David Hilbert was a powerful mathematician. For example, Albert Einstein, after spending eight years trying to derive the equations of General Relativity, even with the help of many geometers, got nowhere until he explained his “grand problem” to David Hilbert. Hilbert spent six months studying Einstein’s “grand problem” and then solved it in two weeks’ time. I’m not aware of Hilbert saying anything about evolution but I suppose that most mathematicians here are Darwinists. I wonder what would be the result if professional mathematicians, with the assistance of knowledgeable Darwinists, tried to formulate their understanding of biological evolution in the style of Hilbert’s mathematical philosophy of physics. The following brief illustration of Hilbert’s mathematical philosophy should suffice for the purpose of understanding my question: “If geometry is to serve as a model for the treatment of physical axioms, we shall try first by a small number of axioms to include as large a class as possible of physical phenomena, and then by adjoining new axioms to arrive gradually at the more special theories. ...The mathematician will have also to take account not only of those theories coming near to reality, but also, as in geometry, of all logically possible theories. He must be always alert to obtain a complete survey of all conclusions derivable from the system of axioms assumed.” http://aleph0.clarku.edu/~djoyce/hilbert/problems.html Suppose, then, that we start with an incredibly well-verified empirical observation: "Species change and the fittest, the most adaptable and the most prolific variants have the greatest chance of survival." My question therefore is this: What should be the next incontestable axiom (i.e., incredibly well-verified empirical observation) to adjoin to the preceding one?