The time urgency to achieve the sustainable development goals (SDGs) calls for a paradigm shift in science to move beyond system boundaries and produce relevant knowledge that is both practical and broadly actionable. Through investigating deficiencies, tensions and disagreements within science and science systems in supporting the SDGs, we characterize major demand for scientific shifts in its focus, scope, processes, and the role of scientists, and suggestions for strengthening the capacity for science to generate disruption. We then highlight controversies and tradeoffs in technological vs. societal advancement, interdisciplinary vs. disciplinary complementarity, global vs. local knowledge creation and innovation, and scientific neutrality vs. objectivity. Deeper understanding and debate around these controversies is indispensable to create a common vision and safe space for transdisciplinary education and collaboration to systematically improve the “disruptiveness” of science in solving global complex challenges of this century. These are also required to ensure the coexistence and complementarity of distinct epistemic communities.