This post won’t have too much math, but mainly musings.
After a four month hiatus from research, it seems my dive back into the world of unknown math is being squandered by my ineptitude. My documentation of the progress made, and the comments in my code seems to be greatly lacking. I’ve spent a good chunk of time trying to recall progress.
I think one of the cooler things Bernstein polynomials can prove is that polynomials are dense (uniformly too IRCC) in continuous functions on a bounded domain. Durrett has a proof in his book using a probabilistic view, which seems much cleaner than an algebraic/analysis proof such as here.