An Experimental Road to Mathematical Truth

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Mathematical theorems often originate as conjectures, which were formulated to explain some observed phenomena or to develop a general theory. Belief in these conjectures---often necessary for their proof---typically rests upon the theoretical justifications.     I'll try to give you some flavor of a path to mathematical truth that is much less traveled, as it is through conjectures supported primarily by overwhelming empirical evidence. This path represents what I believe is an important future trend. This is exemplified by a study and formulation of conjectures concerning a simple method that forces all solutions to a certain class of geometric problems to be real.