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Evolution and mathematics

This idea that mathematical truth can be both creative and objective suggests a new way of looking at the implications of Gödel's Incompleteness Theorem. If mathematics is inherently creative it need not follow a single path of development. By following an ever increasing number of paths it is possible to develop mathematics in a way that is not subject to the limitations Gödel's result implies for single path processes. This is how the mathematically capable human mind was created. Biological evolution has followed an ever expanding number of paths without selecting a single ``correct'' or ``true'' path.

Divergent creative processes like biological evolution always involve tradeoffs between diversity and concentration of resources. By exploring the mathematics of creative divergent processes it may be possible to find boundary conditions for this tradeoff that optimize creativity. Such mathematics may be broadly applicable to many human endeavors.

In the long run mathematics will need to be extended through a creative divergent process if it is to avoid stagnation. There will be an ever expanding number of possible incompatible extensions to mathematics and schools will develop pursuing each of these with no expectation of any final resolution. The expectation will be for ever expanding diversity.

The wider implications of this philosophy are explored in the partial draft of a book availible online[1].


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