Four Departures in Mathematics and Physics

Much of Mathematics, and therefore Physics as well, have been limited by four rather consequential restrictions. Two of them are ancient taboos, one is an ancient and no longer felt as such bondage, and the fourth is a surprising omission in Algebra. The paper brings to the attention of those interested these four restrictions, as well as the fact that each of them has by now ways, even if hardly yet known ones, to overcome them. 1. Two Taboos and a Bondage form Ancient Times, plus a Modern Omission Logic, as is well known, is at the basis of Mathematics. Two ancient taboos in Logic are : • no contradictions • no self-reference The reason for the first taboo seems so obvious as not to require any argument. The reason for the second taboo is known at least since ancient Greece and the Paradox of the Liar, with its modern version