Why Mathematicians Can't Find the Hay in a Haystack [Quanta Magazine]

Dated Sep 17, 2018; last modified on Mon, 05 Sep 2022

Why Mathematicians Can’t Find the Hay in a Haystack. Kevin Hartnett. www.quantamagazine.org . Sep 17, 2018.

Irrational numbers occupy most of the number line. If you were to pick a number on the number line at random, there is literally a 100% chance that it will be irrational (probabilities with inifinities are spooky). Yet, we almost never encounter irrational numbers for we can’t write them down.

The shapes we know best - lines, parabolas, circles, spheres - are the needles, for they can be expressed by simple equations. An overwhelming number of shapes resist such elegance. Because you can’t write down their equations, it’s hard to establish that even one of them exists.

It’s as if you were convinced the oceans were filled with water but every time you took a sample, you came up with something else - a shell, a rock, a plant. Yet to start to believe your hypothesis was correct, you’d hardly need to empty the sea.