Review: Huge Numbers by Richard Elwes

There’s a story about a child mathematician talking to an older mathematician and saying “I think the biggest number is a TRILLION.” The grown-up says “OK, but what about a trillion and one?” The child mathematician looks crestfallen, but only for a moment. “Oh. At least I was close!” If you’ve ever interacted with mathematically-inclined children, you’ll have experienced at least the occasional obsession with big numbers, if only so they can say “I hate you RAYO’S NUMBER times, no backsies”. For the more ancient mathematician, the fascination tends to wear off: as Sam Hartburn notes, “infinity’s pretty big” – no matter how enormous the number you can imagine or write down, most numbers (in some sense) tower over it. A trillion is effectively zero compared to a googolplex, \( 10^{10^{100}} \). A googolplex is tiny compared to Graham’s number. \( BB(6) \) scrapes Graham’s number off of its shoe with a look of mild distaste. As a consequence, Richard Elwes‘s Huge Numbers initially…