bees_buzz
These things were still indispensable on my path to being a mathematician though, they just ceased to be relevant as abstraction increased.
Check out Marques Brownlee's video on this - they probably _were_, it renders your face using the internal cameras in real time and displays that.
Maybe a research group wants to investigate a connection to another discipline.
Maybe the research group comes across a talented student and sees the potential for a research grant (how this works depends on the country).
Maybe the student has the means to self-fund and so the university happily collects a pay-cheque.
I fell into the first category - I did my PhD in a quantum information group despite my background being in mathematical logic. I was accepted because I knew a lot about different formal logic systems, and they wanted to study connections between those and the formalism they were using for quantum information.
???
This paper contains a nice summary of Gödel's interactions with Russell. https://www.cambridge.org/core/services/aop-cambridge-core/c...
Gödel's future work on constructible hierarchies and the dialectica interpretation were directly inspired by Principia Mathematica. I agree that characterizing Gödel's view on Principia as a "step backwards" is overly simplistic, but he certainly mentions and takes inspiration form the work throughout his career.
> as he was mainly criticizing the syntax
If you mean to say that Gödel's criticisms of Principia were just about syntax - that is also incorrect. Gödel had substantial complaints about the truthfulness of the axiom of reducibility that (IIRC) Russell himself thought posed a valid attack on the system in Principia.