The Curious and Counter Intuitive Number -1/12

Smithsonian Magazine writes about the mathematical oddity of the number -1/12 in The Great Debate Over Whether 1+2+3+4..+ ∞ = -1/12 .

It turns out the 1 + 2 + 3 + 4 + .... = -1/12 is utilized in quantum field and string theory.

If one considers Euler's Identity ( e^{i╥} + 1 = 0 ) and re-formulates it as e^{i╥} = -1, the curious relationship noted above can be represented in a way that brings into play three other mathematical constants (e, i and ╥) in provocative and counter intuitive musings:

1 + 2 + 3 + 4 + ... =  e^{i╥} / 12

It's probably no accident that the imaginary number i has been so helpful throughout history, allowing us to mathematically delve into another 'dimension' for problem solving in fields like electrical engineering, also shows up in the infinite sum of positive integers relationship.

Just as interesting is that the number 12 shows in up in a dimensional variation of string theory.