Answer:
p-value (statistic) or Gödel's incompleteness theorem (logic)
Explanation:
Mathematics is a field that have many subfields, could be, algebra, probability, statistics, calculus, etc
A topic for research depends on what you like, in my case, I like statistics and a topic I would choose it could be P-value, it's seems something easy, but there are several discussion about what it is and what it represents.
Another subfield of my interest is logic, that theorem is pretty interesting.