Using examples from your own education, describe the ‘Mathematical Method’
How is it both similar and different from the scientific method? What are the strengths and weaknesses?
The mathematical method uses axioms as building blocks to create hypothesis and theories. It combines deductive reasoning and axiomatic beliefs to formulate explanatory and descriptive theories. It does not require a lab or the observation of external participants, it can be formulated based on already existing theories. The mathematical method leverages existing theories without disproving them.
Both the scientific method and the mathematical method involve the creation of a hypothesis. However, with the scientific method, once a hypothesis is created, you still have to complete many experiments in order to prove or disprove it. With the mathematical method, the hypothesis is often much more absolute and are less likely to be disproven. This is because the mathematics and theories behind the creation of the hypothesis already carry absolute truths, whereas, with science, you can never know when something is absolute as it could always be disproven. Take the Pythagoras Theorem for example. It states that, for right-angled triangles, if you take the sum of the square of the two sides adjacent to the right angle, it equates to the square of the hypotenuse. This theorem was made over 2,500 years ago and it is still commonly used to this day.
A weakness in the mathematical theory is that tt is harder to provide justification for as there is often no physical proof that can be presented. It is also not subject to as much scrutiny as the scientific method is. This is a strength of the scientific theory. Theories and hypothesis in science are continuously being reviewed and revised by new generations of scientists who endeavor to prove or disprove them. However, you are often unable to combine theories in science without disproving one. With the mathematical method, it allows you to combine theories to formulate new ones.