Today, there are 101 papers on mathscinet using the notion of [planar algebra][1], discovered by [V. Jones][2] in 1998.   
As [V.S. Sunder][3] pointed out to me, the fundation of planar algebras theory is waiting for some detailed proved *with all i's dotted and t's crossed*, see for example the post:  
 [What's the detailed proof of "the composition of planar tangles is well-defined"?][4]


  [1]: http://arxiv.org/abs/math/9909027
  [2]: http://en.wikipedia.org/wiki/Vaughan_Jones
  [3]: http://en.wikipedia.org/wiki/V._S._Sunder
  [4]: http://mathoverflow.net/q/207650/34538