Alfred Marshall on the Use of Mathematics in Economics

I retired at the end of last year and have finally finished clearing out my office. In the process I found a number of interesting things, including a printout of a book on transport economics that I wrote thirty some years ago when teaching a course on the subject but never published and thought was lost.

I also found the original of a passage in a letter by Marshall that I have been misquoting for many years. Here it is.

Balliol Croft, Cambridge
27. ii. 06

My dear Bowley,

     I have not been able to lay my hands on any notes as to Mathematico-economics that would be of any use to you: and I have very indistinct memories of what I used to think on the subject. I never read mathematics now: in fact I have forgotten even how to integrate a good many things.

     But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very unlikely to be good economics: and I went more and more on the rules—(1) Use mathematics as a 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 last I did often.

     I believe in Newton's Principia Methods, because they carry so much of the ordinary mind with them. Mathematics used in a Fellowship thesis by a man who is not a mathematician by nature—and I have come across a good deal of that—seems to be an unmixed evil. And I think you should do all you can to prevent people from using Mathematics in cases in which the English Language is as short as the Mathematical.....

Which leaves me wondering how much of the economics of the next century went into Marshall's fireplace.

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