Dear Alma,
Excellent analysis in the spirit of Cartesian doubt. Deep, all-encompassing questions on fundamental questions of Mathematics and Physics and the direction of finding the answers to them:
"That our knowledge manifests gaps around emergent phenomena seems to be an indication that we lack some insight of the mathematical description itself, not just of what happens physically. It may very well be a gap in our total knowledge of the world, not of the physical, or biological or mathematical fields in isolation. Are we just lacking the right mathematics to treat other fields with similar power and rigor as physics? You know you're missing something when there's just too much you can't explain. "
"Our math does not make sense in a million ways, 7 but always choses a certain correct path and discards everything else. We woke up in a place where so many things might have headed in a different direction, yet our universe is very well constrained.
The constants are not changing and reality seems sturdy, like it will last forever. Everything insists to make perfect sense. "
Indeed: "But there's still time. Just wait to see our children."... My high appreciation.
It's time we start the path...
I am sure that current problems of Mathematics and Physics - a problems with the ontology. Dialectics too, do not be afraid, it is a good helper for a deeper vision of the dialogic Nature. Dialectics and ontology help to see Universum as a whole, understand the nature of the information, time, consciousness. The Information age requires revision and updating of the basic concepts of fundamental science. The new paradigm and a new vision of the world, including the Foundations of Mathematics and Physics, filling them with the sense of "life-world" is possible only on the basis of the broadest synthesis, taking into account all accumulated knowledge, teamwork «ratio», «intuition», «emotion».
Good luck in the contest,
Kind regards,
Vladimir