Philosophies of Math

We’ve been doing math since time began but did you ever wonder what Mathematics really is? We know that it is all about numbers, equations and formulas. But until today we still don’t know how to fully describe what math is.

Reuben Hersh, who wrote this book, was enlightened by What Is Mathematics? by Richard

Courant and Herbert Robbins’ book. This book (What Is Mathematics?) fascinated Reuben because they were able to explain what mathematics really is by showing it rather than telling about it which is how it should be.

Part one talks about the different philosophies of math and Reuben’s opinions about each of them. These philosophies of mathematics are Platonism, Formalism, Intuitionism or Constructivism and Reuben’s addition to math’s philosophies, Humanism.

Platonism is Plato’s philosophy that objects exists outside space and time and is therefore free of any ones thought. That objects are real whether we have seen it or not. Simply saying that it exist no matter the circumstances.

 Formalism tells us that mathematics is all about formulas, axioms, definitions and theorems. That there are no mathematical objects. But these formulas could be interpreted with the help of physics and these axioms and theorem could be falsified base on the object.

Intuition is the opposite of Formalism since it is a philosophy that greatly deals with actual or physical representation of mathematical objects. It connects both the potential and the actuality of an object. It was also said that it is the thinking of a Creative Mathematician.

Humanism is a sociohistorical point of view which means that base on the social, historical and cultural (sociohistorical) perspective the meaning of Mathematics need not be further looked into.

Part two shows the philosophical opinions of different mathematicians which would help clarify many doubts and questions of the readers. And the readers would be able to have a view of the mathematicians’ point of view or perspective.

It also shows the brief encounter of mathematical philosophy and theology. This was inevitable before since many mathematicians were influenced by religion therefore thinking that mathematics came from deity is a given. However, this way of thinking slowly vanished because of the development in mathematics specifically the Euclidian geometry which altered the people’s way of thinking. Another reason is that mathematicians’ believe that mathematics should be free of any religious or political influences.

Reuben talked a lot about Platonism and Formalism but what about his alternative philosophy (Humanism)? Reuben was not able to fully incorporate his idea of a sociohistorical understanding of mathematics into the textbook.

Regardless of this, with different options to choose from I believe that the true philosophy of mathematics lies within the person itself because each philosophy has its ups and downs and sometimes these philosophies coexist. That you cannot believe the other wholeheartedly without comparing it to the other two. It is also because each philosophy has a point and that sometimes they cancel each other out.

BY: DAISIC DE ASIS BELLO