Some researchers estimate that as many as one-third of cancers picked up by screening would not be fatal even if left untreated. But right now, nobody knows which ones.

So what are women supposed to do?

…Hoping to make sense of it all, I consulted several experts. All said mammograms were still important — after all, breast cancer kills 40,000 women a year in this country — but they differed about who really needed them and how often. All agreed that research was badly needed to figure out how to tell dangerous tumors from the so-called indolent ones…

Dr. Formenti said the emphasis on screening by groups like the cancer society might have misled the public into thinking that screening could prevent cancer. “It’s a giant misconception,” she said. “…I have to confess that I’m happy if the public gets offended or infuriated” by the debate…"I want taxpayers to say: ‘You have no clarity. Study it. Stop telling us you are a good girl if you get a mammogram.’ ”