May 112011

Question of the Week, 11.5.2011

The Euler-Mascheroni constant γ plays a major role in numerous fields of mathematics and yet, it is not known whether it is rational or irrational, algebraic or transcendental. γ often appears as value or limit of special functions and is especially closely related to the exponential integral, but may be formulated as definite integral as well. Recent numerical computations provided up to several billion digits of γ and suggest that it is irrational. However, a rigorous mathematical proof is yet to be presented.

See for a detailed analysis: J. Sondow, “Criteria for irrationality of Euler’s constant,<>” Proceedings of the American Mathematical Society 131 3335-3344.

Thomas Jagau

  2 Responses to “Is the Euler-Mascheroni constant an irrational number?”

  1. I think I have proved that it is irrational and transcendental. Search for ‘Irrationality of the Euler-Mascheroni Constant’ on

  2. The specific problem with your proof is that both limits are infinity. It does not matter that the series terms tend to 0. It would be best to get your proof off the internet if you can. It will only confuse people.

    If you still do not see what is wrong with your proof, write me explaining your reasoning and I will try to clarify your problem.

    Marshall Ash,