We start with irrationality proofs. Historically, the first ones concerned irrational algebraic numbers, like the square roots of non square positive integers. Next, the theory of continued fraction expansion provided a very useful tool. Among the first proofs of irrationality for numbers which are now known to be transcendental are the ones by H. Lambert and L. Euler, in the XVIIIth century, f...

in this article, after an introduction, two more or less detailed reports of history of science – from the realm of medical science – are provided to clarify that when the scientists face a problem, how they practically solve, interpret, and elucidate it. then, other various types of elucidation are touched upon, defined, and described. further on, these same various elucidations are critically...