You can only become friends by talking to people and finding out whether you get along.
Regretting the past forever won't solve anything.
Who a person hangs out with is their choice. And I couldn't care less about rumors. Until I tried talking to them myself, I wouldn't know... Math is like a puzzle or a game. There's a clear answer, and you're going on a journey to find it. But there are many ways to reach that answer. That's why it's so fulfilling when you find the solution. There are ways to find an answer promptly, or more freely. Even roundabout methods can bring you to a definite solution. The method may not be pretty, but when the answer you worked hard to discover is right, it makes you happy.