Five years ago, Bill Gates invited the world’s scientists to submit ideas for tackling the biggest problems in global health. About 1,600 proposals came in, and the top 43 were so promising that the Bill & Melinda Gates Foundation made $450 million in five-year grants. They recently brought the scientists to Seattle to assess the results and decide on further funding. In an interview, Mr. Gates sounded somewhat chastened, saying several times, “We were naïve when we began.” He underestimated, he said, how long it takes to get a new product from the lab to clinical trials to low-cost manufacturing to acceptance in third-world countries.