Another Perspective of Mathematics

The book “What is Mathematics, Really?” somehow caught me because the points of Reuben Hersh were making sense.  I was surprised to have the slightest interest because compare this book to Percy Jackson series or The Hunger Games series, those books can stimulate interest just by viewing their covers while this book is math book. With ‘Math’ on the cover, people would not dare open it because imagine reading a math book full with concepts and terms that are hostile to you. You simply would just sleep just by reading the preface but some points really caught my attention stimulating my interest. Hersh’s book was about a philosophical part of mathematics and discarded the mainstreams in mathematics which are Platonism, intuitionism or constructivism, and formalism then suggested another philosophical idea for mathematics.

The first part of the book he explained that the 1-3 cube existed and he had detailed solutions for the 4-cube from the 1-3 cubes he had previously. He can have a detailed solution of the 4-cube but that did not simply exist. So if it does not exist, why did math have a solution for the 4-cube that have never existed. The author wanted to declassify the generally approved properties of mathematics.

Hersh rejected Platonism for several reasons: “It violates the empiricism of modern science; it insists on acceptance of a “strange parallel existence of two realities—physical and mathematical; and it does not relate to material reality or make contact with flesh-and-blood mathematicians.”

Another objection of Hersh is Formalism. His point is, ““the notion of strictly following rules without any need for judgment is a fiction” and that it is “misleading to apply it to real life.” I think that this point is true because it is not right to just follow instructions all the time. You have to also analyze if what you follow is right. You just can’t follow math rules all the time. You should really have to ask why and that’s where proving comes into play.

He also rejects Intuitionism because immediate comprehension of mathematics is not universal. A person needs to learn mathematics by level because certain level of maturity is achieved at different stages in life so one does not learn calculus and differential equations during grade one except if you are Sheldon Cooper (shout out to the Big Bang viewers out there!), of course you begin with simple arithmetic like adding and subtracting. His view was supported by the research of Piaget who stated that “natural numbers are not given by God (at least not before the age of seven for most children in Western culture), but are constructed in an individual’s mind by coordinating the concepts of set inclusion and ordering.”