After completing algebra, the discussion suggests focusing on either trigonometry or geometry, with a preference for trigonometry due to its relevance in physics and mathematics. Some participants argue that classical geometry, particularly Euclidean constructions, may not be necessary for self-study aimed at understanding physics. The importance of intermediate algebra is emphasized as foundational for tackling trigonometry effectively. There is a consensus that geometry can aid in visualizing and solving physics problems, but opinions vary on its necessity compared to trigonometry. Overall, the conversation highlights the interconnectedness of these mathematical disciplines and the varying needs of learners.