Transforming dense, unstructured text into interpretable tables—commonly referred to as Text-to-Table generation—is a key task in information extraction. Existing methods often overlook what complex information to extract and how to infer it from text. We present Map&Make, a versatile approach that decomposes text into atomic propositions to infer latent schemas, which are then used to generate tables capturing both qualitative nuances and quantitative facts. We evaluate our method on three challenging datasets: Rotowire, known for its complex, multi-table schema; Livesum which requires numerical aggregation; and Wiki40 which require open text extraction from mulitple domains. By correcting hallucination errors in Rotowire, we also provide a cleaner benchmark. Our method shows significant gains in both accuracy and interpretability across comprehensive comparative and referenceless metrics. Finally, ablation studies highlight the key factors driving performance and validate the utility of our approach in structured summarization. Code and data are available at: https://coral-lab-asu.github.io/map-make.