Mathematical Hocus-Pocus?

I started my career actually leaning toward math and physics and I have always enjoyed listening to and following folks who have a passion for, and can communicate, complex theories to the layman.

1 + 2+ 3 + 4 + 5 … = –1/12

I was perusing YouTube and came across several videos by Numberphile and he does a magnificent job of explaining a rather counter intuitive concept. The ideas is that the sum of all natural numbers (from 1 to infinity, convergent series) produces minus one twelfth. That is right –1/12.

Makes no sense to me either, but the proof is presented here contrary to all that I know to be numerically reasonable.

It is clearly counterintuitive and it is counterintuitive because, you know, intuitively you just want to stop the sequence and the minute you stop the sequence then your intuition for this result goes out the window - Tony Padilla

This mathematical principal actually shows up in the natural world, relating to Superstring theory and the Casimir effect (quantum mechanics).

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