Neo-Darwinian evolution refuses to make quantifiable predictions regarding the amount of time needed for evolution to work. If you ask a Darwinist, "How much time should it take for natural processes to produce life from simple organic chemicals? How much time should it take for Darwinian natural selection to produce a complex eukaryotic cell from a relatively simple prokaryotic cell, or to produce complex animals from sponge-like creatures, or to produce a whale from a land animal?" you will be met with silence. Darwinists have no method of coming up with even approximate estimates for the answers to these questions. That's their dirty little secret. Darwinists can't quantify the time needed for their mechanism to work.
The Nobel Laureate scientist Wolfgang Pauli, who won the Nobel Prize for physics in 1945, astutely identified this weakpoint in Darwinism. Pauli's open skepticism towards Darwinism is discussed by Harald Atmanspacher and Hans Primas in their article, Pauli's ideas on mind and matter in the context of contemporary science (Journal of Consciousness Studies 13, 5-50, 2006). In section 7.1, the authors identify the target of Pauli's criticism: the Modern Synthesis, which, like neo-Darwinian synthesis of 1959, insists that mutation is random, and not adaptively directed:
Before the advent of molecular biology in the 1940s, the mainstream position with respect to biological evolution was referred to by the term Modern Synthesis. A key concept of this position was that the genetic variation within a population arises by random mutations, not by adaptively directed mutations and recombinations (Mayr, 1982).
The authors go on to point out that Pauli was not convinced that the evolution of life could be explained by random mutations only, and that he questioned this aspect of the Darwinian model of natural evolution on mathematical grounds:
"As a physicist, I should like to critically object that this model has not been supported by an affirmative estimate of probabilities so far. Such an estimate of the theoretical time scale of evolution as implied by the model should be compared with the empirical time scale. One would need to show that, according to the assumed model, the probability of de facto existing purposeful features to evolve was sufficiently high on the empirically known time scale. Such an estimate has nowhere been attempted though."
(Pauli, W. 1954. Naturwissenschaftliche und erkenntnistheoretische Aspekte der Ideen vom Unbewussten. Dialectica 8, 283–301. Quoted passage from p. 298.)
Darwinists know that their theory is incapable of coming up with the hard numbers. To cover up their embarrassment on this score, they often put forward proposals for the origin of proteins, the origin of life and the origin of complex animals which are highly speculative. But a good mathematical argument should only appeal to processes that are already known to generate results. As they say in Missouri, "Show me."