A grievance expressed by some PhD students and Postdocs is that science works like a pyramid scheme: Young scientists are encouraged to invest into building scientific careers although the chances at remaining in science are extremely slim. This issue is investigated quantitatively by connecting it with the way authorship on papers is distributed. I analyzed a large bibliographic dataset made available by Microsoft under the name Academic Graph to create a histogram with the number of articles an author produces per year. The histogram has the shape of a pyramid, and different layers in it correlate with positions in the academic hierarchy. The super-prolific authors at the top of the pyramid with more than 40 publications per year are usually heads of large institutes with many subgroups and large numbers of PhD students, while the bottom of the pyramid is populated by PhD students and Postdocs with less than 5 publications per year. The mechanism that allows 'manager scientists' to appropriate publications generated in their sphere of influence is related to other issues, such as the evaluation of scientific performance based on scientometric indicators and the lenient enforcement of authorship rules. A new index, the Ponzi factor, is proposed to quantify this phenomenon.