Writing a mathematics paper As a sequel to my previous post “ Redundancy of letters of recommendation for scientific and mathematical majors”, I wish to ask a relevant question.

I have been informed that a master’s student of mathematics is not required to have published a paper in order to be admitted to a doctoral institution. However, my applications all experienced rejection so I am trying to write my first paper.

However, my knowledge in mathematics is limited and in a limited time I cannot come up with an impressive result. On the other hand proving a small result and having it published is against my scientific principles, but I think I will finally do it.

Is it possible that a high gpa (19.5 out of 20), a simple published mathematical paper and a good TOEFL grade, but not good letters of recommendation or lack of letters of recommendation will guarantee admission to a top-tier university?
To add to @Buffy’s answer, in all math graduate programs I’m aware of, at least in the US, letters of recommendation are a requirement. So a “lack of letters of recommendation” is actually a guarantee that you will not get admitted. This is not something you can solve by publishing either one “simple” paper, or even many non-simple ones, except in the indirect sense that if you publish many papers then good letters of recommendation are likely to follow more or less automatically.

Keep in mind that this applies to all programs, not just “top-tier” ones.