In geometry

Optimization also applies to geometric contexts. Nature was the first to seek it, whether in the shape of honeycomb cells or in that of certain landforms shaped by water or wind. Mathematicians, too, have devoted themselves to it, now using the tools of differential calculus, which have supplanted the ancient methods to the point of making geometry unrecognizable. The very questions themselves have been transformed by the increased efficiency offered by these methods. But not everything reduces to differential calculus. When combinatorial aspects intrude, problems can prove arduous, to the point that certain seemingly simple statements, like that of the Heilbronn triangles, still resist the sagacity of researchers.