Mathematical problem solving remains a challenging test of reasoning for large language and multimodal models, yet existing benchmarks are limited in size, language coverage, and task diversity. We introduce MathNet, a high-quality, large-scale, multimodal, and multilingual dataset of Olympiad-level math problems together with a benchmark for evaluating mathematical reasoning in generative models and mathematical retrieval in embedding-based systems. MathNet spans 47 countries, 16 languages, and two decades of competitions, comprising 30,676 expert-authored problems with solutions across diverse domains. In addition to the core dataset, we construct a retrieval benchmark consisting of mathematically equivalent and structurally similar problem pairs curated by human experts. MathNet supports three tasks: (i) mathematical problem solving, (ii) problem retrieval, and (iii) retrieval-augmented problem solving (math RAG). Experimental results show that even state-of-the-art reasoning models (78.4% for Gemini-3.1-Pro and 69.3% for GPT-5) remain challenged, while embedding models struggle to retrieve equivalent problems. We further show that RAG performance is highly sensitive to retrieval quality; for example, DeepSeek-V3.2-Speciale achieves gains of up to 12%, obtaining the highest scores on the benchmark. MathNet provides the largest high-quality Olympiad dataset together with the first benchmark for evaluating mathematical problem retrieval, and we publicly release both the dataset and benchmark at https://mathnet.mit.edu.