I literally have no idea because I haven't read any of Bertrand Russell's books yet, I just know they deal with proofs and logic. Whitehead is one of my favorite philosophers though, alongside de Chardin and Kant. My understanding is that Russell's work on logic theory laid the foundations for Turing's work which later blossomed into Cybernetics --> Connectionism --> Modern ML/AI.
ML has a lot of linear algebra and probability, lots of matrices & tensors, bayesian and gaussian probability.
It also has formal logic such as with Markov Logic Networks and Inductive Logic Programming. Basically, formal logic is used to provide a semantic framework to evaluate AI actions and the field has historical relevance also, it is more of a historical keystone in the development of ML systems and keeps re-emerging in various forms throughout AI development over the decades.
It's true that, with the rise of Transformers, logic systems are not as relevant to modern AI as they used to be...