Expert mathematicians experience multi-modal hallucinations that develop across time

By exploring the boundaries of systems, we learn about their capacities and their forms. We believe that studying edge cases of what human cognition can do is an important supplement to studying prototypical human cognition. This paper describes a class of experiences we call induced sensory experiences, which we think are (1) rare, (2) trainable, and (3) singularly effective in certain kinds of problem solving. People consistently report non-drug-induced hallucination-like experiences in religious and spiritual contexts. These sensory experiences are often induced through explicit training and practice designed, in part, to invoke them. Here, we report the results of a survey extending this phenomenon to the case of professional and highly trained mathematicians. We document the prevalence of powerful, sensory or quasi-sensory experiences of non-physical objects. In short, we find them to be extremely common: Individual mathematicians nearly universally describe experiences and activities that closely match the pattern of induced sensory experiences. These sensory experiences can be seen as an achievement of mathematical thinking: they tend to develop with time and experience in a domain, and many participants find them to be unique in some way to mathematical thinking. These experiences were not reported to be rare. Mathematicians reported having meaningful amounts of control over their visualization. Finally, explicit belief in the ‘reality’ of these objects was largely unrelated to any measures of sensory vividness or control. Altogether, we believe this work demonstrates how humans are able to build complex and abstract reasoning out of sensorimotor components through extensive training.