The operational definition of quantum is statistical’. In other words, at both ends of the spectrum mathematics breaks down. Or more correctly, all mathematics is statistical – meaning an approximate measure of commensurability conceivable by the human mind at human scale.

We are seeing the emergence of the next generation of what we call mathematics because we are trying to solve questions beyond human scale of cognition given the consequences of causal density and combinetrics – requires computers and simulations and adversarial combinations.

The problems of mathematical limits – per se – are obvious if mathematical concepts are stated with operational names.

Math is the study of measurement by every possible means using the simplicity of positional names, positional naming, and positional dimensions. But at some point the verbal breaks down and we resort to the symbolic. And at some piont the symbolic breaks down and we resort to computation, then to simulation, then to adversarial simulation.

Mathematicians have done a very poor job of describing or communicating how their research into number theory demonstrates this problem. And they gave up on combinetrics.