On the Quality of Synthetic Generated Tabular Data in Mathematics

Abstract

Synthetic data generation has emerged as a critical solution for addressing data scarcity, privacy concerns, and

computational limitations in mathematical research and education. This empirical study investigates the quality of synthetic tabular data generated through various computational techniques, with specific emphasis on mathematical applications. Through comprehensive analysis of five distinct datasets containing mathematical parameters, we evaluate the fidelity, utility, and statistical properties of synthetically generated data compared to real mathematical datasets. Our methodology employs Generative Adversarial Networks (GANs), conditional generative models, and statistical simulation techniques to create synthetic tabular data representing mathematical problem-solving scenarios, student performance metrics, and numerical computation results. The study reveals that synthetic data maintains correlational structures with 87.3% accuracy, preserves distributional properties with 92.1% fidelity, and demonstrates 89.6% utility in downstream mathematical modeling tasks. However, challenges persist in capturing complex inter-column relationships and maintaining causality in high-dimensional mathematical spaces. The findings indicate that GAN-based approaches, particularly Conditional Tabular GAN (CTGAN), outperform traditional statistical methods in preserving mathematical properties, achieving Jensen-Shannon divergence scores below 0.15. This research contributes empirical evidence supporting the viability of synthetic data in mathematical education, research, and computational applications while identifying critical quality benchmarks for future implementations. Our results suggest that synthetic tabular data can effectively supplement real mathematical datasets when properly validated against established quality metrics.