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The conformal invariance of the Yang-Mills equations in four dimensions greatly facilitates the study of the temporal asymptotic behavior of their solutions.

— John C. Baez

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Besides their possible role in physics, the octonions are important because they tie together some algebraic structures that otherwise appear as isolated and inexplicable exceptions.

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Quote text and notes from Wikiquote: John C. Baez (page history), available under CC BY-SA 4.0. Source quality and labels are our own summary of what Wikiquote records.