Philosophy of Math, Really!?!

                 At the start was a funny dialogue between L and R about the philosophy of math. I did get the uncertainty of numbers and mathematical ideas hint there, and I too was influenced to think the same way as L. so many thoughts from a simple dialogue. By the way, I think L here is still a child, and yet I think the same way as her, how sad. With this, I thought that the book would generally be about simple concepts and ideas concerning math, maybe even some abstract theories, nothing that difficult to digest… I was WRONG, so very WRONG.

                This is such a weird book. Why in God’s green earth would the authors tell readers to read chapter 11 right at chapter 1. Not only that, chapter 1 is an exercise! I expected to just read not do more work. I don’t like his writing style, it’s too confusing. Throughout the first few chapters he reverts back and forth from philosophy to logical solving, so much that both are harder to understand.

                The overview was boring and extremely technical. The first part of it was just like the Story of Math in that solutions are derived from conceptual evolution of previous knowledge and that no solution is created in isolation. What followed were some technical stuff about math’s methods and contents. My brain stopped at formalism and Platonism. The discussions were so confusing, like in formalism being undefined, then defined, then undefined again and then the author goes into multiple descriptions and examples…SABAW na jud. Platonism, on the other hand, was too abstract for me to conceptualize. So many quotes, too few brain cell. I can’t even relate to most of them, who the hell is Erdos and what is with The Book? An independent math world? I think that’s crazy, I can’t even conceive the basic premise for that idea. Math is hard by itself, why would I add abstract concepts to it? I think this book should be read only by those who have a high amount of mathematical knowledge. How can you expect me to understand complex math concepts written in old English style?  

                The book continues to delve into subjects I can’t readily understand, mostly philosophical. Most parts are either statements of opinions of certain factions or the deliberation among these opinions as stated by the author, Hersh. There is also a long criteria for determining mathematical philosophy, I cant thinkl of reasons why that is even needed. Next was a social perspective of math. This book really needs a warning like “Don’t Read Unless You Know Stuff”. I also noticed that Hersh likes long and well exampled back stories or definitions which I find annoying since it makes it harder to continue reading. Just get to the point, how hard is that? Chapter 2 just went by, only a few tidbits were actually absorbed by my brain. I especially liked that “the working mathematician is…”. It somehow sums up how abstract and disconnected math is, I mean, even experts can’t completely describe it.

                The next chapter was much more relatable, it generally talked about proof. I say more relatable only because I understood some of the concepts in this chapter such as proof, fallibility and certainty. Same as before, Hersh defined, then enumerated, then self contradicted, then gives another definition, etc. So many paragraphs just for 1 word…. But the book still surprised me by giving so many different perspectives.  The only perspectives I know are that of what he described as “In Class” and “In Research”. I agree with Hersh in that students are too easily convinced, “since a PROFESSOR said it, it must be true”. Hersh then proceeds to certainty, which he fills with contradicting statements of different people and factions. The only thing I got from this part is that even the certainty of mathematical processes is uncertain, isn’t that just stupid. That is when I realized, Hersh really likes to go back and forth, now from agreeing to contradicting. It’s like he purposely wrote this book to disprove everything I know. The next chapter was kind of straightforward, just a few problems and their interpretations and supposed solutions. I think I understood most of them since they weren’t explained too much in terms of philosophy.

                Part 2 of the book was easier to understand. It pretty much resembled a normal math book though a more comprehensive one. First it presented some precursor maths of previous mathematicians, much like the story of math. Hersh noted many important events in the evolution of mathematics and philosophy. Some were the same as the story of math, but this had more information. Like how philosophy and math were combined by Pythagoras in his teachings. The Theology of Infinity, wherein “God is the absolute maximum or the infinite being” and how they used this concept to formulate the characteristics of infinity in math, was also very interesting.

                Then came the mainstream era of math. Like before it just stories, contributions and events in the math timeline. Most of the names here are new to me, and the math could already be considered as somewhat modern. And it is obvious here that Hersh put too many details in some of the life stories. How is someones death by glass inhalation relevant to math? This continued until the end. Later chapters of course had more specific math concepts which took a long time just to grasp.

                As a whole I think “What Is Mathematics, Really?” is a decent book. I neither liked it nor hated it. Maybe if I had more time and references on what Hersh was talking about I could have enjoyed it. In terms of information and mind-opening opinions and concepts, it has a lot, too much even. I am still amazed how such as simple thing such as counting and listing has evolved into something as complex as modern math and as abstract as philosophy of math. I just hope I can understand at least some of it… much math, wow.