Math’s new muse; AI’s impact on numbers

Artificial Intelligence (AI) holds significant importance across various domains and industries due to its transformative potential and wide-ranging applications. AI-driven educational platforms offer personalised learning experiences and adapt content to individual student needs, enhancing educational outcomes.

AI-powered platforms can provide personalised math education and tutoring. These systems adapt to the learner’s level and pace, offering interactive exercises, explanations, and feedback. AI has also made significant contributions to the field of Mathematics in various ways.

For instance, AI techniques are used to solve complex optimisation problems that involve maximising or minimising certain mathematical functions. These problems are relevant in fields like operations research and engineering. Similarly, AI can assist in solving geometric and topological problems by exploring different configurations, patterns, and structures. This is particularly useful in fields like computer-aided design and computer graphics.

However, there are some challenges or limitations in using AI for mathematical research. According to Meera Aggarwal, Associate Professor and HoD-Mathematics, Apeejay College of Fine Arts in Jalandhar, AI algorithms often require large amounts of data to train effectively.

“In mathematical research finding suitable data sets can be challenging, especially for specialised areas. Additionally, the data must be accurate and of high quality to avoid introducing biases or errors into the AI models. Many AI algorithms like deep neural networks, internal workings are not easily understandable. In mathematical research where proofs and explanations are essential, using AI models that provide interpretable results can be difficult,” Aggarwal said.

Therefore, choosing the right AI algorithms for a specific mathematical problem is not always straightforward, Aggarwal opined. “Different problems may require different approaches, and the effectiveness of AI methods can vary significantly across tasks. There are ethical concerns in mathematical research as well. Ensuring that AI models are fair, unbiased and respect ethical standards when handling sensitive mathematical data is critical,” She said and added that researchers are continuously pushing the boundaries of AI and Mathematics to unlock the potential of AI-driven mathematical research.

By combining the strength of AI and human mathematicians, they aim to tackle complex mathematical problems more efficiently and make significant advancements in various mathematical disciplines.

Then there are ethical concerns similar to AI applications in other fields. “There is a concern about whether AI generated proofs can be considered acceptable without human- understandable justifications. AI models can inherit biases from the data they are trained on leading to biased outcomes in mathematical research,” Aggarwal said.

Researchers are now developing novel algorithms and techniques to reduce bias in AI models used in mathematical research. This includes techniques for detecting and mitigating bias during the model training process as well as exploring fair representation methods to ensure equitable treatment of different groups. There is ongoing research to improve the interpretability of AI models in mathematical research. This includes developing explainable AI methods that provide insights into the reasoning behind model predictions, allowing researchers to understand how the AI arrives at particular results.

However, students interested in both Mathematics and AI can prepare themselves for careers in this emerging interdisciplinary field. “They can start by mastering the fundamentals of Math, including Calculus, Linear Algebra, Probability and Discrete Mathematics. A strong Math background is essential for understanding the practical underpinnings of AI algorithms. Gain proficiency in programming languages like Python, as well as data science tools.  Familiarity with data manipulation and analysis will be crucial in AI-related tasks. Develop machine learning techniques and deep learning architectures. Sharpen your computational skills and gain experience in numerical methods and simulations,” Aggarwal advised.

The field of AI and Mathematics is rapidly evolving, so being adaptable and continuously learning will be essential for success in this interdisciplinary domain and in Aggarwal’s opinion some of the most exciting AI driven mathematical applications currently in development include developing AI systems to data driven mathematical modelling that can help in solving cryptographic problems, leading to advancements in cyber security and cryptography.

“Second, creating virtual assistants powered by AI to aid mathematicians in problem solving, theorem proving, or discovering new mathematical conjectures. And leveraging AI for solving complex mathematical equations and systems of differential equations in the field of mathematical physics,” Aggarwal said in conclusion.