Some personal thoughts and opinions on what “good quality mathematics” is and whether one should try to define this term rigorously. As a case study, the story of Szemer´edi’s theorem is presented.
Comment (from this Blueprint): Tao is a mathematician who has written extensively about mathematics as a discipline. In this piece he considers what counts as “good mathematics”. The opening section that I’ve recommended has a long list of possible meanings of “good mathematics” and considers what this plurality means for mathematics. (The remainder details the history of Szemerédi’s theorem, and argues that good mathematics also involves contributing to a great story of mathematics. However, it gets a bit technical, so only look into it if you’re particularly interested in the details of the case.)