A Mathematical Foundation for Automating the Literature Review Process in Academic Research projects.
Abstract
In the desire to automate the literature review process, we turn to the notion of mathematical spaces.
A mathematical space is essentially a set of objects (often called points) with defined relationships between them. It’s a broader concept than the familiar three-dimensional space we inhabit. If the elements of such an underlying set are scientific articles, the definition of the structure can lead to very interesting properties and applications that can facilitate the literature review process.
Keywords
Mathematical space, literature review, citation network, semantic similarity, co-authorship, keyword frequency, publication trends
Introduction
Mathematical spaces are fundamental constructs in various fields of science and engineering. They provide a framework for understanding complex relationships and structures. In the context of literature review, mathematical spaces can be used to model the relationships between scientific articles, offering new ways to analyze and synthesize research findings. This paper explores the application of different types of mathematical spaces to the literature review process, highlighting their potential to enhance the efficiency and depth of academic research.
Literature Review
The concept of mathematical spaces has been extensively studied in mathematics and applied in numerous domains. Euclidean spaces, vector spaces, metric spaces, topological spaces, and probability spaces each offer unique structures and properties that can be leveraged in different contexts¹. In the realm of literature review, these spaces can be adapted to model various aspects of scientific articles, such as citation networks, semantic similarities, co-authorship networks, keyword frequencies, and publication venues².
Methodology
To apply mathematical spaces to the literature review process, we first define the underlying set as the collection of all relevant scientific articles. We then choose an appropriate structure based on the specific research question or application. For instance, a citation-based structure can be represented as a directed graph where nodes are articles and edges representing citations. Similarly, a semantic similarity structure can be modelled as a metric space where distances between articles are based on their semantic content³.
Results and Interpretation
By applying different mathematical structures to the set of scientific articles, we can gain valuable insights into various aspects of the literature. For example, a citation-based structure allows us to analyze citation networks, identify influential articles, and trace the flow of knowledge. A semantic similarity structure enables clustering of articles based on their content, facilitating information retrieval and recommendation systems. Co-authorship networks reveal patterns of collaboration among researchers, while keyword-based structures help in identifying research trends and gaps⁴.
Conclusion
Mathematical spaces offer a powerful framework for enhancing the literature review process. By carefully selecting and combining appropriate structures, researchers can create rich representations of the scientific literature, leading to more efficient and comprehensive reviews. The dynamic nature of the space of scientific articles necessitates evolving structures to accommodate new information, making this approach particularly relevant in the rapidly growing field of academic research.
