Professional Doctorate Thesis
Challenging Mathematical Problems Designed to Evaluate Advanced AI Reasoning
by Dr. Tan Kwan Hong
Research Overview
This research focuses on evaluating the reasoning capabilities of advanced Artificial Intelligence (AI) systems using specially designed mathematical problems. The study presents six complex mathematical problems that test different types of reasoning, including symbolic reasoning, logical thinking, spatial reasoning, recursion, functional analysis, and probability. The main objective of the research is to assess how well AI systems can solve problems that require structured reasoning rather than simple pattern recognition.
The research is based on the idea that modern AI systems perform well in language processing and data analysis but still face challenges when solving multi-step mathematical and logical problems. Therefore, the author designed a set of mathematical problems that are not only computational but also require logical interpretation, constraints analysis, and step-by-step reasoning. These problems cover multiple areas of mathematics such as number theory, algebra, geometry, recursive sequences, functional equations, and combinatorics.
Each problem in the study is presented with a detailed solution and explanation. The solutions demonstrate different mathematical techniques such as recursive backtracking, modular arithmetic, geometric transformation analysis, functional identities, and probability counting methods. These solutions are intended to serve as benchmarks for testing AI reasoning performance and for training future AI reasoning models.
The study concludes that mathematical problem-solving remains an effective way to evaluate advanced AI reasoning abilities because such problems require structured thinking, rule-based logic, and multi-step reasoning processes. The research suggests that future AI benchmarking should include complex mathematical and logical problems to better measure true reasoning capabilities rather than simple information retrieval or pattern prediction.
Overall, this research contributes to the field of artificial intelligence evaluation by providing a structured set of mathematical reasoning challenges that can be used for benchmarking AI systems, improving machine reasoning models, and studying the differences between human reasoning and artificial intelligence reasoning.