I applied to PhD programs in mathematics last year and unfortunately wasn't accepted to any of the schools I applied to (miserable). I was looking for advice in what I can do before December to help push my application forward, and advice can hopefully help others in a similar situation.
Background: I graduated from Rutgers in 2014 with 2 degrees after 3 years, Mathematics and Computer Science. I did research in Graph theory while a student but ended with a GPA around 3.3. In the years between my masters and undergraduate I worked as a software engineer with work in machine learning, apps featured by apple, and some other successes. I finished my Masters at NYU in May 2020, with a thesis in computational algebraic geometry with new results under a very well known professor. One of my other recommenders is very famous too. I taught precalc / numerical analysis recitations while I was there. Ending around a 3.7 for my Masters. I was looking for a program in number theory but after the rejections I'm thinking of changing course to topology where I have several graduate courses and grades reflecting a good understanding (what is life other than failure + corrections :) ).
Now: Disheartened by the result, I've been working at the startup I was at before I went to my Masters. I feel incredibly lost as to what I can do now to help push my application further than I did last year... If anyone has advice that could lend itself to an improvement here in what can be accomplished in the next 6 months I would really appreciate it.
Cheers and good luck to everyone else who is applying for Fall 2022. Thanks!