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Attempting to create a general framework for studying new results ontranscendental numbers, this paper begins with a survey on transcendentalnumbers and transcendence, it then presents several properties of thetranscendental numbers $e$ and $\pi$, and then it gives the proofs of newinequalities and identities for transcendental numbers. Also, in relationshipwith these topics, we study some implications for the theory of the Yang-Baxterequations, and we propose some open problems.

On transcendental numbers: new results and a little history