Major advances in understanding of the physical world have been achieved during the past century by focusing on apparent contradictions between well-established theoretical structures. In each case the reconciliation required a better theory, often involving radical new concepts and striking experimental predictions.

Four major advances of this type are indicated in Figure 1. [1] These advances were the discoveries of special relativity, quantum mechanics, general relativity, and quantum field theory. Let us briefly recall the contradictions that each of these resolved and some of the experimental confirmations that followed.