## A letter from an old friend

Among the letters from the 7/31 issue of the New Yorker, under “Cultural Studies”, this erudite letter from Stephen Isard of Philadelphia PA, about Peter Hessler’s piece “A Double Edcation” in the 7/3 issue:

One of the math problems that Hessler’s daughters attempt to solve, as part of their challenging Chinese curriculum, asks them to find the smallest number that leaves the remainders 2, 3, and 4 when divided respectively by 3, 4, and 5. Is this a trick question of the sort that Hessler depicts his children completing in third-grade math class, the kind designed to trip students up? No. What he describes is a simple introduction to a celebrated mathematical theorem known in the English-speaking literature as the Chinese remainder theorem, which guarantees that any such problem has a solution, so long as none of the divisors (in this case, 3, 4, and 5) have a factor in common other than 1. The theorem has been attributed to the Chinese mathematical text “Sunzi Suanjing,” which was completed between the third and fifth centuries A.D., and it plays an important role in Kurt Gödel’s proof of his incompleteness theorem. Applied here, it gives the answer to the twins’ problem as 59.

Wow, Steve Isard is one of my oldest friends, going back to Cambridge MA in the early 1960s. We collaborated on some little papers in mathematics then, and eventually Steve and his wife Phoebe Acheson Isard (long gone, alas) became close friends with me and my wife Ann Daingerfield Zwicky (also long gone, alas). What a delight to see him still in the education business!