For most people, the term “busy beaver” brings to mind a tireless worker or (for the biologists among us) an absolutely vital ecosystem engineer . However, for mathematicians, “busy beaver” takes on a similar-yet-unique meaning. BB(1), which has just 1 state, necessitates the use of 25 Turing machines. BB(2) and BB(3) are 6 and 21 respectively, but BB(4) is 107 and takes seven billion different Turing machines to solve. “The Busy Beaver problem gives you a very concrete scale for pondering the frontier of mathematical knowledge,” computer scientist Tristan Stérin, who helped start the Busy Beaver Challenge in 2022, told New Scientist.