"I failed an important course due to some justified reasons or terrible excuses, can I get into a decent PhD program?" is probably one of the most asked questions on the Academia Stack Exchange. However, I have a different question.
My question is, what if my low grade is due to my incompetence? No excuses, no external reasons. The only reason is my unsatisfactory intellectual capacity. How should I address this issue on my application?
Let me give more context. I am applying for a PhD in computer science, but my math proficiency is terrible. (Probably above average, but certainly not on par with the top students in my department, let alone those from the prestigious schools) There are several important courses in math and theoretical CS that I did poorly, such as B or C, but never F. (In our school, B and C are usually considered to be the bottom half of students, and are usually regarded as mediocre or poor, but not bad enough to fail the student.)
I have some research experience and have published in decent conferences. There are times when I use some sophisticated math in my research, but certainly not often. When this has happened, I have been given enough time and support to figure out complicated things, so my math incompetence has never held me back except to trigger my math anxiety (which happens quite often). My advisors also wrote strong LoRs (at least that is what they said) and they all believed that I was suitable for graduate studies. One advisor even told me that while it was true that my math skills were not as good as others, they were good enough to do graduate studies in my research areas.
I am now preparing to apply to graduate school, and it is certain that some, if not most, of the people on the admissions committees would notice these outliers on the transcript. How should I address this issue? I am quite concerned that my argument that math incompetence has never held me back will not convince others. I want to (and probably should) be honest and not make excuses.