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In atomic physics is not alwayes possible to reason by analogies consequently modern physics is bound to be, up to a certain extent, pure math

Right, but I would say that our concepts of particles need to be limited to what we can observe, we don't conceptualize things by analogies because of human limitation, but rather because thats the way they exist in real form. In order to get out of the realm of speculation you need to be able to test something.

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It is evident that you did not grasp the concept

For a real gas you must tweak the equation adding the van der Waals constants which depend on the type of gas

No, I didn't read all of the thread now I have looked back and see that you have already taken to account the nature of 'real things'. It appears to me that you were trying to propose that because an equation has a constant that it needs to model real things, which in the example you used, would be wrong.

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modern physics is bound to be, up to a certain extent, pure math

I think a lot of physicists would disagree with you because they seem to value math more for its practical application, rather than for it's theoretical usage. One problem with your reasoning about string theory is in your earlier statement:



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This theory can exactly predict all the features of all the known particles.
It is hard to beleive that it is just by chance

You are essentially adhering to string theory because you feel that the only alternative is that its 'hard to believe that it is just by chance'.