Il premio Nobel a Shapley e Roth

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L'articolo di Gale e Shapley si chiude con una perla sull'uso della matematica.


Finally, we call attention to one additional aspect of the preceding analysis which may be of interest to teachers of mathematics. This is the fact that our result provides a handy counterexample to some of the stereotypes which non-mathematicians believe mathematics to be concerned with.

Most mathematicians at one time or another have probably found themselves in the position of trying to refute the notion that they are people with "a head for figures." or that they "know a lot of formulas." At such times it may be convenient to have an illustration at hand to show that mathematics need not be concerned with figures, either numerical or geometrical. For this purpose we recommend the statement and proof of our Theorem 1. The argument is carried out not in mathematical symbols but in ordinary English; there are no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly needs to know how to count. Yet any mathematician will immediately recognize the argument as mathematical, while people without mathematical training will probably find difficulty in following the argument, though not because of unfamiliarity with the subject matter.

What, then, to raise the old question once more, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable to achieve the degree of concentration required to follow a moderately involved sequence of inferences. This observation will hardly be news to those engaged in the teaching of mathematics, but it may not be so readily accepted by people outside of the profession. For them the foregoing may serve as a useful illustration.


federico de vita 19/10/2012 - 11:17

I'm impressed. Sono anni che cerco il modo di dire queste cose, con scarso successo. Grazie della segnalazione, Marco.

abbastanza sconcertante, devo dire, in un articolo di pura ricerca di base (non una review, non un commento, etc..). Io da referee glielo avrei cassato senza indugi :-)


marco mantovani 22/10/2012 - 11:00

negli articoli più datati non è infrequente trovere digressioni di varia natura che, per quanto belle, oggi non troverebbero mai spazio su un giornale. In fin dei conti, oggi uno può sempre pubblicarsele sul blog...

Mertens (1989 - MOR):  


It is as if every time we think we finally get a hold on what rational behaviour means, we find ourselves having grasped only a shadow. Maybe this means there is excessive ´υβρις in this endeavour: that rationality is something belonging to the gods themselves, and that should not be stolen from them. Maybe it is the tree of knowledge itself, that we should not touch?


andrea moro 22/10/2012 - 16:08

devo cominciare a leggere i classici

Non sorprende la chiusura di GS. E' puro von Neumann-style, il maestro di tutta quella generazione di fondatori della game theory. Basta leggere il cap.1 della Theory of Games, oppure, ancora meglio, "The Mathematician" del 1947, in Taub A.H. (ed.), John von Neumann. Collected works, Oxford: Pergamon Press, 1961-63, vol. I, 1-9. O anche una biografia seria di von Neumann, tipo quella di Israel & Gasca o quella di Robert Leonard (ce ne sono anche di non serie, ma non fatemi far polemica). In particolare, la frase "ogni argomento portato avanti con precisione è matematico" è proprio il fondamento del metodo assiomatico hilbertiano portato in economia proprio da von Neumann. Nel senso che precisione di linguaggio, matematica ed assiomatica vengono di fatto a coincidere.