What would you say are the areas of mathematics that are currently on the cutting edge of research and are still being developed. What new fields of math have emerged in the last few decades?

I find it's interesting that most of math education progresses historically; first we learned the algebra and geometry of the Greeks in elementary and middle school, then the graphs and functions of Descartes time in high school, the Calculus of Newton's time in college, and so on. After Calculus was made math really branched out and that shows with the wide variety of undergraduate and graduate courses.

I wonder what math education will be like a hundred years from now!