To become a math professor, a Master's degree is typically required for junior colleges, while universities generally require a PhD. Mastery of calculus is not enough; critical thinking and the ability to identify and correct errors in mathematical statements are essential skills for a professor. The discussion highlights that while spotting typos is common, recognizing and fixing mistakes in theorems requires a deeper understanding of mathematics. The competitive nature of academia is emphasized, particularly in fields like physics, where even experienced professionals may struggle to secure positions. A focus on specialization is noted, with the importance of dedicating oneself to a specific area of math, as the breadth of knowledge seen in historical figures like Gauss and Euler is less feasible in modern academia. Ultimately, the path to becoming a math professor demands significant commitment and expertise.