Many natural phenomena suggest that biological algorithms are embedded in an organism's genome and expressed in cognition and behavior through complex biological mechanisms. This review discusses these phenomena and proposes methods to explore them, focusing on algorithms embedded in neural systems. The application scope of biological algorithms is not only limited to biology and medicine but also to various engineering fields. The mathematical problems behind biological algorithms also prompt questions about the explainable aspects of artificial intelligence models. We discovered that computational tools can indeed be utilized to recover these algorithms, leading us to conduct some preliminary experiments using existing computational methods. Despite this progress, the current tools have limitations. To overcome these challenges, it will be necessary to design targeted experiments aimed at observing the dynamics of the neuronal gene expression system. In light of this, we will discuss the theoretical aspects and suggest potential research directions that we hope will advance this field in the future.