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Complex reasoning is fundamental to human intelligence and plays a crucial role in advancing education, science, and technology. This talk explores the development of language model systems that exhibit robust mathematical reasoning and facilitate scientific reasoning, marking a significant step toward general artificial intelligence. We introduce novel multi-modal and knowledge-intensive benchmarks designed to assess the reasoning capabilities of large language models (LLMs) and vision-language models (VLMs) in real-world scenarios, including those involving visual data, tabular information, and scientific applications. The talk highlights recent advancements in mathematical reasoning within visual contexts and addresses key unresolved challenges. Additionally, we present cutting-edge retrieval and tool-augmented algorithms that significantly enhance LLM performance in mathematical reasoning tasks. Finally, we explore how agentic systems, leveraging test-time optimization and external tools, can further advance mathematical reasoning and scientific discovery.