Bruce Riedel is a senior fellow at the Saban Center for Middle East Policy at the Brookings Institution. A career CIA officer, he has advised four presidents on Middle East and South Asian issues on the staff of the National Security Council.

IN APRIL, India launched a long-range missile capable of carrying a nuclear bomb deep into the Indian Ocean. The successful Agni missile test fulfilled India’s fifty-year quest to achieve the means of dispatching a nuclear weapon to Beijing. Just about fifty years ago, in October 1962, India fought a brief war against China in the Himalaya Mountains. India lost that war—and vowed it would acquire the capacity to deter Chinese aggression.

The Sino-Indian war also posed a crisis for America’s young president, John F. Kennedy, who had entered office determined to build a strong U.S. relationship with India. But his attention that fateful autumn was diverted to a more ominous crisis—the one involving Soviet efforts to place nuclear missiles in Cuba—that unleashed a dangerous nuclear face-off with the Soviet Union. Thus, Kennedy confronted two simultaneous crises, one far overshadowed by the other at the time and also later in history.

But Kennedy’s handling of the 1962 war—in the midst of a far graver national challenge—offers lessons today for those interested in the ongoing diplomatic conundrum posed by India and its mutually hostile neighbor, Pakistan....