The objective of this article is to delve into the mathematical principles underlying nuclear imaging, tracing its evolution from its inception to the recent integration of artificial intelligence (AI). Nuclear image reconstruction poses a challenge as it is an ill-posed and ill-conditioned inverse problem. The primary concern revolves around devising mathematical models and solutions for reconstructing static or dynamic nuclear images. Several methodologies have been devised to address this challenge effectively. Initially, methods like Filtered Back Projection (FBP) were developed for static scenarios, assuming radioactivity remains constant throughout the scan. Subsequently, techniques were introduced to tackle dynamic scenarios, where radiotracer distribution changes over time in the body. Algorithms such as the Expectation Maximization Filter (EMF) were introduced, emphasizing the significance of Time Activity Curves (TACs). AI techniques like Convolutional Neural Networks (CNNs) have been leveraged to address the limitations of classical methods and enhance the quality of reconstructed images.