Image Credit & Copyright: John Davis
quote for the day------------------------------------
"To develop a complete mind:
Study the science of art;
Study the art of science.
Learn how to see.
Realize that everything
... connects to everything else." - Leonardo da Vinci
Not much thought for the day from me. But, in connection with my pointing out Gelfond's representation theory, I found this recently.
and i'll link to the other one here,
Asymptotics of number fields (Part 2)
Maybe I havn't seen enough lectures, but this lecture seems unusually clear. Even if you're not a mathematician, I think one should view this and see the real exciting mathematics.
As I remarked about Hermann Weyl reopening the invariance theory field after David Hilbert's famous finite basis theorem, so likewise, this guy might be making an area of mathematics that seemed more of a curiosity or dead end in octonians. He also points out at least that his work has applications to (non) commutative algebras. In algebra there was two ways of generalizing; one way led to invariance theory, the other to Galois theory and abstract algebra in general. Emmy Noether in the early 1900s combined both and generalized both. But, then came Lie theory of Hermann Weyl again, and lots of mathematicians for a long time have often said that today, Lie algebra replaces all that algebra in importance. I'd like to note that like the way the Calculus unifies, generalizes much of algebra, geometry, trigonometry, logarithms that mathematicians struggled with before the Calculus, Lie theory does likewise with Abstract algebra in general. Well, here you can see some of the exciting frontiers of mathematics.
----------------------------crazy science/technology for the day
There's a whole bunch,
protein origami , Paul Rothemund is famous for making dna-origami approach to dna-nanotechnology. Now, we have protein origami. Protein origami could allow for harder molecular machine parts and the ability to make arbitrary chemical reactions. If you know enough about nano-manufacturing, you should get excited about this. Dna-nanotech can still be used as a scaffold for these things.