Is stacking oranges like a grocer does really the tightest way to pack spheres?
Stack identical spheres as densely as possible, the way a grocer piles oranges into a pyramid. Is there any arrangement, however irregular, that packs them more tightly than that in an infinite space?
Reveal the answer
No -- this is the Kepler conjecture, proposed by Johannes Kepler in 1611. It resisted proof for nearly four centuries until Thomas Hales completed a computer-assisted proof in 1998, running to over 250 pages of argument and code; it was formally verified by the Flyspeck project in 2014.