How did Giuseppe Peano’s symbolic logic influence Whitehead and Russell?

Giuseppe Peano’s work in symbolic logic significantly influenced Alfred North Whitehead and Bertrand Russell, particularly after the two attended the First International Congress of Philosophy in Paris in 1900. There, they were deeply impressed by the precision with which Peano utilized symbolic notation to clarify the foundations of mathematics.1

Following this encounter, Russell quickly mastered Peano’s notation and extended his methods. This influence is most evident in their collaborative masterwork, Principia Mathematica (1910–13), which adopted several key elements of Peano’s system. Specifically, Whitehead and Russell utilized Peano’s notation for quantifiers and his use of the Greek letter epsilon ($ϵ$) to denote set membership. While the "official" text of Principia Mathematica relied on a combination of symbols taken from Peano and those invented by Whitehead, Peano’s contributions provided a crucial foundation for the symbolic reasoning required to demonstrate that all pure mathematics could be derived from formal logic.123