What is Mathematics, Really?

‘What is Mathematics, Really?’ is a book by Reuben Hersh which focuses on discussing the different point of views of many philosophers of mathematics. Some topics discussed in the book are about Formalism, Platonism, Constructivism, Humanism and others. He tries to debunk the first three and try to introduce what he believes in which is Humanism.

For formalists, mathematics for them is a meaningless game. Because of this, there are not much mathematicians that support formalism. Platonism is much more popular than formalism. Platonists believe that mathematical truth are not invented but discovered. For constructivism, they believe that proof is important to validate that a certain thing exists. An example given is the 4-dimensional cube. Hersh says that these three are just some philosophies of mathematics. What he believes in is “Humanism”. He believes that “mathematics must be understood as a human activity, a social phenomenon, part of human culture, historically evolved, and intelligible only in a social context.”

A part of the book that was interesting for me was about mathematics having a front and a back. What is taught in class is only the front while the back is rarely spoken or just forgotten. What’s taught in class is the “finish product” of what mathematicians have discovered or proved. I thought of all the math classes I had since elementary days and I realized that what he said was true.

Honestly, this book was very hard for me to digest. Every time I tried to read the book, I had to open the dictionary application in my phone. It exercised my brain to think more and understand it better but it was still hard. When reading this book, a person must have enough background about mathematics and philosophy to understand it better. This book aims to explain the content in an easy comprehensible way for everyone, but I think Hersh has failed in this objective. All in all, it was a good book. Hersh tried to explain everything in a modern and fun way. I just hope he could have explained everything better and in a more direct way.