A scientist may publish tens or hundreds of papers over a career, but these contributions are not evenly spaced in time. Sixty years of studies on career productivity patterns in a variety of fields suggest an intuitive and universal pattern: Productivity tends to rise rapidly to an early peak and then gradually declines. Here, we test the universality of this conventional narrative by analyzing the structures of individual faculty productivity time series, constructed from over 200,000 publications and matched with hiring data for 2,453 tenure-track faculty in all 205 PhD-granting computer science departments in the United States and Canada. Unlike prior studies, which considered only some faculty or some institutions, or lacked common career reference points, here we combine a large bibliographic dataset with comprehensive information on career transitions that covers an entire field of study. We show that the conventional narrative confidently describes only one-fifth of faculty, regardless of department prestige or researcher gender, and the remaining four-fifths of faculty exhibit a rich diversity of productivity patterns. To explain this diversity, we introduce a simple model of productivity trajectories and explore correlations between its parameters and researcher covariates, showing that departmental prestige predicts overall individual productivity and the timing of the transition from first- to last-author publications. These results demonstrate the unpredictability of productivity over time and open the door for new efforts to understand how environmental and individual factors shape scientific productivity.