Why Finite Mathematics Is The Most Fundamental and Ultimate Quantum Theory Will Be Based on Finite Mathematics

TL;DR

This paper argues that finite mathematics is more fundamental than classical mathematics and presents a quantum theory based on finite mathematics, challenging traditional views on the foundations of mathematics.

Contribution

It introduces a quantum theory grounded in finite mathematics and posits that finite mathematics underpins classical mathematics as a special case.

Findings

Finite mathematics is more fundamental than classical mathematics.

A quantum theory based on finite mathematics is developed.

Implications for the foundations of mathematics are discussed.

Abstract

Classical mathematics (involving such notions as infinitely small/large and continuity) is usually treated as fundamental while finite mathematics is treated as inferior which is used only in special applications. We first argue that the situation is the opposite: classical mathematics is only a degenerate special case of finite one and finite mathematics is more pertinent for describing nature than standard one. Then we describe results of a quantum theory based on finite mathematics. Implications for foundation of mathematics are discussed.