The human who acquired “Merry Christmas” native a logarithmic duty as displayed on the accompanying picture (relayed on on facebook by mine economist friend Germain Belzile and also Steve Ambler) had actually a stroke of poetic-mathematical genius. The source of the formula indirectly reminds us exactly how mathematics is aesthetic. And it incites us (or at the very least me) to dedicate a few minutes that Christmas 2018 to ponder the controversial question, Is mathematics misused in economics?

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I i will not ~ answer the question, yet only bring attention come a couple of related points. First, we have to not confuse the usage of math in financial theory with its use in statistics and econometrics (I will certainly speak around the former). Second, there is naught wrong through not being economist or mathematician, and nobody can be Pico della Mirandola; yet, with regard to the inquiry asked, we could lend an ext credibility to movie critics who understand something around both mathematics and economics.

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John Maynard Keynes had actually studied mathematics at Cambridge, however apart indigenous attending lectures by the an excellent Alfred Marshall, the had tiny formal cultivate in economics–which go not avoid him from becoming one of the many famous financial experts of our times. Contrary to what some human being seem to assume, Keynes used very small mathematics and was suspiciously of its usefulness in economics. What he created on math in his General theory of Employment, Interest and Money (Macmillan, 1936) would certainly be espoused by the usual Austrian economist:

It is a an excellent fault that symbolic pseudo-mathematical methods of formalizing a mechanism of economic evaluation … the they expressly assume strict independence in between the components involved and lose all their cogency and also authority if this hypothesis is disallowed; whereas, in plain discourse, wherein we space not blindly manipulating but know all the time what we room doing and also what the words mean, we can keep “at the earlier of ours heads” the crucial reserves and qualifications and the adjustments which we shall have to make later on, in a method in which we cannot store partial differentials “at the back” of several pages the algebra i m sorry assume that they every vanish. Too huge a ratio of recent “mathematical” economics are mere concoctions, together imprecise as the initial presumptions they remainder on, which permit the author to lose sight of the complexities and interdependencies of the real world in a maze that pretentious and also unhelpful symbols.

I don’t think that Keynes was a very an excellent economist, but Paul Samuelson definitely was. Samuelson likewise knew lot mathematics. His 1947 publication Foundations of financial Analysis was important in presenting mathematics in mainstream economic theory. The epigraph that the publication quotes mathematician J. Willard Gibbs saying that “Mathematics is a language.” In a 1952 post (“Economic Theory and also Mathematics—An Appraisal,” American economic Review 42, pp. 56-66), Samuelson suggested that anything composed in math was, in principle, translatable in English (or any type of other literature language), and also vice versa:

Mathematics is language. Now I typical this completely literally. In principle, math cannot it is in worse than prose in financial theory; in principle, it can not be better than prose—the 2 media space strictly identical. …

Any fact arrived in ~ by way of math manipulation have to be translatable right into words; and also hence, together a matter of logic, can quite possibly have actually been came down on by indigenous alone. …

When us tackle by words, us are resolving the same equations as as soon as we write out those equations.

Samuelson admits the it might take a many time to build a literary proof indistinguishable to a math one. So math is often convenient. “To get to some destinations it matters a great deal even if it is you walk afoot or journey by train,” he writes. Another major advantage of math is to define one’s reasoning, clearly identify the hypotheses, and also make errors that logic easily discoverable:

The convenience of mathematics symbolism because that handling specific deductive inferences is, i think, indisputable. The is going too far to say the mathematicians never ever make mistakes. Prefer everybody else, they can pull some awful boners. But it is surprising exactly how rare pure mistake in reasonable are. Whereby the really large mistakes room made is in the formulation the premises. Reasonable is no protection versus false hypotheses; or versus misinterpretation of reality; or against the formulation of irrelevant hypotheses. I think it is one of the advantages of the mathematical medium—or, strict speaking, the the mathematician’s customary canons of exposition the proof, whether in indigenous or symbols—that us are forced to lay our cards on the table so the all deserve to see our premises.

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Yet, Samuelson’s appraisal of the function of math in economics was much more balanced 보다 his detractors and also math haters often seem to think. Together career advice to young economists about the mathematical technique in economics, that suggested:

Without math you operation grave psychological risks. Together you prosper older, you are sure to resent the technique increasingly. One of two people you will get an inferiority facility and retire from the ar of concept or friend will acquire an inferiority complex and end up being aggressive about your dislike that it. … The hazard is practically greater that you will overrate the method’s power for an excellent or evil. You might even become the food of charlatans that say to you what Euler said to Diderot to acquire him to leave Catherine the Great’s court: “Sir, (a + bn)/n = x, therefore God exists; reply!” And, choose Diderot, you might slink far in shame.

This item of generally heavy Samuelsonian humor describes a most likely apocryphal story about a prank the Euler would have played top top Diderot. “The story is ludicrous,” says my historian friend Alan Kors. But it led us back to God and December 25: merry Christmas!