Is math capable of predicting social evolution? By the way math and statistics are evolving, it seems possible to me that with time, and as the population increases, we are going to be able to create mathematical models that predict social movements, and I've heard there is some research focused on small predictions like elections and such, but is it mathematically possible, or likely, that math is evolving to a point where we will be able to know with a relatively low error the probability of certain social events to happen?
I mean something like what happened in the middle east, or 2008's crisis, or even a more time consuming evolution. Of course it would not be able to predict individual actions that somehow affect in a significant way this evolution, or natural catastrophes.
More specifically, are there theories being developed? How far are we from this kind of thing? Is it even mathematically possible? Or there are too many variables? And what happens if we consider that the population may never stop increasing (hypothetically)?
 A: The problem of prediction is not so much the math as it is the complexity of those social interactions and sparsity of data. In a very simple physics experiment, knowing all the physical laws and observing the initial state entirely, you can predict what is going to happen when, say, you increase the temperature. But in reality you neither know the laws that govern those social processes, nor do you observe the initial state perfectly. 
A rather recent tool used to predict outcomes are prediction markets. Suppose you want to predict the outcome of the election Obama vs Romney. You create a new market that sells two securities. The Obama security pays \$1 if and only if Obama wins (after election is over), and \$0 otherwise (becomes worthless). The Romney security similarly pays \$1 if and only if Romney wins. Then you let people trade these securities in the prediction market, very much like a stock market. Now, intuitively, if more people think Obama wins, then more people want to buy this security, which drives up the price. Since the security pays at most \$1, you want to pay at most \$1 for that security, and since he might win, you want to bid at least \$0. Hence, the price $p$ takes value $p\in[0,1]$, and the Romney price is $1-p$. Thus, the price fulfills the axioms of probability and can be interpreted as the "market probability", "market prediction" or "market estimate" of the probability that, say, Obama wins.
Indeed, prediction markets have been shown to be more accurate in predicting the outcomes of elections than polls. See here for an older overview article, and here for evidence that prediction markets outperform polls. This may not be suprising if you think about it: insiders can make a lot of money in these markets, so they use that knowledge and drive the price in the right direction.
A: Indeed yes. This is active research field, and what I would suggest you to read is all around the works of Weidlich, I remember some time ago (twenty years ago) with his team we simulated dictatorships, democracies, revolutions etc. Not only complex societies (socioeconomic for instance) can be modelled mathematically predictive but also very primitive such as the models based on predator/prey for primitive societies.
Good starter: "Sociodynamics: A Systematic Approach to Mathematical Modelling in the Social Sciences"
And a smart video here>>>
A: EDIT: If by the crisis of 2008, you mean the financial meltdown, just look at the evidence. There are financial firms with mega-substantial resources that as part of their analysis try to model these things. As you can see things did not go well in that regard. Even today, JP Morgan lost a bundle - $6 billion - where their risk models did not serve them. Some time ago Long Term Capital Management - a model based hedge fund run in part by Myron Scholes (Noble Prize winner for option theory) almost brought down the entire global financial system. In 2008, the FED had models which admittedly did not do the job, and felt the sub-prime mortgage problem would be decidedly contained. Today every major financial firm has risk models, but their performance is questionable in "unusual" times. Just when you need them. Typically what goes wrong is "basis risk" where supposed correlations (positive or negative) go astray, and you are left with big losses. 
Of course in normal times they do nicely reflect the risk exposure and can detect trends. But what kills you are the "Black Swans." That's why they are called that. So from a probabilistic perspective, it's the outliers, hard to model.
So you will see that many financial institution have an enormous notional risk on their books, but claim a substantially smaller net exposure. Thinking they are hedged. When these hedges don't perform as intended (basis risk), all of a sudden your exposure explodes.  
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Some comments regarding the applicability of "evolution" to math or social sciences.
It's interesting that you you "evolution" twice, regarding the math and society. Actually "evolution" has been co-opted to imply "progress" or change. But here is a quote from wikipedia:
Moreover, previously held notions about evolution, such as orthogenesis and "progress" became obsolete.[7]
Obviously evolution has various meanings to various people. But technically, evolution really entails biological reproductive advantage. Advantage has the connotation of change; and this change is first manifest in the genotype, and may emerge in the phenotype. (Simply put, a change in the genes shows up in the physicality of the biological entity.) 
This change in the genes comes about through mutations - so basically by accident in cell reproduction or some insult such as UV radiation. There is a somewhat regular occurrence in the reproductive process - even though cells have some amazing capabilities to alleviate these mutations. DNA repair mechanisms, and checkpoint systems that can cause cell death in certain circumstances. This is often what fails with cancer, where a mutation knocks out a control gene and cell replication goes wild.
In the context of modeling evolution in a given population, there are math techniques that are applicable.
So while this is not explicitly an answer to your question, maybe it gives a perspective on what evolution entails and questions whether it is applicable to social trends or math.
For a much better picture, here is a link to a free on-line video lecture series from a class at Yale:
http://oyc.yale.edu/ecology-and-evolutionary-biology/eeb-122
A: I would certainly argue that this will not be possible. If you got the perfect model and you put in all the data and it states that in 2 years there will be a financial crisis people would change there behaviour and the financial crisis won't happen. If it would state that America will become communistic in 10 years time with a probability of 85%, there would be a sufficiently large group of people that would constantly try to make it not happen.
Hence, if you predict a certain event, the reaction to your prediction ruin your predictions
