Digging Deeper into Mathematics

            Mathematics is simply defined as a science of patterns but that question that keeps on lingering in my mind is, what is mathematics? The question was attempted to be answered by the mathematician, Reuben Hersh on his book entitled “What is Mathematics, Really?” as he investigates the nature of mathematics, its philosophies and his own perspective of in mathematics as he mainly proposes humanist and sociohistorical approach to mathematics.

              The first part of the book commenced with a query about the existence of 4-cube and introduced the three mainstream philosophies of mathematics namely; Platonism, formalism, intuitionism. Platonism or also called as realism implies that mathematical entities and are independent to our thoughts and practices. Platonists define mathematics as a universe of abstract objects that is completely separated from the material universe. It also pointed out that it only allows the mathematician to invent because the existence our knowledge of objects is independent to us which remains fixed. In a formalist approach it is said that “Mathematics is a meaningless game” which means it is governed by rules that explicit yet arbitrary which could be determined through biological properties or to the nervous system of humans as it reflects the physical and biological properties of the Earth. In intuitionism, accepts the set of natural numbers as the fundamental datum of mathematics from which all meaningful mathematics must be obtained through a process of finite construction that does not make use of the law of the excluded middle he considers the work of James Piaget that children before conceived the notion of natural numbers basing on their personal experiences. 

           The humanistic approach of mathematics makes it accessible to the learners and makes as part of the culture of man and the story of the past. He believes that because of people, mathematics has evolved and it continues to develop because of man.

             The questions that were raised in the book makes sense as it become provocative to the readers to make them think about the nature of mathematics. What I like about the humanist approach is that it becomes pro-human because most of us would conceive mathematics as problems that becomes an agony to the humans. The book also showed a theologian approach because some of the mathematicians believe that mathematics has no relationship with divine intervention.

           I recommend that this book should be read by people with great interest in the ideas, notions and different philosophies in mathematics. Readers that doesn’t have a sufficient background in mathematics might find it arduous to understand some of the concepts or ideas presented in the book. 

             The book is very informative and its rich with mathematical ideas and concepts yet I would like to recommend this book for those people who has a really great interest in mathematics. Hersh humanist approach is somewhat convincing yet for me he was not able