamics to infer an eternal truth that was independent of its physics or economics exemplification."
- David Warsh, Knowledge and the Wealth of Nations, p. 116
Of course, anyone really dedicated to the scientism critique is probably going to read this as catching Samuelson red handed. The point is that the narrative is usually "Samuelson borrowed a trick from physics to make economics tractable". That's not the case at all - Samuelson recognized that behavior of systems under constraints would have common characteristics.
Samuelson argued that people who haven't studied physics and economics might be tempted to think that the math was intrinsic to physics. He noted that that was not the case. The math was independent of physics. Mathematical economics is just a language for talking about economics, like literary economics is. And you can use math to describe processes in physics and economics in the same way that you can use Chinese or German to describe processes in both physics and economics.
The truth of the process that the math of thermodynamics describes is independent of any particular applications in economics or physics.
Another way of putting it is that in an alternate universe we could just as easily have had economics as the first science to apply constrained optimization and then have physics pick it up later.
Math is a language.
On the Warsh book in general - I'm about halfway through. It's very good. It offers a lot more than what the blurb suggests. It's really a history of all of economic thought - not just endogenous growth theory. It is like a modern Worldly Philosophers sans Marx and Veblen. That was not what I expected, but it was a pleasant surprise.
Unfortunately, the framing of the history of economic thought is very teleological. Everything is presented as being Adam Smith's leftover problems being fulfilled in the work of Paul Romer. I think htis is a bad way to look at it, but I suppose it makes for a compelling narrative to people. (btw - I felt that the real Smithians today are Arrow, Stiglitz, Romer, and Krugman for a while - but reading Warsh has been a nice reinforcement of that view!).
I like very much how he brings the social context of these thinkers into the book.