So far, i've experienced a little freezing of the video; but, then the video starts up again; hopefully, it's just me and my computer! The hodge conjecture lecture here enforces an observation of mine(which I havn't shared till now) is how the major problems of contemporary mathematics seems to me is the translating and solving of problems(whether algebraic, geometric, or analyses) from geometry or algebra to analyses and back. Either using analyses to solve algebra and geometric problems or the other way around. That doesn't sound to me to communicate the point very well. Maybe an example gives a better idea; for instance, the calculating of algebraic roots from derivatives. Likewise, in my reading(i've tried to read about everything first before putting pencil to paper first; to give me intuitions that maybe would allow me to digest things when I finally try to put pensil to paper; well, i don't know how well that's worked! It's allowed me this insight in this post and my ideas about the nature and origin of mathematical knowledge though!). Anyways, throughout mathematics, whether functional analyses, or topology, I can't help noticing this translating or jumping from one field to another and then translating back. It seems abstract till you do something like solve roots of algebraic equations with comparable ease. Likewise, mathematicians do likewise it seems to me throughout all higher mathematics; it is the major activity. And, you'll see this in this lecture of the hodge conjecture.
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