The notion of mathematics as "the art and science of effective reasoning" is grandiose and blatantly wrong, both in the sense eg no mathematics is performed whe

The notion of mathematics as "the art and science of effective reasoning" is grandiose and blatantly wrong, both in the sense eg no mathematics is performed when an animal correctly flees from a fire, and also that this definition would exclude computer science from mathematics when his whole point is to incorporate it (for almost all formal systems are unreasonable). Math and computer science at their core are more it less the same. Both are concerned with manipulating "digital" equipment that is assumed to respond predictably. Equipment is a prerequisite even for pure mathematics - it is interesting in this case because it is the mathematician themself, who agrees to act that way and respond predictably. Physics is implicated in this in that it forms the basis of that agreement. Certainly it did historically. In the 20th century serious attempts were made to justify it on the basis of notions like consistency and completeness; the failure of that project is not yet fully absorbed. To be fair, the results are devastating because they can only really be understood by students after they have invested greatly in mathematics with the idea that all but a few "facts" derive from reason - when in fact almost none of them do.