Recent studies provide compelling evidence for the idea that creative thinking draws upon two kinds of processes linked to distinct physiological features, and stimulated under different conditions. In short, the fast system-I produces intuition whereas the slow and deliberate system-II produces reasoning. System-I can help see novel solutions and associations instantaneously, but is prone to error. System-II has other biases, but can help checking and modifying the system-I results. Although thinking is the core business of science, the accepted ways of doing our work focus almost entirely on facilitating system-II. We discuss the role of system-I thinking in past scientific breakthroughs, and argue that scientific progress may be catalyzed by creating conditions for such associative intuitive thinking in our academic lives and in education. Unstructured socializing time, education for daring exploration, and cooperation with the arts are among the potential elements. Because such activities may be looked upon as procrastination rather than work, deliberate effort is needed to counteract our systematic bias.