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Peer review is an integral component of contemporary science. While peer review focuses attention on promising and interesting science, it also encourages scientists to pursue some questions at the expense of others. Here, we use ideas from forecasting assessment to examine how two modes of peer review—ex ante review of proposals for future work and ex post review of completed science—motivate scientists to favor some questions instead of others. Our main result is that ex ante and ex post peer review push investigators toward distinct sets of scientific questions. This tension arises because ex post review allows investigators to leverage their own scientific beliefs to generate results that others will find surprising, whereas ex ante review does not. Moreover, ex ante review will favor different research questions depending on whether reviewers rank proposals in anticipation of changes to their own personal beliefs or to the beliefs of their peers. The tension between ex ante and ex post review puts investigators in a bind because most researchers need to find projects that will survive both. By unpacking the tension between these two modes of review, we can understand how they shape the landscape of science and how changes to peer review might shift scientific activity in unforeseen directions.