How did Giuseppe Peano influence the notation used in modern logic?

Giuseppe Peano significantly influenced modern symbolic logic by developing a notation that surpassed that of his contemporaries in its direct impact on later logical systems. While his early work was rooted in the algebraic tradition, he evolved a distinct notation for quantifiers during the 1890s.1

Key elements of his influence include:

• Set Membership: Peano introduced the use of the Greek letter epsilon ($ϵ$) to denote membership in a set, a symbol that remains standard in modern set theory.1
• Adoption by Peers: His notation was notably adopted by Bertrand Russell and Alfred North Whitehead for their seminal work, Principia Mathematica, which helped cement his influence on the field.21
• Formalization: Through his Formulaire de mathématiques, Peano sought to develop mathematics entirely from fundamental postulates using his logical language, emphasizing the necessity of formal development to avoid errors.2

Although Peano himself was not primarily focused on the logicist program, his work—including the Peano axioms—provided a crucial link between logic and mathematics.1