Euler–Mascheroni Constant

The gap between the harmonic series and the natural logarithm — a limit approached but never reached.

Specifications & Metrics

symbol

γ

approx

0.57721566490153…

Core Principles & Analysis

• Euler computed it to six places in 1734; nobody knows whether it is rational.
• It appears wherever logarithms and discrete sums meet, from number theory to physics.
• Proving γ irrational would be a major result — no proof exists after nearly three centuries.