Two takes on Peter Diamond and the use of technical/mathematical economics. First, Steve Levitt:
I was delighted to see that Peter Diamond shared the Nobel Prize today with two other economists (Mortensen and Pissarides...). Diamond’s intellect was legendary when I was a student at MIT. In his research, he worked on very hard problems. He wrote the kind of papers that I would have to read four or five times to get a handle on what he was doing, and even then, I couldn’t understand it all.
And Glenn Loury via Ravi Sethi:
Glenn Loury on Peter Diamond, by Rajiv Sethi: Glenn Loury has kindly forwarded me a letter he wrote earlier this year in appreciation of Peter Diamond, one of the co-recipients of this year's Nobel Memorial Prize in Economics. The tribute was written for the occasion of Diamond' retirement, and seems worth publishing today:...Peter was an inspiration and role model for me during my student years at MIT. ... I recall going over to the Dewey Library shortly after arriving in Cambridge, in the summer of 1972, and digging out Peter's doctoral dissertation. This was a mistake! Peter's reputation as a powerful theorist had been noted by my undergraduate teachers at Northwestern. I wanted to see how this reputed superstar had gotten his start. Just how good could it be, I wondered? I had no idea! What I discovered was an elegant, profound and exquisitely argued axiomatic treatment of the general problem of representing consumption preferences over an infinite time horizon, extending results obtained by his undergraduate teacher and the future Nobel Laureate, Tjallings Koopmans.
I prided myself on being a budding mathematician in those years. Yet, Peter's effortless mastery in that dissertation of the relevant techniques from topology and functional analysis, and his successful application of those methods to a problem of fundamental importance in economic theory -- all accomplished by age 23, younger than I was at the moment I held his thesis binder in my hands! – was simply stunning. This set what seem to me then, and still seems so now, to be an unapproachable standard. I was depressed for weeks thereafter!
Even more depressing was what I discovered as I got to know Peter better over the course of my first two years in the program: that mathematical technique was not even his strongest suit! An unerring sense of what constitute the foundational theoretical questions in economic science, and a rare creative gift of being able to imagine just the right formal framework in the context of which such questions can be posed and answered with generality -- this, I came to understand, is what Peter Diamond was really good at.
This is the part I want to highlight (Rajiv Sethi also points to these remarks):
And so, I learned from him in those years what turned out to be the most important lesson of my graduate educational experience -- that, in the doing of economic theory and relative to the behavioral significance of the issue under investigation, technique is always a matter of secondary importance -- neither necessary nor sufficient for the production of lasting insights. ... And so I came -- slowly and fitfully, because I was rather attached to the joys of doing mathematics for its own sake -- to see the world the way that Peter Diamond saw it. And, in the process, I became a much better economist. ...
Paul Krugman puts it this way:
And by the way, for those of us in the modeling business, Peter Diamond’s work is breathtaking in its elegance — nobody cuts through the complexities with such grace.
It is really hard to convince new graduate students that mathematics without the underlying economic intuition, i.e. technique for the sake of technique, is pretty useless. It's the economics that are important -- mathematics is simply a tool that allows us to better understand the economic content of the models we work with -- the math itself is not the point of the exercise. In fact, the best models are the ones that are boiled down to the essentials so that they isolate important phenomena in a way that makes them transparent. Mathematical complexity is not always the best way to reach this goal. Models should be as complex as needed to highlight the essential issues, to use Krugman's term they should be "elegant," and additional complexity beyond that point detracts from their elegance and obscures rather than clarifies the central features of the model. Sometimes a high degree of complexity is required, but not always.