arXiv:math/0411091math.HO
Irreducible Complexity in Pure Mathematics
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Abstract
By using ideas on complexity and randomness originally suggested by the mathematician-philosopher Gottfried Leibniz in 1686, the modern theory of algorithmic information is able to show that there can never be a "theory of everything" for all of mathematics.
From page 12: > Why should we believe in real numbers, if most of them, it turns out,[^15] are maximally unknowable like Ω? [^16] The footnotes: > [^15]: See the chapter entitled The Labyrinth of the Continuum in [Chaitin, 2005] > [^16]: In spite of the fact that most individual…
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