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79 votes
9 answers
21k views

Results that are widely accepted but no proof has appeared

The background of this question is the talk given by Kevin Buzzard. I could not find the slides of that talk. The slides of another talk given by Kevin Buzzard along the same theme are available here. ...
147 votes
21 answers
23k views

Are there examples of non-orientable manifolds in nature?

Whilst browsing through Marcel Berger's book "A Panoramic View of Riemannian Geometry" and thinking about the Klein bottle, I came across the sentence: "The unorientable surfaces are never discussed ...
43 votes
11 answers
15k views

Open questions in Riemannian geometry

What are some major open problems in Riemannian Geometry? I tried googling it, but couldn't find any resources.
5 votes
5 answers
2k views

Terminology introduced in recent years with more than one meaning

Suppose a term(inology) is recently (in last 20 years) introduced in research mathematics. It might happen that some one who wish to use it, in the same area of research, for different purposes or ...