From simple to complicated by Edwin Banquerigo Jr.

The book “What is Mathematics, really?” evolved on discovering the nature of mathematics in order to understand it deeply. Philosophy and Mathematics is combined in order to unveil the mysteries revolving around mathematics. One funny thing is that I have not taken any philo subjects in my two years of existence in this university because I was trying to avoid it but now I’m reading a book that combines philosophy and mathematics. That is what you call destiny my friends. To start things of Mr. Reuben Hersh showed us three mathematical philosophies: Platonism, Formalism and Intuitionism which he contradicted. Most philosophers treat mathematics as isolated, timeless, ahistorical and inhuman.

Platonism refers to the existence of abstract objects. Hersh stated that mathematics exist outside space and time, outside thought and matter, in an abstract realm independent of any consciousness, individual or social. His philosophy does not fit his own ideals because of its abstract aspects and it does not involve any object. I partly agree with Hersh’s arguments because if mathematics only evolved as an abstract therefore it does not make sense having applied mathematics or using mathematics to solve daily life problems.

Formalism is a theory that holds that statements of mathematics and logic can be thought of as statements about the consequences of certain string manipulation rules. Formalism states that mathematics is not about any other contensive subject matters or in fact they are not about anything. They just exist as numbers or shapes with no use unless given proof or interpretations. I partly agree with these because if no rules applied to shapes there will be no sense in geometry, if no properties applied in numbers there will be no sense in algebra.

Intuitionism is based on the idea that mathematics is a creation of the mind. The truth of a mathematical statement can only be conceived via a mental construction that proves it to be true, and the communication between mathematicians only serves as a means to create the same mental process in different minds ( Brouwer, 1881-1966). I partly agree to this philosophy because mathematics presented in the Story of maths came about by people analyzing and solving many different life problems. Mathematics is merely mental and furthermore used to be applied in objects.

I do not completely agree to Hersh’s contradictions to these different philosophies because most of these philosophies are partly true and applies most of the time. He collected and observed the different flaws of these philosophies and created a powerhouse, mind-blowing philosophy of his own. But he was not able to account that before these philosophies came to existence mathematics has its own philosophy already. Just like the debate on the existence of earth, scientist can’t fully explain where Earth comes from. Many theories came about, philosophers debating and many people wondering but all of this people can’t explain the existence of the Earth. There is no complete evidence that can fully explain the absolute existence of one of the most vital inventions of the mind that helped mankind in ways that you can’t ever imagine. There’s a bigger story why people ponder and tried to understand mathematics. But due to many aspects and points to ponder it is really hard to explain it. One funny thought is that the author this book Mr. Hersh contradicted mainstream philosophies. As I observe in our society most especially in social media, once you contradict some mainstream topics you go viral and famous. Contradicting the mainstream philosophies makes his book more interesting and the philosophy that he presented will be sugar coated and mind boggling.

But because of these mainstream philosophies he was able to present his own philosophy. He presented his own philosophical approach in understanding mathematics and thus beholds HUMANISM. He wants us to understand mathematics in a way that it is a socio-cultural product. Mathematics must be understood that it is a part of human activity, history and culture. If you dig deeper Mr. Hersh was just stating the obvious in a way that mathematics is in co-existence with the community. The culture of Math depends on the culture of the community and it is not formed because it is needed. On a selfish thought the author closes the door of other philosophies that previously existed but we should focus on the thought of his humanism. As I said he was just stating the obvious, mathematics varied in the different cultures it co-existed. The symbols used in the arithmetic of the different civilizations were mathematics co-existed was a symbol of their culture. But I contradict in his idea of mathematics does not serve as a tool because just like a screwdriver it will help you remove screws engraved on an object simply.

I find it hard to read the book because in the first place I am not that much of reading books. I hate reading because it tires my eye and it activates the sleepy side of me. Mr. Hersh has his own writing style that will interest you in a way. His arguments will give you a little and let me coin the word ‘Mind-fuck’ because of all the philosophers and philosophies he involved in his book. Although not all of his points I agreed on but some points ring a bell and make me wonder a little bit. What is mathematics really? Is just a simple question to answer but it depends on your perception on how you will understand it or how will you let yourself accept math. But for me math is just simple it is there to help you understand many unexplainable things but math can’t stand alone, science and philosophy must be there in order for it to function as a whole unit.