There are three things necessary for such a fantastical mathematical model to be possible, and we're approaching them all at an accelerating pace.
Perhaps the easiest for humans to strive for is the numbers required to move humans into statistically governed quantities. Similar to how we can predict the pressure exerted by air when it is compressed, we'd need a very large number of people to make sweeping generalizations. We're approaching seven billion people on the planet, but is that enough to be statistically valid? I think not, but we're probably not that far off.
The is probably the most difficult of the three requirements to achieve. Right now, there are many different areas of study of the human condition. Psychology, physiology, crowd behaviors, emotions, philosophy, political science, and many more. Each of them is revealing insights into how people act as either individuals or part of a group. Each of them is giving a single, minuscule building block to the big picture. To make this work, all the different scientists will have to come together to put their piece into a single model with standard measures. It's like hearing cats, if all the cats have P.H.D's.
The most important one is a computer to run the entirety of the equation. Without a computer of sufficient speed, we would never know the output of our equations, and possibly be unable to interpret them anyway. When we break through the barrier of quantum computing, it opens up the possibility that we will have enough data storage capacity to make possible the complex calculations needed to make an educated prediction on the future of man-kind.
Until all those come together, there will be no way to determine what will happen in the future with any scientific accuracy. We have to rely on futurists and dreamers to help us envision the future and what it means to us. I have no doubt that we'll get there... eventually.