John Palmer has this post on math in economics:
One of the books we all had to read/work our way through as graduate
students in most major economics programmes in the 1960s was Paul
Samuelson's Foundations of Economic Analysis. I note with some pleasure that none -- not one
-- of the economists' book-tag responses that I have read mentions this
book [Though I did see that Craig Newmark listed Samuelson's intro
text].
There is a reason Samuelson's Foundations isn't
listed. As I recently wrote to Walt, who asked me why so many modern
grad schools emphasize math instead of economic logic,
I would say the bad aspects of the trend came with Samuelson's Foundations of Economic Analysis.
Math was used in economics long before then, but his dissertation/book
seemed to set the discipline off in a direction that was not very
productive.
Math is good. Math has helped me. Math has
helped others straighten me out. I was once a macho-math man. But math
isn't worth much without a good appreciation of the Economic Way of Thinking.
I am not a math jock. In fact, through my undergraduate years, I never took a math class beyond college algebra although I was exposed to some essentials of calculus in a mathematical econ course. I was also exposed to more calculus in the footnotes of the intermediate micro text that I used.
I got exposed to more math as a master's student at the University of Nebraska at Omaha, but becuase I worked 44 hours per week as an assistant manager at Walgreens, there wasn't time to take courses other than those required in my major. I could have taken math courses as electives, but my work schedule did not allow me to take any (I took two history courses that fit into my schedule). After I graduated from UNO and was applying to graduate school, most places rejected my application because I didn't have the math.
In a stroke of luck, one of my professors (and references) from UNO knew one of the members of the graduate committee at the University of Missouri - they were graduate students together (it is a small world) and respected each other. My reference wrote that while I didn't have a lot of math, my academic record was not stellar (it was solid, especially in the latter part of my undergraduate career), I thought about problems in the "correct way," i.e. using a comparison of costs and benefits - in other words, I thought like an economist. It was that letter that got me into Mizzou.
During the winter of 1992-93 and the spring and summer of 1993, the time immediately prior to the beginning of my graduate studies, I spent my time reading a calculus book and a linear algebra book. My time at UNO told me that to be successful in a graduate program, I needed to know that stuff. I read and took notes from every section of the calc book that covered material typically covered in calc 1 and 2 and the material on partial differentiation. I read and took notes from nearly the entire linear algebra text. I worked through most of the problems in the back of the books and in their accompanying study guides. In short, I taught myself calc 1, 2, parts of 3, and linear algebra in the space of about 9 months. In my life, this was one of the best investments I made.
At Mizzou, I chose my dissertation advisor, Dave Mandy, in part because he was very strong in theoretical and mathematical modelling (another good investment). All of these choices have helped strengthen my ability to do and comprehend mathematical economics.
But still, I think the fact that I knew how to think about things in the "correct way" is what helped me get through graduate school and helped me throughout my career as a professional academic economist.