Perceiving structure in mathematical expressions

Despite centuries of using mathematical notation, surprisingly little is known about how mathematicians perceive equations. The present experiment provides an initial step in understanding what sort of internal representation is used by experienced mathematicians. In particular, we examined if mathematical syntax plays a role in how mathematicians encode algebraic equations, or if just a simple memory strategy is used. Participants in the experiment performed a memory recognition task that required them to identify both well-formed (syntactically correct) and non-well-formed sub-expressions of equations. As hypothesised, performance was significantly better for well-formed sub-expressions, a result which suggests that mathematicians do indeed use an internal representation based on mathematical syntax to encode equations.