The claim is that some areas of knowledge are discovered and others are invented. I neither agree nor disagree with these claims because some areas can be viewed as only discovered or as only invented and to the person viewing those areas that way, they are correct. On the other hand, some people, such as myself, view the same areas of knowledge as both discovered and invented, and to myself, and everyone else who views them this way, they are correct as well.
When it comes to mathematics and scientific explorations, they both tend to lead to the discovery of mathematic equations and/or scientific equations. The exploration and discovery of a mathematic formula that works is quite clearly a discovery. An example of this form of discovery would be Pythagoras and his discoveries of how the shorter two sides of a triangle squared are the same length as the longer side squared.
With this knowledge Pythagoras invented the theorem which is now world widely used and called, most accurately, The Pythagorean Theorem1.
One well-known example of scientific theory based from facts that have been discovered over many years is the Theory of Evolution. This theory and its many battles with and against creationism have led it to become a highly controversial topic for the classroom. Most schools no longer teach the theory of evolution due its controversial nature, which is caused by the predominate Christian influence in the United States.
Depending on how one looks at facts and interprets them, history can be viewed as either invented or discovered. In American history, it seems that quite a bit of facts are either covered up or phased in such a way that they seem better then they really were. These changed or rephrased facts can be viewed as history...