In my opinion an invention may be defined as a new device, method, or process developed from study and experimentation whereas a discovery is an act or process of finding something or somebody, or learning about something that was not known about before. Another way of differentiating discovery and invention is in the following: A discovery is something someone else can test for himself and find out if it is true or not. An invention is something that is true (and exists) only because of the inventor. Some people would say: Invention is of our making while discovery is what we can learn from God’s making or from the nature. There are many different areas of knowledge, from natural sciences (most notably physics, chemistry and biology), mathematics up to areas like human sciences, history, religion and arts. As a generalisation it can be said that discoveries play a bigger role in natural sciences and even in mathematics than in areas like religion or arts. Art, be it a painting or a piece of music or certain literature, is generally invented by individuals. If a piece of art would not have been invented it simply would not exist. Laws of nature like the gravitational forces are not invented. They exist on their own and can only be discovered. Such laws are generally described in mathematical terms, by using equations and mathematical models or systems. Discoveries are unleashing something that already exists. Many discoveries only became possible because of inventions (like the microscope, the telescope, the transistor or many other machines) made before which enabled new observations. I’m not aware of any inventions contained in the human body; it simply exists and certain discoveries can be made, i.e. regarding the cell structure or how the human brain works. However, certain machines can be invented. An invention is something new that did not exist before, like the transistor, the integrated circuit or the internet.
Many scientists including for example Francis Bacon observed that nature is ruled by laws and the task of the scientist is to discover and describe them. A scientific method has been developed which includes observation, the development of a hypothesis, predictions on the basis of a model and the development of laws and theories. A law discovered can be correct within a certain range and fail beyond such range. This was the case with Newtonian Physics. So rather than thinking that scientific laws once discovered are eternal truths we should always be prepared to question and test their validity.
Discovery directly relates to nature. It can comprise new laws of nature (like electromagnetic forces or gravitation) or new components like electrons, protons or quarks. Discovery often relates to something that exists in nature. A discovery frequently leads to the development of a new theory. However, things are more complex and at times it can be the other way around, as I will demonstrate below.
Mathematics is needed to describe observations made in natural sciences. Mathematicians are still puzzled when asked if their area of knowledge is discovered or invented. There are different schools taking either position. It seems to me that both views have their merits. Plato believed that mathematical objects exist “out there” and that they are even more real than physical objects. Mathematical objects have clarity and immutability; the Pythagoras theorem discovered two thousand and five hundred years ago still holds and is apparently timeless. It seems that the underlying truth has been discovered. At the same time one can argue that (at least large parts of) mathematics is simply invented. Every mathematician can define a set of axioms and invent a system around this.
This was the case when Riemann defined axioms different from Euclid. Amongst others he stated that two points can determine more than...