TITLE: Relevance of Landau's Algorithm for Denesting Radicals
QUESTION [6 upvotes]: I just came across a Wikipedia article Nested Radicals that mentions Landau's Algorithm for deciding, whether a nested radical can be denested, but that Wikipedia article is just a stub.
Googling "Landau's Algorithms" produces references to the Wang and Landau Algorithm.

Question:
What role does Landau's Algorithm play in mathematical research, i.e. did it pave the way for further progress, e.g. towards a deterministic algorithm for denesting radicals, or did it "just" solve an isolated problem?
I am asking because the original article is freely accessible online, but isn't described in the omniscient Wikipedia.
Is my impression right, that because Ramanujan provided some examples of denested radicals, that the topic is of some relevance?

REPLY [4 votes]: This 2017 article Gkioulekas - On the denesting of nested square roots summarizes the status of this topic. Landau's algorithm is not a "final" solution because it runs in exponential time with respect to the depth of the expression that one is attempting to denest. To find a general algorithm that runs in polynomial time remains an open problem. See also this related MSE posting.