Math: Eternal? If so Who Created It?

Another interesting aspect of mathematics is the way it demonstrates how an extraordinary degree of complexity arises from extremely simple concepts.Consider, for example, the mathematical concept of a "group", that is, a set with an operation (for example, addition) an identity element (for example, the zero) and a few simple rules (that every element has an inverse, a "negative" element such that if you combine the two you get the identity and other simple principles). Things that can be considered "groups" come in great variety, from the group with two elements {0,1} with the operations 0+0=1 0+1=1 and 1+1=0, to the set of all integers to the set of all permutations of the real numbers. etc. etc. etc.One of the most intriguing is the famous Fischer-Griess "Monster" group (https://math.berkeley.edu/...whatismonster/whatismonster.pdf http://www.math.s.chiba-u.ac.jp/~kitazume/monster3.jpg). Such an extraordinary degree of complexity from such simple principles...An important indication of how easy it would be for complex organisms to develop naturally, wouldn't you say?

Thanks! I'm happy to find a discussion on mathematics in a creationism/evolution website. From what I've read the topics of evolutionary biology and the Bible have been gone over in great detail (though there's always room for one more!) but not much on math and its interesting philosophical implications (chaos theory, undecidability, non-Euclidean geometry, the Liar Paradox, etc.).

Thanks!

Can you clarify what you mean when you write, "Godel's theorem ... the whole area of model theory that shows the ambiguity in what any mathematical statement refers to "ontically" "

But doesn't the set of real numbers have the cardinality of the set of all subsets of the natural numbers, regardless of what model you're working in?

But how can a set (in any kind of set theory) have the same cardinality as the set of all its subsets?

Oh, but in this case it does! The definition of a vehicle doesn't include plans for a Model A, so if you ask the question, what are the possible configurations of a "vehicle" based solely on the definition you don't get much of an answer. But for groups you get very specific blueprints!

How was the structure derived, if not from the axioms?

You are merely describing how the structure was determined by algebraists, not the reason for the structure itself.Here's an example. Michelangelo carved his David out of marble. The structure of the young man was not inherent in the marble itself.The Venus de Milo was discovered by a Greek peasant two thousand years after it had originally been sculpted.This is not to denigrate the work of the algebraists. Their work is incomparably more difficult then digging up a field on an island in the Aegean, but they did not shape the group whose structure they described.Another sculptor with another block of marble could produce a different sculpture than David, but anybody else would have discovered the same Venus de Milo. And even if they hadn't discovered it, it still would have existed!