Lately, I’ve found myself in a number of conversations with students about the use of mathematics in economics research and teaching. Personally, I always think of Alfred Marshall as the founder of modern, mathematically rigorous economics. I think he sums up nicely the use of math in economics with the following “guide” to research (from a letter to A.L. Bowley).
(1) Use mathematics as shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life (5) Burn the mathematics. (6) If you can’t succeed in 4, burn 3. This I do often.