Bernoulli umbra is defined in classical umbral calculus as [here (page 16)][1] or [here][2]. [This paper][3] shows that $\log (B+1)=-\gamma$ (the later paper uses the symbol $B$ for what is defined as $B+1$ in the first paper). Since we can define Bernoulli umbra as a formal Laurent series in Levi-Civita field as $B=\varepsilon^{-1} -\frac{1}{2}-\frac{\varepsilon }{24}+\frac{3 \varepsilon ^3}{640}-\frac{1525 \varepsilon ^5}{580608}+\dotsb$ and $B+1=\varepsilon^{-1} +\frac{1}{2}-\frac{\varepsilon }{24}+\frac{3 \varepsilon ^3}{640}-\frac{1525 \varepsilon ^5}{580608}+\dotsb$ (the numerators of the terms are given in https://oeis.org/A118050 and the denominators are in https://oeis.org/A118051), the question becomes simple: what's the intuition behind the fact that $\operatorname{st}\log (B+1)=-\gamma$ (in some closure of Levi-Civita field under logarithm operation)? Here $\operatorname{st}$ meant the $0$-th coefficient of the power series. [1]: https://people.brandeis.edu/~gessel/homepage/papers/umbral.pdf [2]: https://arxiv.org/pdf/1101.0770.pdf [3]: https://arxiv.org/abs/1011.3352