a $500 prize for anyone coming up with the solution to the distance problem, which has long considered one of the most challenging problems in geometric combinatorics.
Using that framework, Katz and Guth then implemented the polynomial ham sandwich theorem to create the new kind of cell decomposition that left points in the plane either in the interior of cells or on the walls of the cells.
I'm actually more impressed by advancements in mathematics than I am new technology inventions. It takes something pretty impressive to add to what we already have for math...