Five Departures in Logic, Mathematics, and thus either we like it, or not, in Physics as well ...

Physics depends on "physical intuition", much of which is formulated in terms of Mathematics. Mathematics itself depends on Logic. The paper presents three latest novelties in Logic which have major consequences in Mathematics. Further, it presents two possible significant departures in Mathematics itself. These five departures can have major implications in Physics. Some of them are indicated, among them in Quantum Mechanics and Relativity.