This common and unfortunate fact of the lack of adequate presentation of basic ideas and motivations of almost any mathematical theory is probably due to the binary nature of mathematical perception. Either you have no inkling of an idea, or, once you have understood it, the very idea appears so embarrassingly obvious that you feel reluctant to say it aloud.
But anything that can be called "rigor" is lost exactly where the things become interesting and non trivial.
Understanding what and why did not work may be more instructive than celebrating our successes.
But 'the physical level of rigor' is higher on certainty than the logical one, since reproducible experiments are more reliable than anybody's, be it Hilbert's, Einstein's or Gödel's intuition.
A mathematician would hardly call a correspondence between the set of 64 triples of four units and a set of twenty other units, "universal", while such correspondence is, probably, the most fundamental general feature of life on Earth.
There is no significant difference between human activities and those by amoebas and even bacteria, well, on the GRAND SCALE.
