In recent years there have been major, diverse, sometimes surprising advances in experimental mathematics  for a variety of sophisticated uses such as developing/deriving exact formulas, theorem ...
I'm always intrigued by the lack of numerical evidence from experimental mathematics for or against the P vs NP question. While the Riemann Hypothesis has some supporting evidence from numerical ...
As in, the area of the papers in the ACM Journal on Experimental Algorithmic JEA. Which were the foundational works? What are the main results? How are they characterized? Any interesting connections ...