The discussion centers on the derivation of a paraxial equation using a Cartesian approach, with the original poster expressing a desire to share their findings from years of hobbyist study in trigonometric ray tracing. There is a request for improved formatting using LaTeX for clarity, though the poster is hesitant due to time constraints and a lack of familiarity with the software. The conversation also touches on the distinction between exact ray tracing and paraxial optics, with some confusion about the purpose of the derivation. Additionally, the poster seeks advice on suitable academic journals for publishing their work and recommendations for PDF editing software that can handle trigonometric equations effectively. Overall, the thread highlights a blend of sharing knowledge and seeking guidance on academic presentation.