What Mathematics Is,
Really (A book review by Denzelle Freya Del Puerto)
The
book written by Richard Courant entitled, “What
Mathematics Is, Really”, and according to many reviews is written lively
and amusing for a detailed philosophical book.
The author of the book had approached the question by means of
presenting expositions and great deals of mathematical philosophies and
concepts (some parts with added humor).
The
book offered three main points of views in debate in mathematical context; some
called it mathematical mainstreams of mathematical philosophy: Platonism,
Formalism and constructivism. Platonism saw mathematics as an “experimental
science”, studying what is there that they think is there, although clearly,
they do not exist in physical sense and or material sense. The formalists argue
that mathematics is really a proper manipulation of symbols based on subjective
axioms. The intuitionists rejected the "law of the
excluded middle" or the claim that a mathematical statement is always
either true or false, and were willing to give up large tracts of classical
analysis that didn't fit this point of view.
Mathematics according to the author
is neither of the three. As what I have understood, mathematics the author
contrast the 3 mathematical mainstreams and considers mathematics with
humanistic approach; meaning, mathematics must be understood as a human
activity, a social phenomenon, part of human culture, historically evolved, and
intelligible only in a social context.
What
is Mathematics, Really? reflects an insider's
analysis of arithmetical existence, and will be debated by any person with curiosity
in mathematics or the philosophy of science.
No comments:
Post a Comment