There is no good maths outside physics

by RuiXi

“You mathematicians and physicists, are friends? No, we’re brothers. Why so? Friends are chosen”. I’ve heard this joke often, but with slight variations. It always refers to people which, in the end, are the same. Arabs and Jewish, KDE and GNOME freakies, Polish and Russians, Buenos Aires and Montevideo, Pakistan and India, trekkies and star wars…

Good mathematics and physics are, in the end, the same. Why? Main reason: I could not find a clear cut difference when asked about one, no matter how hard I tried! Good maths start with the real
world. Then, sometimes, when the dark side gains control, it loses sight of its original target and becomes a pure game in itself. This game has no relation with physics, it’s true. But it isn’t good maths
anymore.

Take the axiomatic view of mathematics. A set of axioms makes up a model. In science people is used to models. When they do not work, they are rejected. In dark-side mathematics, not-working models are
also good. You can publish papers on it with one condition: that there are other guys like you which like that game too.

There is another risk in axioms, even if they are good: the excess of faith in logic. Let’s suppose that the axioms, as any good model, are 99% good. Whenever you apply a deductive rule, your chances of
deviating from the real world increase. If you keep lots of rules without checking the validity of the intermediate steps, discarding human mistake (which I should not), your chances of getting a sensible
answer have come to zero. But for dark-side mathematicians this is not a problem: the result is then, simply, highly counter-intuitive…

What about good “old” maths? Anything as pretty as $e^{ipi}=-1$, checked everyday in physical applications? As Jacobi once noted, the fact that the presentations of a whole number as a sum of four squares and real time evolution of a pendulum are related by the same function is a really wonderful discovery.
Ehm… but these ideas were explained much better by Vladimir Arnold, in a conference he gave in Paris, to critizise the “French” abstract mathematics. The text can be found here.

Mathematics, in Greek, means “what you learn” (mathesis), and physics means, simply “nature”… What can we learn, if it is not about nature? And what can we do with nature which does not imply learning?

Thanks to prof. Jorge Lewowicz, for very useful discussions!

Una respuesta a There is no good maths outside physics

  1. Superwoman dice:

    ¿Ves como puedo acusarte con fundamento de enriquecer el nivel intelectual hasta de los fraudes como yo? En serio, no podía dejar de leer, y tratándose el texto de lo que se trata, eso es que es bueno…
    Un supersaludo

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