Mathematical neuroscience is the branch of interdisciplinarity between mathematical modeling and neuroscience through computational techniques to study the structure, function, and dynamics of the brain. The objective of this paper is to undertake a comprehensive review of research trends in mathematical neuroscience and important developments in the period from 1973 to 2024. From this source of bibliographic data, Scopus alone returns 727 retrieved documents, consisting of journals, book chapters, and conference papers. The analysis showed an annual growth rate of 6.51% in this field and significant contributions from authors of 1957 sources. Specific tools were used in this review for in-depth analysis of publication patterns, co-authorship networks, keyword co-occurrences, and thematic evolution within this discipline. The most influential authors, dominant publication sources, and most active countries in the field were identified. The survey also underlines various other emerging trends, of which the highly increasing approach to the integration of machine learning and artificial intelligence (AI) with mathematical neuroscience is certainly the most interesting. Results highlight the dynamic and collaborative features of research in this area and provide insight into the intellectual landscape for research in this field, along with its future directions.