Imagine trying to teach a computer to solve complex math problems, not by cramming its memory with endless formulas, but by giving it the ability to create its own practice questions. That’s the innovative approach explored by researchers in their paper "JiuZhang3.0: Efficiently Improving Mathematical Reasoning by Training Small Data Synthesis Models." Traditionally, boosting AI's math skills involved either training massive language models (LLMs) on mountains of math textbooks or using powerful AIs like GPT-4 to generate tons of practice problems. Both methods are expensive and resource-intensive. The JiuZhang3.0 research takes a different tack. Instead of using a huge model, they train a smaller LLM to generate math problems. This smaller model learns by mimicking GPT-4, which is fed carefully crafted prompts based on different education levels, from grade school to college. This ensures the generated problems cover a wide range of mathematical concepts and difficulty. To further refine the process, the researchers use a clever technique called 'gradient-based influence estimation.' This helps them identify the most valuable math texts, the ones that will be most helpful in training the smaller LLM. The result? JiuZhang3.0 requires significantly fewer resources than previous methods, needing only a fraction of the GPT-4 API calls and training data. Yet, it achieves state-of-the-art performance on various math reasoning datasets, outperforming even larger, more resource-intensive models. This research opens exciting new avenues for developing more efficient and cost-effective ways to train AI for complex tasks. By focusing on smarter data generation, we can unlock the potential of smaller models and make significant strides in AI capabilities without breaking the bank.