Can Maths Predict The Future? The Maths Behind Chaos Theory and Sudden Change

Since Newton, we are used to science making confident predictions about the future. For example, the motion of the planets and the times of the tides. However, some things seem very hard to predict, such as the stock market, or the weather in six months' time. Is this a fault in the way we model these systems, or is there a genuine limit to how far we can predict the future? One explanation comes from the theory of chaos, which illustrates why small changes now can lead to large uncertainty ...