In the special theory of relativity, each event is a point in 4d spacetime. And we can represent our life as a world line in the spacetime. Then, if we somehow find out the mathematical equation of somebody's world line, then can his future be predicted?
As Anna v has pointed out, this is not something unique to SR. Even classical physics allows for us to "predict the future". Anna's answer gives why this is unreasonable due to QM, but even if that could be overlooked (it can't though), there are other problems.
You are made up of cells, which are made of molecules, which are made of atoms, and so on. To predict your future you would need to know the world lines of all of your parts. All of your biochemical reactions and decisions would need to be predicted (assuming that your decisions can be determined from the interactions of these different parts, but biology is very complex, so this is pretty much an impossible task already). You (I'm assuming) interact with others on a daily basis, so you would need to do this for them as well. But they interact with others as well. And on and on. Nothing is in isolation. To predict the future of one thing we must essentially predict the future of all things.
So really it's impossible to predict the future this way. It doesn't come down to finding a single math equation for a single world line. I would say you have better luck consulting a psychic at this point.
If you have the mathematics of a moving body then its future is predictable in classical mechanics. It would be the same in the extension of special relativity though for a person it is a big IF.
Nature though is not classical, classical emerges from an underlying level of quantum mechanics, which is inherently probabilistic. Therefore there is no mathematical equation of somebody's world line. One could fit a world line up to the present after the fact, but the future is probabilistic because it is quantum mechanical and only probabilities can be predicted . The Heisenberg uncertainty, HUP is a convenient summary.
To clarify after comments:
Any recording of a world line means an interaction has to take place. The world line of the past has been recorded , left a trace of interactions that were picked up from the probability distributions according to the quantum mechanical laws. A future world line will be one instance at each (x,y,z,t) picked from a probability distribution, decided at each point.
The HUP is a convenient envelope in describing uncertainties, as any world line of a particle or an object will have both a space envelope and a momentum/energy envelope. If there is no momentum there is no activity, and according to the HUP the space dimensions will be undefined.
Your thoughts are similar to that of Laplace's Demon, and may be better suited for a philosophy board.
Wikipedia sums it up well:
According to determinism, if someone (the Demon) knows the precise location and momentum of every atom in the universe, their past and future values for any given time are entailed; they can be calculated ...
Laplace notably refers to the best model(s) of physics available to him at the time (he refers to the "tiniest atom").
Despite our better models now, the sensor and computational capabilities required for a perfect model to predict the future faster than realtime are quite unrealistic.
It's still a wonderful thought experiment.