Why is $J$ often used to denote $\mathbb{N}$ or $\mathbb{Z}$ in older texts?
Solution 1:
Earliest Uses of Symbols of Number Theory mentions: "The second edition of Birkhoff and MacLane, Survey of Modern Algebra (1953) ... has J for integers." This answer to a secondary student's question says that is the earliest reference she can find and speculated the same thing as @Gerry.
Sorry, only answering because I don't have the reputation points yet to comment.