@YCor This is the usual sense of algorithm. The point is that the algorithm has to recognize whether a given finite presentation is of a 3-manifold group. Contrast this with the problem of recognizing 4-manifold groups, which is trivially solvable because any finitely-presented group is the group of a 4-manifold. As you point out, the corresponding problem for 0-manifold groups is clearly not solvable.

Grothendieck was not the first eminent mathematician to give 57 as an example of a prime. Hermann Weyl (American Mathematical Monthly 1951, p.532) mentioned Goldbach's conjecture about "primes of the smallest possible difference 2, like 57 and 59."

@Yosmite Sam A good reference is Silverman and Tate's Rational Points on Elliptic Curves, which starts elementary and gets quite sophisticated.

@Wojowu Oops, sorry -- I failed to notice the nonsingular condition.

@Wojowu The first problem in the paper is the membership problem, which has the mortality problem as the special case $M=$ zero matrix. So by solving the membership problem they also solve the mortality problem for $2\times 2$ matrices.

Is this it? (By the way Cherry was one of my teachers in the 1960s. I recall being told by a fellow student that Cherry mentioned some fiendishly complicated result of his own in class.) books.google.co.uk/…