In the middle of 19th century, it appeared to scientists, that the answers to all scientific answers about the universe have been already found, or will soon be found. Mathematics has disturbed this with the finding, that natural phenomena are chaotic.
Until then, the universe seemed like a well-constructed machine, that the creator put in motion to obediently tick according to laws of physics and mathematics. That is what Newton’s idea looked like, following Newton’s laws of motion and gravity from the 17th century. However, unanswered questions remained, e.g., problem of three bodies. In a system of two bodies (such as the Earth and the Moon), Newton’s laws worked quite well, the problem occurred, when a third body, such as the Sun, came into play.
Progress was made in the late 1980s by the French genius Henri Poincaré, who took the first steps towards chaos theory. He noted that insignificant changes in the speed or position of the three bodies, which interact by gravity, increase over time, leading towards completely different system behaviour. Despite the irregularity the bodies do not deviate from a fixed point (e.g., planets from their orbits). What kind of mathematics can describe such chaotic behaviour?
Another example is a double pendulum – a system of pendulums driven by harmonic force mounted to an oscillating point. The behaviour of the system depends on the frequency of both components of the pendulum and at the same time the frequency of the oscillations of the suspension point. It can drastically change depending on frequency changes or oscillation times.
Chaos theory is often explained with a butterfly effect. Seemingly insignificant change in the airflow, which is caused by a flutter of a butterfly wing (symbolising the already mentioned slight change in the system) can lead to major consequences, such as a strong windstorm.