Scientific breakthroughs often emerge from synthesizing prior ideas into novel contributions. While language models (LMs) show promise in scientific discovery, their ability to perform this targeted, literature-grounded synthesis remains underexplored. We introduce insight anticipation, a generation task in which a model predicts a downstream paper's core insight from its foundational parent papers. To evaluate this capability, we develop GiantsBench, a benchmark of 17k examples across eight scientific domains, where each example consists of a set of parent papers paired with the core insight of a downstream paper. We evaluate models using an LM judge that scores similarity between generated and ground-truth insights, and show that these similarity scores correlate with expert human ratings. Finally, we present GIANTS-4B, an LM trained via reinforcement learning (RL) to optimize insight anticipation using these similarity scores as a proxy reward. Despite its smaller open-source architecture, GIANTS-4B outperforms proprietary baselines and generalizes to unseen domains, achieving a 34% relative improvement in similarity score over gemini-3-pro. Human evaluations further show that GIANTS-4B produces insights that are more conceptually clear than those of the base model. In addition, SciJudge-30B, a third-party model trained to compare research abstracts by likely citation impact, predicts that insights generated by GIANTS-4B are more likely to lead to higher citations, preferring them over the base model in 68% of pairwise comparisons. We release our code, benchmark, and model to support future research in automated scientific discovery.