It is shown that educated adults routinely make errors in placing stimuli into familiar, well-defined categories such as triangle and odd number. Scalene triangles are often rejected as instances of triangles and 798 is categorized by some as an odd number. These patterns are observed both in timed and untimed tasks, hold for people who can fully express the necessary and sufficient conditions for category membership, and for individuals with varying levels of education. A sizeable minority of people believe that 400 is more even than 798 and that an equilateral triangle is the most "trianglest" of triangles. Such beliefs predict how people instantiate other categories with necessary and sufficient conditions, e.g., grandmother. I argue that the distributed and graded nature of mental representations means that human algorithms, unlike conventional computer algorithms, only approximate rule-based classification and never fully abstract from the specifics of the input. This input-sensitivity is critical to obtaining the kind of cognitive flexibility at which humans excel, but comes at the cost of generally poor abilities to perform context-free computations. If human algorithms cannot be trusted to produce unfuzzy representations of odd numbers, triangles, and grandmothers, the idea that they can be trusted to do the heavy lifting of moment-to-moment cognition that is inherent in the metaphor of mind as digital computer still common in cognitive science, needs to be seriously reconsidered.