### What are Breakthroughs in Mathematics? (Part 1)

What is the nature of mathematical breakthroughs? What are common characteristics among diverse mathematical fields? What are specific signs of mathematical breakthroughs? How do breakthroughs create new mathematical fields or objects or discern deep relationships between diverse mathematical fields? How to distinguish mathematical breakthroughs from normal good math?

## What are Breakthroughs in Mathematics? (Part 1)

## Discussion