Mathematical and Statistical Frameworks Fostering Advances in AI Systems and Computing

The rapid expansion of artificial intelligence (AI) areas and applications has become an everyday social reality and the development of computing methods and of technology, in order to accomplish for the respective needs, emerge as one of the biggest challenges of this century. However, a strong background in Mathematics and Statistical fundamentals is crucial to foster the robustness of AI Systems and to attain for the correspondent generalization capabilities. Thus, recognizing the importance and benefits of integrate multiple mathematical methodologies that can leverage the unique strengths of each to create synergistic effects, is here discussed. In the literature it is possible to find diverse connections of Mathematical and Statistical frameworks with AI Systems and Computing. For illustration: Algebra - can be used to manipulate data in high-dimensional spaces; Statistical Analysis - helps on providing confidence in decision-making; Linear Regression- can be used on data modelling and accuracy assessment; and Bayesian statistics - can be used in probabilistic programming for AI applications. This work particularly highlights the evolving role of Hadamard Matrices and Coding Theory, illustrating their synergy with AI Systems and Computing, and how such synergy is driving innovation in various fields and approaching the new reality of Quantic paradigms.