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What is the ultimate limiting nutrient in the ocean? The dominant theory, which was first proposed by Redfield and later formalized by Tyrrell[1, 2], states that despite the scarcity of fixed nitrogen (N) in the surface ocean, phosphorus (P) availability ultimately determines primary productivity. Two recent findings directly challenge the assumptions of the Redfield-Tyrrell paradigm: the discovery of systematic variations of phytoplankton cellular N:P:Fe and widespread iron-limitation of phytoplankton. Here we use a simple model of nitrogen, phosphorus, and iron (Fe) cycling to show how the resource demand ratios and biogeography of phytoplankton interact with external resource supply ratios to govern nutrient cycling and primary productivity. We find that all three nutrients can limit global primary productivity, and that the ratio of geochemical supply to biological demand of each nutrient in each ocean region determines the limiting nutrients, with nitrogen N fixation providing a mechanism for the cycles to interact. These results have important consequences for our understanding of biogeochemical cycles, ocean-atmosphere interactions, marine ecology, and the response of ocean ecosystems to climate change. Our work demonstrates the importance of resource ratios and suggests that future studies of the physiological and geochemical regulation of these ratios are indispensable to building accurate theories and future predictions of nutrient cycling and primary productivity.