What is Mathematics, Really?

          I, personally, am no fan of books.  I don’t have much patience reading a book so, honestly, I’m having a hard time grabbing the gist of what is being tackled about in this book.  I know that I’m too lazy to read and comprehend whatever the book was trying to depict but I think I’ve already done what I could to patiently and enthusiastically as far as I could to understand every idea it was saying, so that I could make a reaction of it since we were told to do so. I know I am not dumb but sadly, I get to understand and retain in my mind only few points in what I have read, so before anything else I would like to say that I’ll be honest in stating my feelings with regards to this book and whatever comes out in my mind that I’ve decided to put in this review, I will state it to my heart’s content whether what I’ll manage to write is wrong or right and that I am not that confident with what I understood so bear with me.

        Platonism, as what the author had stated about it, is the idea that “mathematical entities exist outside space and time, outside thought and matter, in an abstract realm independent of any consciousness, individual or social”. Formalism, states that mathematics is an otherwise meaningless game played by explicit, but arbitrary, rules. While, Intuitionism accepts the set of natural numbers as the fundamental datum of mathematics from which all meaningful mathematics must be obtained through a process of finite construction that does not make use of the law of the excluded middle. These three philosophies are all rejected or objected ( I’m not pretty sure what is the right term to be used) by the author. Since for the author these philosophies are not enough or are just not adequate to be the philosophy of mathematics. First, he rejected Platonism for his reason that; it does not relate to material reality or make contact with flesh and blood mathematicians; it violates the empiricism of modern science; and it insists on acceptance of a “strange parallel existence of two realities-physical and mathematical” but does not explain how the two interact. In Formalism, his reason for not accepting this philosophy is that as to him, the rules are not arbitrary but rather, are “historically determined by the workings and interactions of social groups, and the physiological and biological environment of earth”. He also asserts that this is not how mathematics is actually done, that “the notion of strictly following rules without any need for judgement is a fiction” and that it is “misleading to apply it to real life”. In the case of Intuitionism, he objected it by adopting the anthropological point of view that the intuition of the natural numbers is simply not universal. While rejecting these three philosophies he offered another philosophy, which is the Humanism. He stated that “There’s no need to look for a hidden meaning or definition of mathematics beyond its social-historic-cultural meaning”.  In other words, one finds answers to a big question by basing it to what is done in the society and by how people deal with mathematical situations in their daily living. So, this is what the book was mainly tackled about.

      Honestly, I have something in my mind, more like a question or something that I expected to be addressed after reading such lengthy book. From the title “What is Mathematics, Really?” I was expecting different answers, well for my own way of thinking, I could say that the book focused on the philosophy of mathematics, what I wanted to know was that what is mathematics in our lives, yes, we know that mathematics is responsible for all this progress we are experiencing and so many to be stated but what I would really want to know is that how come mathematics have this huge impact on our lives, I mean, what is so great with mathematics that we have been affected drastically because of this mathematics. In fact, mathematics has been the talk even by our ancestors. Well, I’m just simply curious and though I’ve learned a lot about the history and such of mathematics yet I’m still not that satisfied with all of those knowledge, I think I wanted to know more, I wanted that something that would convince me on what is mathematics really.  Going back to the content of the book, still I appreciate the author’s effort on trying to state what mathematics is really and I could say that somehow I also agree with his ideas but it’s just that I was expecting a different idea on what is mathematics is really. The author had just a different approach and for me it was too scientific (?) that I could not very much understand. However, overall I have learned something new, about those philosophies that before I have no idea of. Maybe, I could not say more about my feelings, reaction or whatever you call it because like what I have said, I did not much understand the whole content or plot of the book, well, I’m just being honest. At least I have done my effort and I think I did my best in trying to express what I have to express in this given matter.