Humans share with many species a non-verbal system to estimate absolute quantity. This sense of number has been linked to the activity of quantity-selective neurons that respond maximally to preferred numerosities. With functional magnetic resonance imaging adaptation, we now show that populations of neurons in the human parietal and frontal cortex are also capable of encoding quantity ratios, or proportions, using the same non-verbal analog code as for absolute number. Following adaptation to visually presented constant proportions (specified by the ratio of line lengths or numerosities), we introduced novel relative magnitudes to examine the tuning characteristics of the population of stimulated neurons. In bilateral parietal and frontal cortex we found that blood oxygenation level-dependent signal recovery from adaptation was a function of numerical distance between the deviant proportion and the adaptation stimulus. The strongest effects were observed in the cortex surrounding the anterior intraparietal sulcus, a region considered pivotal for the processing of absolute magnitudes. Overall, there was substantial overlap of frontoparietal structures representing whole numbers and proportions. The identification of tuning to non-symbolic ratio stimuli, irrespective of notation, adds to the magnitude system a remarkable level of sophistication by demonstrating automatic access to a composite, derived quantitative measure. Our results argue that abstract concepts of both absolute and relative number are deeply rooted in the primate brain as fundamental determinants of higher-level numerical cognition.

Prefrontal cortex (PFC) and posterior parietal cortex are important for maintaining behaviorally relevant information in working memory. Here, we challenge the commonly held view that suppression of distractors by PFC neurons is the main mechanism underlying the filtering of task-irrelevant information. We recorded single-unit activity from PFC and the ventral intraparietal area (VIP) of monkeys trained to resist distracting stimuli in a delayed-match-to-numerosity task. Surprisingly, PFC neurons preferentially encoded distractors during their presentation. Shortly after this interference, however, PFC neurons restored target information, which predicted correct behavioral decisions. In contrast, most VIP neurons only encoded target numerosities throughout the trial. Representation of target information in VIP was the earliest and most reliable neuronal correlate of behavior. Our data suggest that distracting stimuli can be bypassed by storing and retrieving target information, emphasizing active maintenance processes during working memory with complementary functions for frontal and parietal cortex in controlling memory content.

Although the concept of whole numbers is intuitive and well suited for counting and ordering, it is with the invention of fractions that the number system gained precision and flexibility. Absolute magnitude is encoded by single neurons that discharge maximally to specific numbers. However, it is unknown how the ratio of two numbers is represented, whether by processing numerator and denominator in separation, or by extending the analog magnitude code to relative quantity. Using functional MRI adaptation, we now show that populations of neurons in human fronto-parietal cortex are tuned to preferred fractions, generalizing across the format of presentation. After blood oxygen level-dependent signal adaptation to constant fractions, signal recovery to deviant fractions was modulated parametrically as a function of numerical distance between the deviant and adaptation fraction. The distance effect was invariant to changes in notation from number to word fractions and strongest in the anterior intraparietal sulcus, a key region for the processing of whole numbers. These findings demonstrate that the human brain uses the same analog magnitude code to represent both absolute and relative quantity. Our results have implications for mathematical education, which may be tailored to better harness our ability to access automatically a composite quantitative measure.

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