My favourite subjects

Mathematics is a vast body of knowledge, in order to become 'current' on any subject it is important to focus on a topic as soon as possible. Specialization is possible once you have studied that part of math which is assumed to be common knowledge of all mathematicians. This includes undergraduate courses in
- Analysis
- Differential equationals
- Linear algebra
- Abstract Algebra
- Geometry
- Number Theory
- Graph Theory
- Combinatorics
- Probability ans statistics
When these topics are studied at the undergraduate level you are still far from the gate of the castle where some of math's big secrets are kept. Few will arrive at the gate, fewer will find the castle's door, it seems that only a few chosen ones are allowed to enter the castle. In the documentary about unlocking Fermat's last theorem Andrew Wiles told how he spent eight years at the castle. It's completely dark in the castle. Years are lost by finding where the lights are.

There are so many topics I truly like: group theory, number theory, combinatorics just to name some. How on earth do I become 'current' in any of them?