Math-Life Balance - Algebraic K-Theory


The first time someone got a Fields Medal for a definition! See Daniel Quillen. I watched some of these and always found myself floundering after about a minute or so, ... I should have watched this one first.

There is an amazing gallery of graphs of algebraic surfaces here: https://www.imaginary.org/gallery/herwig-hauser-classic The surfaces are just the 3D coordinates of a set of points (x,y,z) which satisfy some equation. For example the set {(x,y,z)∈ℝ^3 : x^2+y^2+z^2=1} is the surface of a sphere which includes irrational points such as (1/√3,1/√3,1/√3). These shapes are called algebraic varieties: "Classically, an algebraic variety is defined as the set of solutions of a system of polynomial equations over the real or complex numbers." So the subject of Algebraic Geometry seems to hinge on the idea of closed fields (such as the rationals or the reals) when they are considered as the domains of functions which represent systems of polynomial equations and questions about the structure of vector spaces over these fields.

Images by Herwig Hauser: Licence Creative Commons BY-NC--SA-3.0

It started out well! I liked this idea of group completion. Janet was talking about the idea the other week: Janet Axelrud and Roger Penrose on Singularities and Gabriele Carcassi on Quantum States. It's always astonishing to me how my brain can contain three or more distinct meanings for one word (like Variety, for example!) and never even notice that these are the same word, because the meanings seem so distinct! See  Janet Akselrud and The Museum of Ideas - Creating the Dictionary of the Future. Then for some more Variety see Daniel Tubbenhauer's Algebraic Geometry Syllabus, Julian Barbour - Complexity as Time, Aristotle on God and Lana Del Rey in Variety!

It was this video posted yesterday that prompted me to go back and look at this weird stuff again:


So then I watched this one about mushrooms:


At some universities they don't go pick mushrooms in the forest, they just farm their own, ...

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I was listening to London Grammar's album The Greatest Love whilst doing this, ...

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