Yet another classic, at last found its way to my library.
I'm wondering. If #computability and #unsolvability theories are mostly concerned with the existence of algorithms for classes of problems, if one could prove or disprove such a thing (class of theorems?) starting from #geometry.
I'll explain. I've recently understood (Steenrod et al, "First concepts of topology") that #topology is mostly concerned in proving existence theorems. The subject matter of this book sounds, in a way, like an attempt to prove such theorems. So naturally I came to wonder if anyone had attempted tackling them with topological means and tools instead. I haven't looked to see if this question even makes sense, but my humble instinct says that maybe yes, and that most likely at least someone has worked on it in the past.
++ Video is visually appealing, compact (28'). Tries to present the question of finiteness || infiniteness of Universe within the context of relativistic #cosmology. Intros to 2D #topology + #curvature are fair. Publicity for my group's research is nice :).
The relation to 3D topo+curv is absent; there are several bloopers in the narration.
Wie fängt eine #Mathematikerin einen #Löwen?
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Ganz einfach: Sie besorgt sich einen Käfig, bringt ihn in den Düppeler Forst, setzt sich hinein, verschließt die Tür und definiert:
It's fascinating to me that giving someone a "beat down" is the same thing as "beating them up". It implies that beating exists in some sort of non Euclidean space that folds in on itself.
Anyone know of work on visualizing simplicial complexes in 3D? Laying out edges, triangles, and tetrahedra, etc. I'm thinking something along the lines of the work on graph layout and visualizing #networks, but doing it in 3D, and for simplicial complexes and hypergraphs/#HigherOrderNetworks.
This past October, dozens of mathematicians gathered in Pasadena to create the third version of “Kirby’s list” — a compendium of the most important unsolved problems in topology, the study of deformable shapes.