TITLE: Results that came out of nowhere.
QUESTION [91 upvotes]: Most big results in mathematics are built on years and years of groundwork by the author and other mathematicians, such as Wiles' proof of FLT or the classification of finite simple groups.  Nevertheless, there is this big romantic idea in pop culture where a young genius comes up with a brilliant proof of a major conjecture, based on some creative new idea which flies in the face of the mathematical community.
What are some examples where this has actually happened?  That is, which results stem from independent work by a mathematician who came along "out of nowhere" and solved a huge problem by surprise through nonstandard techniques?
I read that the recent proposed proof of the ABC conjecture comes from years of autonomous theory by Prof Mochizuki, most of which ventures far outside of the current literature; this would seem to qualify as one example provided the proof turns out to be true.

REPLY [2 votes]: Vapnik and Chervonenkis work on classification and learning via Support Vector Machines (SMV) is said to have come "from left field." 
Though SMVs are more technology than math - since the kernels have to be engineered to specific applications (and further SVMs are but one method out of a long list applied to learning), their definition VC dimension is now a basic part combinatorial geometry.