The theory has serious mathematical problems

The argument

A central objection from critics of evolutionary theory is that the mathematics of chance does not give the process enough time to work. Proteins, the machinery of life, are chains of amino acids that must fall into precise sequences to function, and the number of possible sequences for even a modest protein is astronomically large — far more than the number of atoms in the observable universe. Critics argue that the probability of assembling a single working protein by undirected mutation, let alone the thousands an organism requires, is so small that the roughly four billion years of Earth's history provide nowhere near enough trials. The mathematician and astronomer Fred Hoyle gave the objection its famous image of a tornado in a junkyard assembling an aeroplane. The complaint sharpened into a formal challenge in 1966, when mathematicians and biologists met at the Wistar Institute in Philadelphia. Several mathematicians there, including Murray Eden and Marcel-Paul Schützenberger, argued that random mutation could not search the vast space of possible genetic sequences efficiently enough to produce observed complexity in the available time, and that natural selection lacked a mathematical mechanism to guide the search. Critics contend these objections were never satisfactorily answered. Defenders of the theory reply that selection is not random search but a cumulative ratchet that preserves partial successes, vastly improving the odds. But proponents of this argument answer that selection cannot preserve a half-formed protein that does nothing, so the improbability of reaching the first functional sequence remains. On the numbers, they conclude, the theory asks for more lucky trials than the universe could ever have run — and those mathematical problems show it is flawed.

Premises

Counter-arguments

Evolutionary biologists regard the probability objection as resting on a false model of how evolution works. Functional proteins were not assembled in one random shot from a blank sequence space; they arose by duplication, mutation and selection from simpler precursors, and many different sequences fold into working proteins, so the 'target' is vast rather than a single point. The Wistar objections were addressed as evolutionary computation and molecular biology matured, showing cumulative selection climbing 'Mount Improbable' in small steps — and directed-evolution experiments now routinely generate novel functional proteins in the lab.

Rejecting the premises

[Rejecting P1] Many distinct sequences fold into functional proteins, so the 'one precise target' premise vastly overstates the improbability; the functional space is large and richly connected. [Rejecting P2] The single-shot calculation is the wrong model — proteins evolve by duplication and stepwise modification of existing genes, not de novo random assembly — and the Wistar concerns were answered as evolutionary computation developed. [Rejecting P3] Selection does preserve partial function: precursor proteins with weak or different activity are retained and refined, as laboratory directed evolution demonstrates. [Rejecting C] Corrected for cumulative selection and sequence redundancy, the mathematics is consistent with the available time, so the objection does not show the theory is flawed.

Further reading

https://www.hoover.org/research/mathematical-challenges-darwins-theory-evolution-david-berlinski-stephen-meyer-and-david