A friend of mine asked me the following ‘I just learned that mathematicians assert (not necessarily in an argument to support God) that there hasn't been enough time for the theory of evolution to be viable. I'm making an assumption you have been aware of this given your profession and scientific mind and I'm curious of your take on this.’
My initial response was along the lines of ‘I don’t have time for a substantive response at the moment but the short answer is that some mathematicians are dumbasses.’
This represents my more substantive response because I know she is interested in an actual answer. A problem comes from the nature of the question itself. I do not know the context with which these statements of mathematicians came up. Was the discussion with an actual mathematician or is this some second hand remark made by a stealthcreationist. (Although the conversation may not have been directly related to a god concept, I am unaware of any general concerns with the theory of evolution that is not steeped in religion.) What was the conversation that led up to this point? I do not know the answers to these questions, but I have a couple of educated guesses what the context was, but if I am far from the mark my friend can let me know and I’ll add another post if needed.
So my two thoughts on how a conversation related the issue of mathematics and time for evolution can be grouped into the following categories: 1. Historically Inspiring; 2. Tedious Probabilities.
Historically Inspiring (please be this one).
The theory of evolution is a dramatically different beast from that first outlined by Charles Darwin in the 1859 publication Origin of Species. (This is not a drawback of science, it’s a feature. Science progresses.) When Origin of Species was written, geologists had calculated the age of the Earth as 20  400 million years old. By geologists, I refer to Lord Kelvin of absolute zero fame. My friend may remember Lord Kelvin from Mr. Daigle’s chemistry class as the person who calculated absolute zero as 273°C or 0°K (the K stands for Kelvin). Anyway, Lord Kelvin calculated how long it would take the Earth to cool to its current temperature if it started as a molten ball and came up with a range of 20  400 million years in 1864, 5 years after Darwin published.
Kelvin ultimately settled on a more narrow range of 20  40 million years. Regardless, Kelvin believed this was too short for evolution to explain the diversity of life on Earth. You know what, Charles Darwin concurred. Darwin knew that his theory requires that the Earth to be extremely old. In the first edition of Origin of Species, Darwin argued that the time necessary for erosion to form the Weald in England is at least 300 million years (But we would also need to factor in the time to deposit all the material to be eroded among other things, which brings us to an age of billions of years). However, based on Kelvin’s calculations, Darwin removed these arguments from later editions of Origin of Speices and referred to the problem (or Kelvin) as an ‘odious spectre’ in letters. To be clear here, both scientists had data to back up their claims, but Darwin was quite cautious in his claims.
Smarter than me, but
still totally wrong

The interesting point is that Kelvin was flat out wrong. Based on what was known at the time, Kelvin’s approach was defensible. However, this was before we knew about radioactivity. The Earth did cool, but it is not simply a loss of heat issue, as assumed by Kelvin. Radioactive decay generates heat, and there is a lot of radioactive decay within the planet. Kelvin thought the Earth’s core was solid and that all heat transfer was by conduction (wrong on both counts).
By making a number of assumptions, which were defensible at the time, Lord Kelvin mathematically derived an age of the Earth that undercut the Theory of Evolution as well as most of geology. However, data was already in existence that suggested the Earth was much older than the age calculated by Kelvin. As more knowledge was gained, it became clear that Kelvin’s assumptions were invalid and thus his calculation wrong. Turns out the Earth is ~4.5 billion years old, which is plenty of time for geological formations to arise and giraffes to evolve. Interestingly, molecular geneticists have calculated that the last common ancestor of life lived ~3.6 billion years ago, which is not long (relatively speaking) after the planet formed. Supportive evidence for these dates comes from the earliest fossils, which are ~3.4 billion year old bacteria.
(Point of reference, Kelvin, a faithful Christian, calculated that only a moron can believe the Earth is a few thousand years old.)
Tedious Probabilities (probably this one)
Another common way to try and use math to disprove the theory of evolution is to misuse probability. The idea is to come up with a probability statement and then use that to show there is not enough time in the age of the universe for life to have occurred. If the odds against an event happening are so huge, it is impossible for the event to have occurred within the time frame the universe has existed. There are two problems with these approaches. First, it is trivial to come up with probabilities that sound impossible for events to occur even those for those events that have already happened. Second, those making the probability statements make assumptions that have nothing to do with biology or reality for that matter.
Making big numbers to impress those not used to big numbers.
Let’s start with a simple probability idea and work our way up. If we get a penny and flip it, the chance of it coming up heads is ½ or 50% (the other possibility being tails of course). The odds of getting heads twice in a row is ¼ (½ x ½) or 25%. Similarly the odds of flipping a coin and having it come up heads and then tails is also ¼. We can take this a little further, the chance of flipping a coin 10 times and having it come up heads each time is 1/1024. 1/1024 is the same as 0.0009765 or 9.77x10^{4} or ~1x10^{3}_{.} It’s about 1 time in a 1000. The important thing here is that the odds of getting any specific combination of heads and tails in 10 flips is about 1 in a 1000. However, if you flip a coin 10 times, you will get a specific combination. I just flipped a nickel 10 times and got T(ails), T, H(eads), T, H, T, H, H, T, H. Was the chance of that happening 1 in a 1000? Well, it was before I flipped the nickel the first time, but now that it has happened the chance that it happened is 100% or 1/1.
When making these kind of arguments, the person picks a really big number to be awe inspiring, like the number of atoms in the entire universe. The number of atoms in the entire universe is ~1x10^{81}, which is a 1 followed by 81 zeros. Everyone knows the universe is really fucking big (what’s bigger?) and atoms are really fucking small, so it makes intuitive sense that the number of atoms in the universe is probably the biggest big number of them all. So, if you can come up with a probability that is greater than the number of atoms in the universe, it must be impossible right?
Remember when we flipped the coin 10 times above? The odds were ~1/1000 (a 1 followed by 3 zeros) that any specific sequence would come up. Well if we flip that coin 270 times, the odds of it coming up heads every time, or any other specific sequence, is 1/1.9x10^{81}. If I flip that coin every 15 seconds, it will take me just over an hour to get enough flips to get a sequence of heads and tails. If we calculate the odds of getting that sequence ahead of time, we get a number greater than the number of atoms in the universe! Using the creationist logic, then it was impossible to get the sequence of 270 Heads or Tails we just got.
Maybe a more current analogy is in order. Powerball! The odds of a specific set of Powerball numbers coming up is 1/1.9x10^{8} (1 time in 190,000,000 tries. Face it, while someone will win occasionally, you won’t). The odds that the last 3 drawings would give rise to the numbers 13,28,49,51,59, 33; 2,24,46,52,56, 19; 4,19,33,41,59, 9 is 1 in 6.86x10^{24}. However, these numbers were in fact drawn. On Dec 9^{th} the odds were 1 in 6.86x10^{24} now they are 1 in 1 or 100%. The difficulty with thinking about these types of calculations is that we forget that although any specific event may by improbable, a specific event will happen.
Just to get a number bigger than the number of atoms in the universe, the biggest big number, let’s go back 12 Powerball drawings, which would be drawings that occurred over roughly the last month (11/9/2011  12/17/2011). The odds of all the specific numbers being drawn were ~1/2.21x10^{99} which is more than the number of atoms in the universe by 1,000,000,000,000,000,000 times (10^{99}  10^{81}). Ergo, those numbers could not possibly have been drawn! But these odds were only true before the Nov. 9^{th} drawing. Again, the odds today are 100%, because this event already happened. It’s pretty easy generating really big numbers to sound impressive, but just because someone has a big number doesn’t mean he knows how to use it right.
Which leads us directly to the second problem here, the assumptions.
The assumptions used to make the calculations regarding evolution in the first place are suspect (wrong is a better word, fraudulent is the best word because those making these arguments have had it explained to them before). For example, the assumption in these types of calculations is that there were a bunch of chemicals and then ...
...these chemicals came together to form the first cell. First, no scientist worth her salt has ever made such a claim, although a lot of creationists have. I don’t want to get into a discussion about the origin of life in this post, but I do want to stress that I have never seen the absurd idea that cells just poofed into existence fully formed from scratch except by creationists. Irony alert: creationists think life zapped into being en masse by god, but ridicule biologists for thinking cells zapped into being en masse by evolution (even though biologists don’t think that).
The ‘calculations’ I have seen use assumptions like the following. Let’s assume that a cell needs 100 different proteins to survive and a protein is on average 100 amino acids long. (This is great because then the creationist can then honestly state that these are conservative estimates. As far as we know a cell needs more than 100 types of protein to live and proteins average length is more like 300 amino acids. This serves to make the result of the creationists argument that much more impressive.) With these (wrong) assumptions, what are the odds that the 20 kinds of amino acids will randomly come together to form all these proteins simultaneously to allow for a viable cell.
Using these assumptions, which have nothing to do with reality, the following ‘calculations are made. The chance of a single protein randomly assembling is 1/1x20^{100} the denominator, as you know, is a number bigger than the total number of atoms in the universe. Add in the factor that you need this to happen 100 times (for each protein). It ain’t never gonna happen! CHECKMATE biologists, the theory of evolution is impossible.
Of course, no biologist thinks or suggests that the above happens. But why let reality interfere with your delusions.
To summarize:
There was a legitimate concern about the age of the Earth and whether there was enough time available for evolution to explain the diversity of life (and geology to explain the geological formations around us). This concern was resolved soon after by physicists and geologists.
Probability is poorly understood and can be used quite effectively to convince people of erroneous ideas. This provides a chance to reinforce the importance of critical thinking and skepticism.
It is easy to demonstrate something cannot be true if you are comfortable being a liar. First, misrepresent the position you are arguing against. Second, make up a bunch of bullshit premises you state represent the position in question. Third, show why the position is wrong because the bullshit premises are bullshit.
If that does not address you question, please let me know.
Regardless, if it wasn't clear enough, here is what the Rolling Stones have to say on the matter.
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