How did Ludwig Wittgenstein influence Bertrand Russell’s later views about logic and mathematics?

Ludwig Wittgenstein significantly influenced Bertrand Russell’s later philosophical views, particularly by challenging the foundations of Russell’s earlier work in logic and mathematics. Through their interactions, Wittgenstein persuaded Russell that the truths of logic and mathematics are analytic rather than reflections of an eternal, Platonic realm of ideas.1

Specifically, Wittgenstein’s work, notably the Tractatus Logico-Philosophicus, undermined the approach that had inspired Russell’s contributions to the philosophy of mathematics. Wittgenstein convinced Russell that there were no "truths" of logic in the traditional sense; instead, logic consists entirely of tautologies. According to this view, the truth of these statements is not guaranteed by external facts in a realm of ideas but lies solely in the nature of language.2

This shift marked the final step in Russell’s "retreat from Pythagoras"—his move away from the belief that logic provided access to an immutable, eternal world of truth. Consequently, Russell became convinced that logical analysis was the essence of philosophy, further incentivizing him to move away from technical logic toward other pursuits.12