How Will AI Shape the Future of Mathematical Formulas?
The field of mathematics, considered for centuries to be the ultimate boundary of human intelligence and abstract reasoning skills, is entering a major transformation process with the development of artificial intelligence technologies. Recently, 30 elite mathematicians gathered at Harvard University to evaluate the performance of a next-generation AI model equipped with advanced reasoning capabilities. Developed by technology pioneers such as OpenAI and Google DeepMind, these new systems go beyond predicting from data. By establishing complex logical chains, these systems showcase the ability to quickly solve or disprove deep-seated mathematical conjectures, including Paul Erdős’s famous 80-year-old problem.
Conversely, detailed examinations by experts also reveal the structural limitations of current AI systems and the technical issues encountered. Evaluations determined that hallucinations occurred in some of the complex proofs generated by the models, and in certain solutions, symbol sequences from past papers were copied directly without citation. Furthermore, the fact that the ‘‘thinking process’’ behind the correct results reached by the AI is presented in thousands of pages of data blocks makes it difficult for humans to practically understand and verify these solutions.
These ongoing scientific developments bring along new approaches toward the future of the discipline within the academic community. Scientists state that rather than replacing human intelligence in the field of mathematics, AI models should be positioned as an auxiliary tool that will expand researchers’ horizons and accelerate complex processes. In line with these global developments, a new working model based on human and computer collaboration is expected to become established in mathematical discovery processes.