I'm "philosophically" confused of this book, really.

What is Mathematics, Really; exercises the brain to think critically and philosophically about the true nature of mathematics. Each individual has their own personal opinion or stand about numerous ideas, issues, points and phenomena. Sometimes these unique opinions lead to contention among each individual. Regarding this matter, some philosophers of mathematics have their own unique opinion about the true nature of mathematics. The author of the book Professor Reuben Hersh, has a unique point of view on mathematics compared to the idea of most mathematics philosophers about the said field of study. Professor Hersh wrote the book to express and to justify his own philosophical ideas about the whole nature of mathematics. His book had lead most readers even I myself to a high degree of critical thinking.

The title of the book “What is Mathematics, Really?” was coined from a book written by Richard Courant and Herbert Robbins entitled “What is Mathematics” that Professor Hersh had read before. The book wasn’t enough to satisfy the professors craving of knowledge regarding the subject of what is Mathematics really all about. He decided to impart his own opinion about mathematics nature, where did it come from, and what is the phenomenon behind it through writing this book. The main objective of his books is to explain why he rejects the three mainstream philosophies regarding mathematics; plantonism, formalism, and intuitionism and prove that his own idea of humanism is more superior over the other three philosophies.

His book is divided into two parts. The first part of the book talks about how Professor Hersh disagree with the three mainstream philosophies about mathematics as mentioned earlier; plantonism, formalism and intuitionism. In this part of the book he wants to prove that his own philosophical idea about mathematics; humanism is more exceptional compared to the three main stream philosophies. The second part of the book Professor Hersh was focusing on the philosophical analysis of mathematics.

These were how Professor Hersh had explained the three mathematical philosophies. According to Professor Hersh plantonism is a “mathematical entities exist outside space and time, outside thought and matter, in an abstract realm independent of any consciousness, individual or social.” Formalism according to Professor Hersh is an “otherwise meaningless game played by explicit but arbitrary rules”. The last philosophical element, intuitionism according to Professor Hersh is where natural numbers are accepted as a fundamental datum of mathematics. As an alternate to the mainstream philosophies that Professor Hersh had rejected this was how he explained his humanist or sociohistorical point of view; he says that; “There’s no need to look for a hidden meaning or definition of mathematics beyond its social-historic-cultural meaning.” In other words he wants to explain that mathematics is a part of a mathematician and by “ordinary people’s” everyday life.

I would agree with Professor Hersh’s stand against Platonism because it is true that we could not feel mathematics. Mathematics is just out there floating in our minds and ideas, we could think about it but we could not literally see or feel it. This idea does not connect the interaction between physical and mathematical. The knowledge may be passed on to generation to generation or this knowledge is used all the time but the people in the physical world and mathematical realm would never connect with each other physically.

In formalism Hersh points out that rules are not are not just a simple product of chance but it is historically determined. Mathematical solutions are passed on through generation and are being applied. For me it is true that mathematics are passed on by our ancestors and we would pass it on to our descendants but it doesn't’t mean that we and the future generation would not be able to have their own way of using mathematics.            

Lastly intuitionism for Hersh is a process of finite construction which means that each individual thinks critically in a unique way. All of us think of mathematics in a different way we are capable of understanding and constructing a conception of the natural numbers based on our daily experiences and certain ways of thinking.

For me Professor Hersh was confusing from the beginning of the book. I could not understand why he wants the reader to read chapter 11 when in fact the reader is still reading the first paragraph of the first chapter. I don’t agree on how he presents his philosophical ideas and point of views I could understand that he wants to prove that his own stand is more accurate compared to the other mainstream philosophies about mathematics but he had failed at some points of proving it because again, he is so confusing. Some parts of his ideas were contradicting each other which had leaded me to be uncertain if I should believe his philosophical views.

During the course of writing this reaction paper I had realized that maybe Professor Hersh had made this book confusing and challenging to read because that is how math was presented to us and He wants to show us that reading his book is like solving an entire math problem; even if it is confusing if we would critically think about it we would be able to understand and finally have answers to our confusing questions. But maybe this rationalization might be wrong because this is just my own opinion based on my observation.

          

 In conclusion I agree and disagree in some of Professor Hersh’s philosophical ideas. I don’t recommend this book as a good basis for direct answer on philosophical ideas about mathematics because this book was published 16 years ago and many things had changed around us that might affect the own personal point of view of the author. But I recommend this book if a person wants to challenge his or her intellect regarding the philosophy of mathematics.