The weak type (1,1) bounds for the maximal function associated to cubes grow to infinity with the dimension

Let M-d be the centered Hardy-Littlewood maximal function associated to cubes in R-d with Lebesgue measure, and let c(d) denote the lowest constant appearing in the weak type (1, 1) inequality satisfied by M-d. We show that c(d)->infinity as d ->infinity, thus answering, for the case of cubes, a longstanding open question of E. M. Stein and J. O. Stromberg.