What is mathematics,
really? That is the question that has been bothering my mind ever since I met
Math. I wonder why Math is really hard that just by looking at numbers and
different types of equations, your nose will bleed (well, not literally) and
your head starts to ache. I also find it odd that there are some people who
excel at this subject while I on the other hand, can’t even crack a simple
equation even if I will stare at it for several hours. What’s in it for Math
that it makes our lives harder and is feared by many? I know I am
not the only one wondering about this for I am sure that you had these same
questions in your mind. To know what is mathematics - really, let us look
into Reuben Hersh’s book entitled “What is Mathematics, Really”
The book was written in a
humanist’s point of view and was divided into two main parts. Part one is
programmatic while in Part Two, Hersh gives us a capsule account of different
individuals. In Part One, Hersh explains why he rejects these three mainstream
philosophies: Platonism, Formalism and Intuitionism. According to
him, Platonism is dominantly hard to talk about in public and is not adequate
as a philosophy of mathematics. He also has several reasons why he rejects this
idea and one of this is: Platonism insists an acceptance of a “strange parallel
existence of two realities – physical and mathematical.
Hersh’s another objection
is Formalism. According to him, rules are not arbitrary but rather are
“historically determined by the workings of society that evolve under pressure
of the inner working and interactions of social groups, and the physiological
and biological environment of earth”. He also pointed out that “the notion of
strictly following rules without any need for judgement is a fiction” and is “misleading
to apply literally in life”.
He’s last objection
is Intuitionism. Hersh adopted the anthropological point of view that “the
intuition of the natural numbers is simply not universal”. This view is
supported by the research of Piaget.
In Part two, Hersh gave us
a capsule account of the philosophical thinking of different individuals, from
Aristotle to Wittgenstein. I must say that this is very helpful to us who are
reading the philosophy of mathematics for the first time. Hersh paid great
attention to the work of Piaget and acknowledged the tremendous impact of his
writings on cognitive Psychology.
Reuben Hersh did a
wonderful job in delivering his points and expressing his own ideas especially
his humanist approach to Mathematics. Though there were times that I feel at
lost with what he was trying to say and the terms that he used, he still made
an impact to me. Also, he let us know that mathematics
must be understood as a human activity, a social phenomenon, part of human
culture, historically evolved, and intelligible only in a social context.
I thought I was the only one. :) This book is one deep reading but Hersh has great ideas though.
ReplyDeleteGood explanation about the philosophies behind math, although deep comprehension must be applied to this kind of book.
ReplyDeleteI really find it difficult at first to relate to what Hersh has been trying to explain us since I'm really not a fan of Math and as what Kim said "deep comprehension must be applied to this kind of book" but in the end, I was able to appreciate how he persuaded the readers to believe in his philosophy. By the way, I can really relate to your first paragraph. Well done :)
ReplyDeletePersonally, i am also wondering what mathematics is really. Now, i'm a bit enlightened :) . You did a nice job in summarizing the gist of the book.
ReplyDeleteif you look at it closely Mathematics is not really hard its just that there are people (like me) who doesn't have the ability to like or have any interest in the subject and that is why mathematics becomes hard to understand.
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