In mathematics, a simple problem is often not what it seems. Earlier this summer, Quanta reported on one such problem: What is the smallest area that you can sweep out while rotating an infinitely thin needle in all possible directions? Spin it around its center like a dial, and you get a circle. But rotate it more cleverly, and you can cover an arbitrarily small fraction of space. If you don’t...

# A Tower of Conjectures That Rests Upon a Needle

In mathematics, a simple problem is often not what it seems. Earlier this summer, Quanta reported on one such problem: What is the smallest area that you can sweep out while rotating an infinitely thin needle in all possible directions? Spin it around its center like a dial, and you get a circle. But rotate it more cleverly, and you can cover an arbitrarily small fraction of space. If you don’t...