Number theory (NT) on the arXiv is a big section. In fact over the last two years, a little over 5700 papers have been posted there. Just for fun I wrote a Python program to help me find the most popular words in the titles and abstracts of the papers. Excluding common english words and common mathematical words such **prove**, **function**, and **theorem**, here are the top twenty keywords I found:

- prime
- group
- integer
- modular
- rational
- elliptic
- quadratic
- series
- polynomial
- zeta
- class
- bound
- galois
- algebraic
- abelian
- representation
- adic
- sequence
- diophantine
- linear

And how does this compare to algebraic geometry (AG), with almost the same number of papers posted?

- projective
- algebraic
- curve
- smooth
- moduli
- group
- complex
- variety
- surface
- rational
- degree
- field
- finite
- point
- real
- surface
- toric
- bundle
- dimension
- genus

What about rings and algebras (RA), one of my favourite areas with a little under half of the above categories?

- algebra
- finite
- group
- ring
- field
- module
- hopf
- matrix
- category
- commutative
- simple
- graded
- generated
- polynomial
- characteristic
- linear
- quantum
- ideal
- free
- dimension

Again, all of these were approximately over the last two years. The program was a little crude and might have made a mistake here or there but looking at the words it found these seem like an excellent approximation.