Creationist mathematics

Creationist mathematics (or more accurately, the creationist misuse of mathematics) refers to arguments using mathematical and physical formulae to argue that something is too improbable or impossible to have occurred, thus rendering the opposition's argument invalid. However, creationists who use these arguments often ignore one or more major factors, thus rendering their arguments invalid.

BIG NUMBERS
One type of creationist mathematics is the use of BIG NUMBERS. The larger the number of possible options, or years it would take to occur, or types of things necessary to obtain a positive result, the better: a really high number supposedly means that the possibility of the event occurring is far too low to have occurred at all.

Chance
Often the argument rests solely on "chance." That is, the math shows that there is such a low amount of chance that the event cannot happen, or would take far too many opportunities for the event to occur. In fact, typically the number of opportunities isn't even mentioned: the odds are given as if there was only one opportunity for a given event to happen ever.

Failure of Factors
Often with the arguments above, the creationist tends to ignore one or more important factors. For example, arguing that the evolution of a new functional gene is too improbable, based on math that the new gene would have to result purely by random chance, ignores the factor that new functional genes form from previously functional genes. Thus, one small change in one functional gene can give rise to another new functional gene, limiting the odds against such an event to occur to much lower than their arguments claim.

Another factor often overlooked is the number of chances for an event to occur. Arguing that a new functional gene requires many changes ignores the factor that a population of organisms has thousands, if not millions or billions, of chances in one generation to attempt the random event.

Abiogenesis
One argument often used by creationists is that it is so improbable for abiogenesis to occur at a given point that it could not have happened by chance alone. But, setting aside for a moment any misjudgment of the probabilities involved, this ignores the fact that abiogenesis had the entire universe to happen in, and hundreds of millions of years over which to roll those dice.

For example, if someone enters a lottery with odds of one in a million, although it is unlikely that particular person will win anything, if a billion people entered the lottery it is likely that about a thousand of them would win.

Or, put in more general terms, if the probability of some event occurring in some particular place is $$1/P$$, then even with only $$P$$ possible places for it to occur, the probability of it occurring in at least one place converges on $$1-\frac{1}{e}\approx 63\%$$ as $$P$$ increases without bound. In reality the number of possible places is likely much higher than any constant $$P$$.

Speciation
(Or, what might be called meta-speciation.) In a post discussing Johnny Hart's (of the B.C. comic strip) creationism, someone challenged people to answer just how long it would take a prokaryote to evolve into a eukaryote in the lab. This shines a light directly on the common approach of pretending there aren't many opportunities for said unlikely event to happen. The answer, of course, runs something like "If your lab is the size of the Earth, with conditions like on early Earth, round about 2 billion years."