Mathematics In A Different Light

"Whatever Mathematics we look at, out of the huge pile that humanity has created, one thing can always be said - it was interesting to someone, some time, somewhere." - p. 217 of What Is Mathematics, Really? by Reuben Hersh

I agree with this simple quote from the book. From the documentary films we have watched these past few days, I can really say that Mathematics had and still has a great impact to humanity and the world. Mathematics was shaped by the people who invested all their efforts on it simply because they were driven by their interest with it.

Reuben Hersh aimed to change the perception of the people about the philosophy of Mathematics. He wanted people to see and learn Mathematics in a different light. He believed that the passion of the Mathematicians in the early times regarding this matter can be revived by the present people today if they only understood the different philosophical theories of Math.

He stated and went on to explain the three major views of Mathematics and its nature. He tackled about Formalism, Platonism and Intuitionism. He argued with different perspectives of other Mathematicians to defend his arguments.

The book was also about many philosophical issues, with Hersh trying to convince readers that Humanism was the fit philosophical approach to Mathematics and explaining why the rest of the philosophies won't work in his opinion.

What triggered or rather inspired Reuben Hersh to write this book was when he read the book entitled "What Is Mathematics?" by Richard Courant and Herbert Robbins. He was not satisfied with what was written on the book and he was still left with a lot of questions. He also said that the authors only showed what Mathematics is but not telling what it really is. Another inspiration comes from his observation of the condition of Mathematics education in the United States.

I agree with what Hersh said, that Mathematics has a front and back. The front is the answers and results obtained by us, the people, which we are ready to show everyone. The back is the equations, formula, concepts and patterns we use to arrive at a specific answer.

In rejecting the three philosophies mentioned above, he offers Humanism which believes that “Mathematics must be understood as a human activity, a social phenomenon, a part of human culture, historically evolved, and intelligible only in a social context.” I somehow support this kind of view he proposed. My opinion is influenced by my current knowledge about Mathematics and its history due to the documentary films I've watched. It is indeed both a human activity and a social phenomenon, evolving through time - everywhere you go, in every person you meet, and in every task you complete, Mathematics is a part of it, though it's not always obvious. But this notion has its own limitations. It does not wish to define what is Mathematics beyond its social, cultural and historical meaning.

Furthermore, Hersh failed to express in the book that philosophy of Mathematics is exactly what it is - a philosophy. It is not Science, a subject which he made a comparison with in some parts of the book. This means that it just can't deny the many philosophical issues, views and concepts that overlaps regarding the philosophical nature of Mathematics.

There were a lot of people's Mathematical and philosophical views stated on the book. Each of them may have supported and went against the beliefs of Hersh. This is one of the assets of the book - it tried to provide as many references it can to try to express the main purpose.

His purpose to change the views of people by explaining Math in a philosophical way, in my opinion, was quite risky. Not everyone indulges on the subject of Philosophy and not everyone would easily believe his arguments if he failed to defend his points. It is also a hard task to try to change the way Math teachers and educators think to reform the Mathematics education in a nation. But also, I think reading a book like this opens your mind to different ideas that can help you understand the subject of Mathematics in a whole new perspective. This book is "a means to an end and not an end itself," encouraging Mathematicians, scholars and the like, to have debates and discussions about the philosophical nature of Mathematics to know what points they agree on and let each other understand the issues and arguments at hand.

The author did not quite achieve his purpose effectively. He spent so much time talking about his views against the ideals of Formalism and Platonism regarding Mathematics. He also did not vigorously defend his views about Humanism. If he really wanted to let people understand why he supports this kind of philosophy so much, he should have put an extra effort in it.

Even though there were lapses in this book and there were parts where I could not understand what it was trying to convey, I still think that this book deserves to be read by a lot of people, of course equipped with a little knowledge about philosophy (if not, you are really going to have a hard time understanding it). I'm not saying this because I agree with Hersh's point of views, but because I also think that only in knowing and understanding different arguments and issues regarding the matter, will you know what you really believe and where you stand with.