The increasing availability of large-scale datasets has fueled rapid progress across many scientific fields, creating unprecedented opportunities for research and discovery while posing significant analytical challenges. Recent advances in large language models (LLMs) and AI agents have opened new possibilities for human-AI collaboration, offering powerful tools to navigate this complex research landscape. In this paper, we introduce SciSciGPT, an open-source, prototype AI collaborator that uses the science of science as a testbed to explore the potential of LLM-powered research tools. SciSciGPT automates complex workflows, supports diverse analytical approaches, accelerates research prototyping and iteration, and facilitates reproducibility. Through case studies, we demonstrate its ability to streamline a wide range of empirical and analytical research tasks while highlighting its broader potential to advance research. We further propose an LLM Agent capability maturity model for human-AI collaboration, envisioning a roadmap to further improve and expand upon frameworks like SciSciGPT. As AI capabilities continue to evolve, frameworks like SciSciGPT may play increasingly pivotal roles in scientific research and discovery, unlocking further opportunities. At the same time, these new advances also raise critical challenges, from ensuring transparency and ethical use to balancing human and AI contributions. Addressing these issues may shape the future of scientific inquiry and inform how we train the next generation of scientists to thrive in an increasingly AI-integrated research ecosystem.