A Piece of Meat in the Blender

The book "What is Mathematics, Really?" is a 368 page book about the philosophies that wish to understand Mathematics for what it is. The author of this book, Reuben Hersh, discusses these three basic philosophies, namely, Platonism, Formalism, and Intuitionism. He also presented a philosophy that he thinks is more appropriate for Mathematics. He calls this philosophy, Humanism. 

According to Hersh, Platonism, states that Mathematics is an independent form of knowledge. It is not influenced by anything; it exists in a different dimension of some sort. It's like saying that it exists whether man discovers it or not. In my own words, Platonism believes that Mathematics exists all on its own, doing what it wants, all the while leaving patterns of its work behind. This pattern just happens to have been found by humans.

Formalism in Mathematics, according to Hersh, is the belief that Mathematics follows a set of rules that can be changed.

Intuitionism is a philosophy that some believe governs Mathematics. It states that Mathematics is all in the human’s mind, that it is fabricated by finite beings such as humans. Therefore, Intuitionism rejects the idea of infinity.

All in all, this book was a bit painful to read and hard to digest for me. It was as though the author was fiercely throwing ideas—ideas I couldn’t catch thus causing pain instead of helping. This book is thought provoking in a sense but it is not for people who don’t have enough knowledge about the Philosophies and such or those people who just have no interest in this topic. A certain foundation about this subject should be established before it is tackled by a person.

I think people should just believe what they want to believe. The standards or rules are employed by those educated enough and by those who chose to dedicate their life in the name of Mathematics but the choice of which Philosophy governs over Mathematics belongs to the people. Why do I have to dig deeper than what I need to and want to know? I mean, I haven’t thought of these things before and so far I’m not doing bad at Math. Some may say that this kind of thinking is narrow and close-minded but that’s how I am and honestly I don’t think there’s anything wrong with that. We can’t all be Mathematicians or Philosophers. I didn’t sign up for Applied Mathematics or BS Mathematics. I’m open to appreciating what Math has contributed to society and just our way of living now and how it was used by the people from ages ago to solve their problems or to build great walls. It’s amazing—it’s great. The technological advancements, the beautiful buildings, the Pyramids, they all exist because there’s Math. I appreciate that—more than appreciate it. I am truly grateful for it but I just don’t see why others should expect that I learn the Philosophies or the nooks and crannies of Mathematics when I know for a fact that this is not the field I want to pursue.