Artificial intelligence (AI) methods are poised to revolutionize intellectual work, with generative AI enabling automation of text analysis, text generation, and simple decision making or reasoning. The impact to science is only just beginning, but the opportunity is significant since scientific research relies fundamentally on extended chains of cognitive work. Here, we review the state of the art in agentic AI systems, and discuss how these methods could be extended to have even greater impact on science. We propose the development of an exocortex, a synthetic extension of a person's cognition. A science exocortex could be designed as a swarm of AI agents, with each agent individually streamlining specific researcher tasks, and whose inter-communication leads to emergent behavior that greatly extend the researcher's cognition and volition.