Natural language processing (NLP) for low-resource languages remains fundamentally constrained by the lack of textual corpora, standardized orthographies, and scalable annotation pipelines. While recent advances in large language models have improved cross-lingual transfer, they remain inaccessible to underrepresented communities due to their reliance on massive, pre-collected data and centralized infrastructure. In this position paper, we argue for a paradigm shift toward open-ended, interactive language discovery, where AI systems learn new languages dynamically through dialogue rather than static datasets. We contend that the future of language technology, particularly for low-resource and under-documented languages, must move beyond static data collection pipelines toward interactive, uncertainty-driven discovery, where learning emerges dynamically from human-machine collaboration instead of being limited to pre-existing datasets. We propose a framework grounded in joint human-machine uncertainty, combining epistemic uncertainty from the model with hesitation cues and confidence signals from human speakers to guide interaction, query selection, and memory retention. This paper is a call to action: we advocate a rethinking of how AI engages with human knowledge in under-documented languages, moving from extractive data collection toward participatory, co-adaptive learning processes that respect and empower communities while discovering and preserving the world's linguistic diversity. This vision aligns with principles of human-centered AI and participatory design, emphasizing interactive, cooperative model building between AI systems and speakers.