"What Is Mathematics, Really?" - a book review

          “What is Mathematics, Really?” is a book written by Reuben Hersh which was published in the year 1997 by Oxford University Press. Hersh is an American mathematician known to have written books and analogies about mathematics. He made a somewhat “sequel” or based the book from Richard Courant and Herbert Robbins’ book entitled “What is Mathematics?”.
           So why should we read the book? Hersh imposes that mathematics must be viewed as a part of human activities in a “socio-histo-cultural” framework which he also calls the “humanist” approach. Given with this scenario, people might be able to relate easily in the philosophy of mathematics.

At first, it started an atmosphere on how you personally think whether this or that exist. It tries to give us a solution to the question and yet ask you again and again if it really does exist or if the argument is valid, making you hesitant about the possibilities. In one way or another, he pointed out that there might be things that exist only theoretically and cannot be seen or touched physically which makes us also doubt the physical existence of mathematics, as well as to what maybe it’s relevance to the physical world.

Nature of mathematics was observed and analyzed in terms of Platonism and formalism views according to mathematicians. General public can’t understand immediately in a Platonism view since it is a metaphysics of mathematical entities which are independent of our consciousness, in language and practices. Herewith, it is being said that mathematics must be discovered and not invented. On the other hand, formalism is being associated metaphorically to a game. Perhaps this view can be understandable to the general public; however, working mathematicians might find it as the last resort. Hersh argues the regulations about formalism. He thinks mathematical rules are not random nevertheless, it is something that evolved through “physio-biological” and social history of the environment.

Histories of philosophy from Pythagoras down to Descartes and so on and so forth to Rudolph Carnap and to the mavericks who foresee mathematics as a human work of art, were taken into account in this book. More likely, it contains an assessment of mathematicians’ and philosophers’ views and opinions about what math is. A lot of arguments about infallibility, intuition, existence of infinite objects and implications for education about mathematics were also discussed. Each of these aspects was assessed thoroughly about its impacts to mathematics. However, as it went by, the thought already loses the argument inflicted at the start of the “conversation”. It seems like the deliberation is being recurring and redundant. Some were shortcuts; meaning, it seems like only those people who understand the topic can understand the flow.

In the end, there was nothing that was really proved or something like a general conclusion. At first, Hersh have been trying to tell to use a humanistic approach in order to understand more about the philosophy of mathematics. But, what I can see is that he was trying to criticize the philosophies and yet it lacks and loses the power of using the “humanist” approach.

In conclusion, this book is good in terms of using philosophies in analyzing and assessing mathematics. It’s just that, the author lost his objective on how to discuss it which is to use the “humanist” approach. It could have given the audience a new way in learning or understanding what mathematics is really all about.