3 published verifications about Riemann Zeta Function Riemann Zeta Function ×
“By analytic continuation, the Riemann zeta function satisfies ζ(-1) = -1/12.”
Standard mathematical references agree that the analytically continued Riemann zeta function has value ζ(-1) = -1/12. This does not mean the ordinary series 1+2+3+4+⋯ converges to -1/12; it means the unique analytic extension of ζ(s) to s = -1 takes that value.
“The sum of all natural numbers (1 + 2 + 3 + 4 + ...) equals -1/12.”
The statement is not correct in standard mathematics. The series 1+2+3+4+... diverges, so it does not equal any finite number under ordinary summation. The value -1/12 refers to a specialized regularization of a related function, not the literal sum of all natural numbers.
“The sum of all natural numbers (1 + 2 + 3 + 4 + ) equals 1/12.”
The claim is not supported as stated. In ordinary mathematics, the series 1+2+3+4+⋯ diverges, so it does not have a finite sum and certainly does not equal -1/12. That number arises only in specialized frameworks such as zeta-function regularization or Ramanujan summation, which are not the same as the usual sum of the series.