Thread by @Rey_Skywalker8

@johncarlosbaez @duetosymmetry Proof of Irrationality of Euler’s constant (γ) by mathematical induction
Expressed in Gregory coefficients (Gn) series
γ = ∑ |Gn|/n = 1/2 + 1/(12 2) + 1/(24 3) + 19/(720 4) + 3/(160 5) +…
γ = ½ + 1/24 + 1/72 + 19/2880 + 3/800 +...
#Mathematics @wtgowers @LondMathSoc

@johncarlosbaez @duetosymmetry @wtgowers @LondMathSoc ∑ 2 terms = ½ + 1/24 = (24 + 2)/(2 24) = 26/48
∑ 3 terms = 26/48 + 1/72 = (26 72 + 48)/(48 72) = 1920/3456
∑ 4 terms = 1920/3456 + 19/2880 = (1920 2880 + 19 3456)/(3456 2880) = 5595264/9953280

Numerator and denominator are increasing as I add more terms.

@johncarlosbaez @duetosymmetry @wtgowers @LondMathSoc Since the series is infinite, the exact value of γ requires infinitely large numerator and denominator. No 2 integers, no matter how large, will give exact value of γ. Therefore, γ is irrational

This is a great unsolved problem in math! Is there a Breakthrough Prize for it? 😀