Proceeding within a proof sometimes depends on both breaking and exploiting the symmetry of the situation. (three examples: the proof of the 6-people theorem, the solution of problem 6 of IMO 1988, and the fact that introducing coordinates breaks the symmetry of the synthetic plane, while introducing new possibilities of symmetry, such as about an axis , or about the origin, or about the line y = x) It may be that what Nassim Nicholas Taleb calls ‘antifragility’ is simply a general term for the more favorable status that results when the symmetry of a natively symmetric entity is broken.
keywords: mathematics, strategy, tactics