The scientific method is a specific approach to inductive reasoning. In inductive reasoning, you generalize from a set of effects or observations to produce laws or rules. Deduction is the opposite, you would start from a rule to deduce an effect. The ancient Greeks discussed induction widely, and this discussion was continued by Arab Alchemists and many medieval European philosophers. The scientific method refines the process of induction so that it could more consistently produce valuable new knowledge. This page only briefly summarizes the scientific method.
The scientific method taught in second level (high) schools around the world is key to all science. Even so, it is important to realize that there is a lot more to the workings of science including social and creative factors. The textbook description of the scientific method might read as below:
If it is agreed that the experiments properly test the hypothesis and the results agree with the expectations then the hypothesis becomes a theory and is accepted as proven. If the results of all the experiments do not agree with the expected results then the hypothesis is rejected or modified and retested. It should be remembered that the measure of a good test would be that it maximizes the probability of disproving the hypothesis. A simplified flowchart of the scientific method is shown below.
The description above is missing some fine points. In practice, the scientific method can only disprove a hypothesis, not prove it true. With any experimental regime, you are only testing a subset of the possible events,scenarios or individuals. How can we be sure that what we tested was representative of what we didn't test. This means that there is an element of trust when we say that an experiment proved a hypothesis true. Maybe saying the theory has been accepted is better than saying it has been proven. Regardless, we know the scientific method has been very productive.
One event illustrates some of the subtle problems with scientific method. Proofs must account for any consequences of a hypothesis and proofs are subject to limitations of scientific observation and measurement. In the 16th and 17th century the hypothesis that the earth revolved around the sun was proposed. But there was a necessary consequence of that hypothesis; if the earth revolved around the sun then there should be changes in the relative positions of the stars over the year (see Stellar Parallax). This stellar parallax could not be observed. Based on this and other 'facts', the scientists of the time were correct to reject the proposed proofs. What they did not know was that the stars were far more distant than they thought, billions of kilometres away instead of millions. Given the power of the telescopes of the time, they would not have been able to detect this parallax. There was another problem with telescopes of the time. Because of distortions by the lenses (diffraction) the distant stars would appear much larger than they actually were. The hypothesis was rejected on facts, flawed equipment and a false assumption. Even so, The Copernican Theory was not proven by Galileo as many believe (see The Galileo Myths, Myth 8) but in the eighteenth and nineteenth century when stellar aberration and stellar parallax was finally observed.
It is difficult to credit any one individual with the invention of the scientific method. The development of the scientific method seems more an evolution than a discovery or invention. Although Galileo is often credited with its invention, there were well known physicists and philosophers who were advocating similar ideas and conducting similar experiments before and during his time. Galileo's writings on method focused on the demonstrative regress of his predecessors at the University of Padua and the Jesuits' Collegio Romano. Giuseppe Moletti, a professor at the University of Padua, performed and recorded a well-designed and well-controlled experiment on free fall when Galileo was only 12 years old (see Galileo's Contemporaries). Another criticism of the single inventor approach is based on the belief that craftsmen throughout the world could not have achieved such high levels of craftsmanship without using the approach described in the scientific method.