Defining Good Mathematics

The discussion centers around the question of what constitutes good mathematics, a query that has intrigued mathematicians for decades. Terry Tao reflects on his past as a graduate student, realizing that no central authority dictates the worth of mathematical inquiries; instead, each mathematician approaches the field with diverse values and methods. Despite these varying perspectives, there seems to be a convergence on what is deemed valuable in mathematics. Tao connects this notion with Eugene Wigner's observation about the unexpected effectiveness of mathematics in the physical sciences, illustrating that truly good mathematics tends to resonate across different fields, ultimately aligning with both beauty and practical application.