Research

A top-level map from stable math and paper-reading skills into theorem families, active directions, surveys, and venue cultures.

Keywords

research, theorem families, surveys, venues, directions

1 Why This Section Matters

Research is where the site stops acting like a curriculum and starts acting like a literature map.

The job of this section is not to throw you into random current papers. Its job is to help you answer:

• what theorem family is this paper using?
• which direction does this result belong to?
• should I read a survey first?
• what kind of venue culture am I looking at?

That makes this section the layer between:

• stable math
• paper-reading workflow
• active research literature

2 Recommended First-Pass Order

Use this order:

1. Theorem Families
2. Directions
3. Surveys
4. Venues

That order is deliberate:

• start with recurring theorem and proof patterns
• then see which active directions are built on top of those patterns
• then choose good literature entry points
• finally learn how venue families shape audience and evidence expectations

3 When To Open Which Page

• Theorem Families: open when a theorem feels dense, but the bigger pattern is still unclear
• Directions: open when you want to know where a stable topic leads in current research
• Surveys: open when you need a structured entry point instead of jumping into recent papers
• Venues: open when you want to understand audience, evidence culture, and where a line of work tends to live

4 How This Section Connects To The Rest Of The Site

• Paper Lab teaches you how to read papers
• Research helps you choose what literature patch to read next
• Applications shows where the math reappears in modern models
• Roadmaps gives you longer study paths when you need a sequencing layer

If Paper Lab teaches workflow, Research teaches orientation.

5 Sources And Further Reading

• Paper Lab - First pass - the workflow layer you should use before diving into theorem families and literature maps.
• AI / ML Theory Roadmap - Second pass - a strong route when your research interest is specifically theory-facing ML.
• Theorem Families - Paper bridge - the best first research page when theorem statements still feel isolated and opaque.
• Directions - Paper bridge - the best next page when you want to know which frontier areas grow naturally out of the site’s stable math.