The Arcane of Mathematical Zenith

“Mathematics has a reputation for being hard. Like any deep field one can really only has a deep appreciation of it after a long period of study (Mount, 2008)”.

What is mathematics, really?

A classical yet deep question thrown many times over past generations; in a span of 12 years (and counting) of studying mathematics, I can honestly tell that it is only for people who are smarter and more patient to allow themselves exposed to such difficult subject.  But for those 12 years, there is no such time that I asked myself the true meaning of math. Maybe because I could certainly say that it is just about numbers and solving problems or just because I didn’t let myself think beyond the norm.

As a student who find math as odd as can be, I can say that Hersh’s perspective of math helped me in understanding this amazing yet complicated subject by paying attention to everyday mathematical practice and trying to answer the question stated above. In his book “What is Mathematics, really?” he exposed some of his points by means of experience as an own mathematician. His experience grew into realizations that math has a setting hidden and unreported behind those burnish proofs. Thus it is a delinquency to not appreciate this activity, in which according to Hersh, leads philosophers into the custom formalist, Platonist or constructivist view of mathematics, disregarding the richness of a mathematical activity.

The book is divided into two parts, bracketing these between a preface and a summary and recapitulation. For the first part, Hersh is concerned in creating the concept of a “humanist” view in mathematics that according to him, understands math as a social phenomenon. Having set out of his criteria, and actually defended them, Hersh continues to consider more myths and mistakes, and discusses the ideas of intuition, proof and certainty.

While the second part of the book clearly deals with the history and philosophy of mathematics. This section provides useful information for rookies to the concept of the history of the philosophy of math. He paid great attention to the work of Piaget and acknowledged the impact of Piaget’s writings on psychology. And according to one who made also a review in his book, John Ollason, there was also a tendency in the nineteenth century to attempt to discover the foundations of all mathematics. Like reducing algebra, geometry, number theory to a single base and the base chosen was the theory of sets. Indeed, the whole section just attempted to prove that mathematics was believed to be separated from other forms of human knowledge. The crisis, so stated by Hersh, was a primary incentive to philosophers, and that their contribution to the understanding of what mathematics really is actually occupied the second half of the second part of the book.

To be precise, Hersh delivered a well-written, well-explained view of his strong points that spearheaded some of the commons. But to be honest, this positive dilemma will only be appreciated if, mind you, has a parallelism to what Hersh is actually saying as a mathematician. You need to be in his shoes to be able to fully understand and appreciate the contents of his book. He viewed the reality and the philosophy into the eye of somewhat of a god. Though his solutions are impressive, as well as his views, there’s just a gap between his and mine’s comprehension to things. But nevertheless, I was convinced to his proposition that mathematics is a social construction that one can make, regress or even impel.