10 Awesome Theorems & Results

Or, how to start your week off feeling really stupid!
7. Functional analysis: here it’s a relatively minor result that I ended up remembering distinctly: Given z1.. zn which are linearly independent in E, show that there exists a d such that for each w1…wn that follow ||wi – zi|| < d for each i, are also linearly independent. The footnote says that such a finite, linearly independent group is called stable. When visualizing I think of it this way: given a such a group, kick it. As long as you don’t kick it too strongly – it will stay linearly independent. Now that’s stable.
Well, I guess that depends on your definition of "stable"!

Everything I ever needed to know about complex math I learned from Jonathan Coulton (caution:  swears).