# Consistency, non triviality and redundancy in mathematics

## TL;DR

This paper examines the concepts of consistency, non-triviality, and redundancy in modern mathematics, analyzing formal and informal criteria through examples from dynamical systems research over the past 50 years.

## Contribution

It provides a comprehensive discussion on the different conceptions of these criteria, bridging formal logic and informal rational perspectives in mathematical research.

## Key findings

- Analysis of formal and informal criteria of mathematical validity
- Illustration with recent results in dynamical systems
- Discussion on the evolution of mathematical standards

## Abstract

We explore the rational, formal and non-formal criteria of consistency, non-triviality and redundancy in the mathematical research now a days. We develop a paradigmatic discussion by analysing the different conceptions of those criteria, from the logic-formal ones to the non formal ones (but still rational criteria).We illustrate the discussion with concrete examples obtained form the mathematical reseach, particularly from the results that were published in the last 50 years in the mathematical theory of deterministic dynamical systems.