Mathematics: Wait, There's More

                Reuben Hersh, the author of the book entitled “What is Mathematics, Really?” was trying to tell his readers what the classic book entitled “What is Mathematics?” failed to present. As he has mentioned in the preface, the aforementioned book only tried to show what math was but did not really talk about what math actually was. In this book, Hersh was trying to illustrate that math was a product of human activity as seen in the perspective of philosophy.  He mentioned that this book was a tribute for “the love of Mathematics and gratitude to its creators. It was stated that between philosophy and mathematics, a parallelism could be drawn out of it. Mathematics is subject to change or is very dynamic just as philosophy is.

                A dialogue between Hersh and a 12-year old girl named Laura transpired and was stated in the book. From that conversation,  it can be inferred that in Math, a lot of questions are yet to be answered or they may never be answered and you are never entirely sure about anything because just like philosophy, math is infinite and limitless. The possibilities in everything are limitless and ever-changing.  

Part one had two goals and the main topic of interest was the existence of a 4-cube.  There was also an inquiry about how many parts does a 4-cube have? This was a very challenging question. According to the problem solving principle of Polya, “If you can’t solve a problem, make up a related problem that you may be able to solve”. Through this, the harder questions may be answered and as what this statement suggested, related problems were formulated in order to dig up the answer of the unanswered inquiries and it has provided us with the answer that a 4-cube has 81 parts. But when philosophy comes into the picture again, the existence and all other details of the possibility of the 4-cube is highly questionable. Even the actuality of a cube had been questioned.            

                 In this book, Hersh repudiates these three mainstreams of the philosophy of math namely: Platonism, formalism and intuitionism or constructivisim. Platonism and formalism are the two dominating views among the minds of mathematicians. Platonism is a very varied form of philosophy. It stands to tell that math exists outside space and time and even in realms unknown to mankind.   Formalism was mainly stating that “Mathematics is a meaningless game”.  Lastly, intuitionism or constructivism exemplifies that the natural numbers are the fundamental basis of mathematics. For Platonism, I could agree with the disapproval of Hersh due to the contradiction of the definition and what actually exists in the real world. Mathematics most definitely exists here in the finite world, ever-changing and dynamic. It stands to give a connection in the phenomena happening in the physical world. It is present here in our dimension. Mathematics is certainly interacting and will be interacting with the physical world. In formalism on the other hand, as stated that math was only just a meaningless game with arbitrary rules governing it. But Hersh disagrees with that statement. The rules are not arbitrary. In fact, they have been long determined through “society which evolved under pressure of the inner workings and interactions of the social groups” and the biotic and abiotic factors of the earth.  Along with these factors, they could also have been ascertained by the “biological properties” that allowed us, humans to evolve. They are definitely complicated and mysterious, undoubtedly. But they most certainly are not arbitrary. Finally, for intuitionism, Hersh strongly disapproves due to the fact that adopting the natural numbers is certainly not universal. This philosophy is flawed because natural numbers may only be relevant and significant if they have been acquired from a finite construction. It also is contrary to the belief that mathematics is infinite and dynamic.  

                As I have stated earlier, Hersh strongly affirms the humanist view of mathematical philosophy. For him, mathematics should come first and philosophizing would follow. Math is indeed a human activity that has been applied to society and has evolved throughout history and although these tiny details have been irrelevant to the philosophical question, “what is mathematics?” without social and historical input, the philosophical problems of math are troublesome. As he pointed out, math has a “social-historic reality” which is not controversial. And another point that he added was that it was not necessary to search for hidden meanings or definition of mathematics which is beyond its social-historic-cultural state. All that it needed to be was social-historic.  

                This book has been an excellent bridge which paved the way for me to appreciate Math in a whole new level. I did not really hate Math. In fact, I liked it for it never failed to surprise me. Every time I get the chance to learn Math, I have always been excited in some way because I know that there was always something new in store for me as an addition to my knowledge. Although it was not really easy to learn, I assumed that Math could be anywhere and that statement that Math is the language of the universe definitely holds true. This book just strengthened that liking and I did not regret reading it even though it was very long. Some parts were a drag but there were more exciting segments that made me understand why Math was like that.  The book managed to relay its message to me and  I hope that  a lot of people would read this because indubitably, there’s a whole lot more to Math than what we already know and perceive.