Final answer:
According to Plato's "The Republic", one should study mathematics and geometry to become a philosopher, as these disciplines allow access to the realm of immutable Forms, which are crucial for understanding the true nature of reality.
Step-by-step explanation:
To become a philosopher according to Plato in "The Republic", one should undertake an education grounded in mastery of mathematics and geometry. Plato's concept of the philosopher-king, as laid out in the Republic, emphasizes the role of philosophers in understanding the true nature of the world, which he believed was best approached through the study of abstract reasoning and mathematics, rather than the physical and sensual world. It is through this sort of contemplation and intellectual pursuit that individuals could come to understand the immortal Forms—the true essence of everything that exists.
In addition to mathematics and geometry, the education of a philosopher-king also included the study of dialectics and astronomy, all culminating in the knowledge of the Form of the Good. The intensive physical training and athletics, developing persuasive rhetoric and public speaking skills, and learning the art of war and military strategy, while valuable, were not on their own deemed sufficient for the making of a philosopher in Plato's ideal state.