His speech was met with skepticism in both Congress and the Kremlin, but not for the right reasons. Critics and doubters in both countries argued that there were substantial political roadblocks to achieving this goal. In the Kremlin, America’s Europe-based missile defense system, which Russia has fiercely opposed, seems to be a stumbling block. In Congress there is broad resistance to the idea of Mr. Obama’s negotiating arms reductions without approval from the Senate.

But politics aside, several fundamental questions about the president’s speech remain: Why have we waited this long for such a proposal? Why are we stopping there? And, perhaps most important, why doesn’t the United States simply make the reduction on its own? Why do we need to negotiate with Russia?

It is hard to seriously suggest that from a national-security standpoint, 1,000 warheads are not enough to protect the United States. Such an arsenal is literally overkill, sufficient to destroy every major population center on the planet outside of our borders.

We would lose no real strategic security by such a reduction. The New Start treaty called for cuts in the number of deployed strategic warheads to 1,550. But even these levels are an anachronism, left over from the cold war. The president’s proposed level of 1,000 warheads would still provide an equivalent level of mutually assured destruction even against Russia, were it still a cold war aggressor. In the current climate, when more likely possible aggressors have fewer than 10 percent of this level, 1,000 weapons is more than adequate.

If we wish to convince countries like Iran that the development of nuclear weapons is not in their best interest, we need to demonstrate that maintaining or enhancing our own arsenal is not in our interest.

This is particularly important now, not just to dissuade nations like Iran from building nuclear arsenals, and others, like North Korea, from adding to theirs, but also to stem what may be a much more worrisome and unstable situation in Pakistan and India. With each country holding estimated stockpiles of around 100 weapons, and as historic tensions continue to flare between the two, the possibility of a nuclear conflagration there remains very real.

The effects of even a limited nuclear war between Pakistan and India would not be confined to that region. Scientific studies by the physicists Alan Robock of Rutgers University and Owen B. Toon of the University of Colorado, Boulder, and their colleagues found that a nuclear war in South Asia involving the detonation of even 100 Hiroshima-size weapons, far smaller than those in their arsenals, could kill as many as 20 million people from the blasts and resulting fires and radiation, and generate so much smoke that it would block 7 to 10 percent of the sunlight reaching the earth for at least a decade.