For some unknown reason, or probably because of my early education, I am closer to the mathematical way of proving than to the physical way of proving. It is only now that I see that physicists have a rather odd and silly way of proving things. Of course, I totally disagree with the physicist’s way of proving things because I see it as very limitative. On the other side, maybe there is a point… what’s the difference: well, usually when I bring some arguments based on some proved theorems and go from one result to the other choosing some adequate theorems that make the connections for me the proof is obvious… Physicists are used to calculate (and beware, have the impression that mathematics means making lots of calculations on some models). THIS IS WRONG! Most of the time it is best to avoid doing ANY calculations at all and just to bring logical arguments that lead you from one proposition to the next. Sometimes you have to verify something directly, true, but that is the UGLIEST part of the endeavor. If I tell you that following from this and that theorem, this or that structure induces a group structure via this or that map to this or that space and the proof that this happens is there I don’t have to explicitly VERIFY it again for a specific example. Mainly because the SPECIFIC example will be a particularization with a FAR LOWER proving power than the general theorem! When I compute something by applying a theorem to a specific case I reduce the power of that theorem to a specific case. THAT IS UGLY! 

So, not the models are those that create knew knowledge! They just create new examples. It is the ETERNAL proof that is important and lasts forever and it is there you have to invest most of the time to make it as rigorous as possible! 

A model is just a model… it brings nothing fundamental to knowledge. It may bring some applications but that is the engineer’s work… 


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