False discoveries permeate science. A false lead can have significant economic and opportunity costs to the scientific enterprise. However, dismissing a true finding to chance can be a serious setback to scientific progress. How can we control and measure the chance of false-positive scientific results without hindering scientific discovery? The probability of a false-positive finding increases with the numbers of statistical tests and analyses. With recently expanding possibilities for mass data collection, concerns about the effects of multiplicities on false-positive discoveries in the scientific endeavor have increased; however, that awareness has not permeated evenly throughout all branches of science. The panel will consider the problems of statistical multiplicities in science, approaches for addressing these problems, and their implications for science. Through that lens, the current state of two specific scientific areas will be explored, health and the environment, with respect to the impact of false-positive findings. Statistical multiplicities abound whether searching the genome, studying scores of behavioral and lifestyle factors, or monitoring countless environmental exposures that may affect health. The role of new statistical approaches will be discussed, such as the false discovery rate for controlling false-positive findings as well as the impact of false-positive findings on science, policy, and society.