Computer algebra-based systems such as Wolfram|Alpha and AI (Artificial Intelligence) systems like ChatGPT offer substantial support to students and researchers in the design and mathematical analysis of models derived from science and engineering disciplines.

Wolfram|Alpha is a computational knowledge engine that generates outputs by performing calculations based on its Wolfram Knowledgebase. Unlike AI systems designed to emulate human cognition, Wolfram|Alpha is, in words of its developers, an “engineered artifact”, whose primary function is to execute directed computations rather than operate as a human intelligence. Thus, very often, it cannot process problems posed in natural language and, consequently, it may be not able to offer suggestions or responses.

In contrast, AI systems like ChatGPT excel at providing suggestions or generating responses. However, when they come to formulating solutions or performing precise mathematical computations, they often fall, just as humans in such contexts. ChatGPT excels in areas where subjective or approximate responses are acceptable but struggles when tasked with providing precise, accurate information or calculations.

This study presents a comparative analysis of how both systems can aid students and researchers in model design and mathematical analysis. Specifically, the comparison focuses on the following criteria: the underlying knowledge base used to generate responses, the human-machine interaction process, efficacy (or capability), precision, and efficiency (or speed).

This analysis suggests that neither system, in isolation, can provide comprehensive and fully accurate assistance. Therefore, as a main implication, we infer that an optimal solution lies in combining both AI systems like ChatGPT and computer algebra-based systems as Wolfram|Alpha, to integrate the ability to process natural language and provide responses, and the computational and mathematical power, respectively.

Keywords: Computer algebra-based systems, artificial intelligence systems, technology-enhanced learning, long-life learning and research.