Comment by zkmon
2 hours ago
It's time that mathematics need to choose it's place. Physical world is grainy and probabilistic at quantum scale and smooth amd deterministic at larger scale. Computing world is grainy and deterministic at its "quantum" scale (bits and pixels) and smooth and probabilistic at larger scale (AI). Human perception is smooth and probabilistic. Which world does mathematics model or represent? It has to strongly connect to either physical world or computing world. For being useful to humans, it needs to be smooth and probabilistic, just like how computing has become.
> Physical world is grainy and probabilistic at quantum scale and smooth amd deterministic at larger scale.
This is almost entirely backwards. Quantum Mechanics is not only fully deterministic, but even linear (in the sense of linear differential equations) - so there isn't even the problem of chaos in QM systems. QFT maintains this fundamental property. It's only the measurement, the interaction of particles with large scale objects, that is probabilistic.
And there is no dilemma - mathematics is a framework in which any of the things you mentioned can be modeled. We have mathematics that can model both deterministic and nondeterministic worlds. But the mathematical reasoning itself is always deterministic.