Classical Genetics through a Mathematical Lens: Foundations, Genomic Relevance and Future Directions

AbstractClassical genetics, rooted in Mendelian principles and quantitative models, is a mathematically structured framework for studying heredity and phenotypic variation. From a mathematician’s perspective, its elegance lies in transforming biological observations into algebraic and statistical systems. In the genomic era, classical genetics provides the scaffolding to interpret high-dimensional genomic data, bridging genotypes and phenotypes. This review defines classical genetics, highlights its enduring importance, and explores how mathematical tools like statistical genetics, algebraic geometry, persistent homology, and genetic algebras etc. advance its applications. These tools and their roles in modeling epistasis, recombination, and population dynamics has been summarized in this review. With the help of mathematical tools, classical genetics can address complex genetic interactions, enhancing future applications by emphasizing interdisciplinary mathematical approaches to unlock new insights into genetic systems.