What
is Mathematics, Really? is a book written by American
mathematician Reuben Hersh, who is known for popularizing the social impacts of
mathematics. First published in 1997, the book is a response to the book What
is Mathematics by Richard Courant and Herbert Robbins. Hersh found the book
dissatisfying because it just showed the surface of mathematics. He also said
that the method of "just showing how" made it difficult for students
to understand math. He then explained in his book the context of mathematics:
its sense and history.
The major topic of his book is the great debate
regarding the nature of mathematics. According to Hersh, there are two major
philosophies that attempts to explain its nature. The first one is formalism,
which states that mathematics exists independently of humans and we just need
to discover it. On the other hand, Platonism states that mathematics
does not exist independently of humans, and new mathematics is created. Methods
and rules can be made, improved or destroyed, which means their existence are
not found in a physical sense. Both philosophies had a common characteristic:
they don't recognize the function of humans in the identity of mathematics.
The third philosophy which Hersh is attempting to push
is humanism. It states that since mathematics is an approach of dealing
and understanding the world around man, the methods and theorems formulated by
him is a manifestation of his mind, thus, mathematics, like other bodies of
knowledge, is uncertain for the fact that the human mind is made up of much
uncertainty.
Primarily, I see math in the way of formalism.
It is there but has to be discovered. Therefore, I have to learn how to
manipulate it in order to understand it further and deeper. However, after
learning Hersh's perspective, I see purpose in learning mathematics. Purpose
complements the enjoyment of action. The stand I have after reading the book
elucidates the pleasure and reason of why I am doing mathematics. The book,
however, stated that it is easily comprehensible to anyone. Readers who don't
have any prior knowledge about the philosophies and history of mathematics
might find the book hard to understand. But overall, the book in enlightening
and encouraging in understanding mathematics.
It is true that the author wrote the book as comprehensibly as possible to fully understand by readers especially those that do not or cannot appreciate math and its nature.
ReplyDeleteSo after reading the book, do you see math now by the Theory of Humanism as 'pushed' by Hersh?
ReplyDeleteHe categorically states in the last paragraph that he views mathematics through the lens of formalism.
DeleteI think most of us agreed that the book was not "easily comprehensible" after reading it
ReplyDeleteTruly the book was a hard read for the most of us. But the author's in-depth explanation to the other philosophies really gives mathematics a different perspective.
ReplyDeleteAs mentioned in your review, Hersh wrote in his book that "What is Mathematics" was dissatisfying for him. Ironically, I find his book tiresome to read because it is difficult to comprehend for the most part. If he wrote this book in the hopes of helping students in the college level or below, i would say that, judging from the comments and posts i have read so far, he may have missed his mark.
ReplyDelete