Can mathematical models predict the future?

The BBC's Horizon has madea  television programme on how using mathematical models on the large amounts of data now available can do  incredible things such as:

• Predicting where and when crime will occur before it happens
• Mapping out the entire universe
• Financial formulas for scientifically predicting whether stock prices will go up or down rather than relying on gut feeling
• Using genetics (a vast data set) to predict and understand diseasesso they can be cured

The programme can be found on the  BBC's iplayer here

Im figuratively drooling over the huge possibilites this kind of research has for the future.