Mathematics of Data and AI
Artificial intelligence is the theory of systems capable of mimicking cognitive abilities of human minds, such as learning and problem solving. Modern AI takes place in the presence of big data, and consequently, it requires an understanding of the structure of complex data and how to make use of it. The mathematics of data and AI calls upon fields including geometry, algebra, topology, mathematical statistics and combinatorics to address such questions and lay a foundation for the development of intelligent systems in the new millennium.
The mathematics of data and AI aims to provide a foundational understanding of the structure of complex data and the intelligent systems capable of working with it. The foundational theory for AI systems was developed by computer scientists in the mid 1900s, but its consequences were limited due to lack of data and computer resources.
Technological developments in the new millennium have shown the enormous potential of AI in many applied areas. However, the recent availability of big data also underscores the limitations of these techniques and the need for the continuation of foundational research in AI. Research in this area lies at the intersection of mathematics, mathematical statistics, computer science, and engineering. Ongoing research focuses on topics such as the geometry of machine learning, combinatorial methods in causality, topological data analysis, geometry in optimization, and complexity theory.