This is a place to collect MathOverflow success stories!
Was some of your research inspired by something on MathOverflow? Do you know questions & answers that led to interesting research? MathOverflow citations? Open problems solved on MathOverflow? Then add your story in an answer! (One story per answer, please!)
If you want to help get this thread started, you can use this search to find MathOverflow citations on the arXiv or migrate some old stories from tea.mathoverflow.net.