Chaitin discusses an algorithmic information-theoretic understanding of Gödel incompleteness and concludes:
The bottom line is that these metatheorems show that the world of pure mathematics has infinite conceptual complexity, infinite information content, but any mathematical theory has finite conceptual complexity, and can therefore capture only an infinitesimal part of mathematical truth!And furthermore:
The psychological defense mechanisms of the mathematics community have rejected incompleteness, they have decided that incompleteness is insignificant. They prefer to continue to believe, that they, not physicists, are the unique possessors of absolute truth. Incompleteness is too dreadful, let's forget about it, let's suppress it.But Chaitin himself has a more optimistic interpretation:
But in the past few years, my work on biology has led me to a radical reinterpretation of incompleteness. Incompleteness is good, not bad! Incompleteness means, as Post stated a long time ago, but which it has taken me many years to understand, that mathematics is creative. Math is an open, not a closed system. I now see the incompleteness theorems as the first steps in the direction of a mathematical theory of creativity, and as providing a bridge between pure mathematics and biology. I think that mathematical creativity and biological creativity are related.
*Is God a computer programmer, not a mathematician? Building the world out of information and computation. Accessed from academia.edu