Journal of Physical Mathematics

What Mathematics is the Most Fundamental?

Lev FM

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Standard 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. In the first part of this note we argue that the situation is the opposite: standard mathematics is only a degenerate case of finite one in the formal limit when the characteristic of the ring or field used in finite mathematics goes to infinity, and finite mathematics is more pertinent for describing nature than standard one. In the second part we argue that foundation of finite mathematics is natural while foundational problems of standard mathematics are not fundamental.

Article information

J. Phys. Math., Volume 6, Number 1 (2015), 4 pages.

First available in Project Euclid: 23 July 2015

Permanent link to this document

Digital Object Identifier

Primary: 03Axx: Philosophical aspects of logic and foundations 01Axx: History of mathematics and mathematicians

Standard mathematics Finite mathematics Infinity Galois fields


FM, Lev. What Mathematics is the Most Fundamental?. J. Phys. Math. 6 (2015), no. 1, 4 pages. doi:10.4172/2090-0902.1000129.

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