As any child knows, the first step in counting is summing up individual elements, yet the brain mechanisms responsible for this process remain obscure. Here we show, for the first time, that a population of neurons in the lateral intraparietal area of monkeys encodes the total number of elements within their classical receptive fields in a graded fashion, across a wide range of numerical values (2-32). Moreover, modulation of neuronal activity by visual quantity developed rapidly, within 100 ms of stimulus onset, and was independent of attention, reward expectations, or stimulus attributes such as size, density, or color. The responses of these neurons resemble the outputs of "accumulator neurons" postulated in computational models of number processing. Numerical accumulator neurons may provide inputs to neurons encoding specific cardinal values, such as "4," that have been described in previous work. Our findings may explain the frequent association of visuospatial and numerical deficits following damage to parietal cortex in humans.