The limits and guesses in math

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This article is speculative. It covers topics that are not straightforwardly derivable from current knowledge. Take it with a grain of salt. See: "exploratory engineering" for what can be predicted and what not. 
Even math is not achieving absolute truth.
There is no way around faith in at least a few axioms outside the proof system.

Disclamer #1:

  • Math is the best and most formal system we have and (as it very much looks) the best and most formal system we will ever have
  • This page is not meant to undermine the faith in math and science.

Disclaimer #2:

  • All "certainties" in this article (and anywhere else in this universe) are in the very end only certainties to the degree of practicability from experience.

About realizing the unprovability of fundamental axioms

Here's a way how one could maybe question one of the most fundamental axioms of math: That every natural number has an successor.

Does a number which is not representable by the means that our universe provide (amount of demixing in the big bang) even exist? Ridiculously large numbers can easily be represented by simple compression methods (e.g. the Ackermann-function) but between those numbers there are gaping holes of unrepresentability. While we don't know which of the ridiculously big numbers we can represent in a smaller compressed form we can be certain that there are many more which certainly can't be represent within the limits of our universe.

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