Can anyone think of a mathematical economics proposition that was accepted that was not consistent with what Kenneth Boulding called the literary vagueness of classical economics and economic sociology:
Conventions of generality and mathematical elegance may be just as much barriers to the attainment and diffusion of knowledge as may contentment with particularity and literary vagueness…
It may well be that the slovenly and literary borderland between economics and sociology will be the most fruitful building ground during the years to come and that mathematical economics will remain too flawless in its perfection to be very fruitful.
If mathematical economics came up with a result that was not reproducible through economic intuition, did the result become popular or were they ignored? Until this barrier is passed, mathematics will be a shorthand language rather than an engine of enquiry, as Alfred Marshall argued long ago:
[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 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.
saw that excessive reliance on this instrument [mathematics] might lead us astray in pursuit of intellectual toys, imaginary problems not conforming to the conditions of real life.