What is the nature of discovery? As a human being and a physicist, I can only observe one mind at work first-hand. This mind accepts every new scrap as a discovery, whether it originates in the external world of knowledge or springs from an internal process. To explore the nature of discovery from the point of view of the inner observer, I chose to turn over past experiences, fitting together days on which years of determined and dogged plodding resulted in a finished equation, or finally, a coherent assembly of disparate ideas gave the clue to why storm damage in breakwaters is like a phase change in liquid crystals. Old, unfashionable methods are suddenly useful with new computer architectures. Theory, experiment, observation, and simulation fit together as aids to thinking. The properties of complex systems can provide intuitive insight into the social science of science. We will need every ability to assemble the puzzle pieces in the coming years to discover how to extricate the planet from the difficulties in which we have placed it: as an observer and actor, I suggest that the evolution of human thinking, and of aids to thinking, are critical.

Human beings form beliefs about the way the world works according to the information that is available to them, their processing ability, and their existing knowledge. However, in such an information-rich world, they sometimes trust their intuitive beliefs rather than their reflective ones. Intuitive beliefs tend to have a bad press in our modern world, as they are often regarded as suboptimal and even erroneous. In the present chapter, we aim to restore their reputation. First, we provide an overview of the two types of beliefs, in the light of dual-process theories whereby people can engage in either fast, almost automatic thinking processes, or slower, more deliberative ones. We then identify contexts in which intuitive beliefs provide compelling cues for daily human activities and sometimes outperform reflective beliefs. Finally, we discuss how intuitive beliefs can even be beneficial for reasoning and learning.