[funnygiraffe]

Why are we so sure that a lot of "previously intractable problems" are/will be solved with this family of methods? (and I mean real-life/real-world problems, not toy problems constructed specifically to show the proposed methods in the best light possible in the research papers) Of course others above have pointed out drug or protein design as a potential area, but there still seems uncertainty as to the practical impact on the real world. Other than that, I don't see areas of impact for these approaches so far.

[johmathe]

One of the authors here. Thanks for your comment! While a lot of this research is theoretical and does not have immediate use cases, we have tried to summarize some of them in the last paragraph of the paper (VII. Applications of Non-Euclidean Geometry). See page 26. We present some in Chemistry and Drug Development, Structural Biology and Protein Engineering, Computer Vision, Biomedical Imaging, Recommender Systems and Social Networks and Physics.