AI-augmented mathematical creativity: Exploring novel approaches to problem-solving

The advances in artificial intelligence and its integration into mathematics has elevated and exceeded the simplistic perspectives of problem-solving. AI-enhanced mathematical creativity increased means now exploring yet another dimension of human thinking where technologies improve problem formulation and new knowledge construction. May I ask, does artificial intelligence advances mathematics through problem definition, region suggesting, theorem's proof, application of theorems to a problem or all of them? Focusing on points AI practices and their applications to mathematical tasks, we define these basic approaches to the expansion of imagination as the opposite of monotony in human mathematics. F.L. Linton, "creativity in mathematics thinking processes does not differ from creativity in other fields, it includes such abilities as: reasoning in relation to an abstract structure, which is necessary for developing new ideas; reasoning toward something new that has yet to be explained; and the process of modeling something new."Patterns in detail previously unseen by any individual can now be discovered using AI advancements such as machine learning, deep learning and know it all neural networks. Such algorithms do not answer the question, why; they are of some assistance, however, in one way or another, the formulation of the approaches to the specific question which is posed in the article. In particular, the artificial intelligence made neural networks are able to look through data and find hidden correlations while artificial intelligence that is symbolic is able to use mathematics addresses logic and values in an attempt to search for new theorems. This paper itemizes several instances of the use of AI aimed at enhancing creativity in mathematics. For instance, AI assisted tools have been effectively used in algebraic problems, operations research, number theory, and optimization in the development of models and hypotheses which later have been proved or disproved by human mathematicians. In these particular contexts, the contribution of AI is not limited to performing the necessary computing work only but gives room for improving the definition of the problem and even providing solutions to related future work. The interaction of AI and the human brain in this regard could be construed as simply increasing the bar in terms of what was possible within the paradigm of mathematics by looking for further application of known theories and developing completely new ones. From another perspective, we discuss the idea of AI as a co-creator of this or that about the mathematical theories, where such AI models are trained to learn the mathematical concepts and generate or solve some unseen concepts by themselves. This cooperative model suggests that AI is not necessarily a point of threat to human capability but rather a team player in the processes of mathematical problem solving, who complements the inherent and professional abilities of human specialists.