**Abstract**

The chapter examines a review and revisit to the current study of advancements in mathematics and statistical methods underlying the most sorted topic of artificial intelligence (AI). Inclusion of references is done for better and smooth discussion for more clarity to the underlying difficulties faced by readers. Mathematics motivates image processing and image processing improves methods involved with mathematics, which is to be explored. Mathematics stands as a back bone and with discussions of basics of neural network the path way to artificial neural network would be build. The struggle to recall the prerequisites faced by researchers is addressed in this chapter. The chapter will provide you through an ariel view by stating the definitions of prerequisites such as mathematics for image processing, mathematics for forensic image processing which includes basics of neural network and prerequisites of probability theory as a subsection. Forensic sciences utilize the concepts of probability density to a great extent. The topics briefed would provide the readers to have a quick recap of the concepts which though seem to be from different specializations but are deeply connected to one another. Section one is dedicated to mathematics for image processing and Section two connects mathematics, image processing with forensic sciences.

**Keywords:** mathematics, probability, forensic sciences, image processing, neural network, score- based likelihood
