With all due respect, you are not really saying that the series 1+2+3+... converges to -1/12 with the obvious metric, are you? Because that's the only reasonable way to interpret 1+2+3+... = -1/12 (and it is false). The fact that there is some physics, that relies on particular results from complex analysis (I guess), which can imply that the sum of the positive integer is "in some sense" -1/12, does not exempt anyone from giving those symbols their true meaning, or they risk looking fool rather than smart.
Not sure what you mean by the last sentence here, can you elaborate? What I'm saying is that the fact that this strange mathematical result happens to give correct results in a physical experiment must be a pointer to something.
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+...
