What I'm saying is that there is no strange mathematical result whatsoever related to the sum of the positive integers, which should be the only meaning reserve

What I'm saying is that there is no strange mathematical result whatsoever related to the sum of the positive integers, which should be the only meaning reserved to 1+2+3+... There are stuff like this https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%C2%B7_%C2%B7_%C2%B7 https://en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%C2%B7..., but writing 1+2+3+... = -1/12 is purely formal and pretending to deduce it from physics is silly because you are not performing any sum at all.