Mathematics, what art thou?

So get this, I was supposed to make a review of a 368-page book in less than a week (with a lot of papers on the side). A review about a math book, a math book. So I set to work because that’s what a student gotta do. I’m not one to half-ass my work (pardon my terminology) so I really tried to read, understand, finish, and make sense of everything but sometimes things just don’t go your way. Anyways, the following paragraphs are my understanding of the information found in the book.

What Is Mathematics, Really? is an attempt by Reuben Hersh to answer the title itself. This idea was brought upon after he read Courant and Robbins’ book ‘What Is Mathematics?’ According to Hersh no definite answer was given by the authors so, he decided to make his own book that would give a precise answer to that otherwise difficult-to-answer question.

Hersh used philosophical approach to explain the meaning of mathematics. Instead of using the three existing philosophies of math – Platonism, Formalism, and Constructivism – he suggested another option. He called this Humanism. To him, mathematics is a trial and error process that is part of people’s lives.  He used humanism to perceive “mathematics as a human activity, a product, and a characteristic of human culture and society.”

Do I conform to his ideas? I still can’t answer that. Hersh has a tendency to undermine the perspectives that contradict his and put his own above others. His explanations of ideas also jump from one point to the other without really giving detailed information. So really, how can you make a fair judgement? It would be much appreciated if he were more objective.

Hersh also tried to respond to age-old question whether math was invented or discovered. His answer was neutral; he thinks math is both.  After you invent a new theory (example group theory) you must discover its properties (find, for example, how many simple finite groups exist). And you may have to invent a trick to discover the solution of a problem. Thank you Jaume Puigbo Vila from Barcelona, Spain for that example; couldn’t have said it better myself. I go with Hersh in this one because going back to its history (or if you have watched The Story of Maths) mathematicians used their predecessors works as references for their own invention.  

On the whole, this is a thought-provoking book, although it would be difficult for those non-mathematically or –philosophically inclined to comprehend with all the words and principles that make the mind go blank. Anyone interested in the philosophy of math might be a little disappointed with this book and should consider reading other materials.