> In this blog post I will give my personal view on the recent counterexamples to the unit distance conjecture and sum-product conjecture over the reals (see [90] and [52] respectively). My goal is to sketch the constructions and try and give some intuition as to where they came from and why they work. *My main target audience is the me-of-a-month-ago*

Thomas Bloom is a world-class mathematician working at the frontier of his field. He explicitly did not write this for you, and your stopping reading it is fine.

Size of a finite set. It’s common notation in this field.

I stopped reading earlier, when they used superscript without explaining its meaning. Its clearly meant for someone with more domain expertise than me, with my hazy recollections of college math.