geometry – Konrad Voelkel's Blog – Mathemagically

Is it possible to prove the Quillen-Suslin theorem analogous to the classical theorem on vector bundles over contractible spaces via representing the vectorbundle-up-to-iso-functor in the homotopy category by infinite Grassmannians?

A solution to exercises 3.17.4, 3.17.5, 3.9.5, 3.28.3 in Jet Nestruev: "Smooth Manifolds and Observables", Springer, 2003 and similar problems, along explanations.

On dimensions-math.org you can see a whole bunch of before unseen geometry videos introducing 2-, 3- and 4-dimensional space, complex numbers and even more to the non-mathematician.

Mathematics for non-mathematicians: I recommend a talk by Dan Freed, "The Hodge Conjecture". You'll get a glimpse on some central ideas of geometry from this talk, even if you're not interested in the Hodge Conjecture.