Denzelle Freya A. Del Puerto
What Mathematics is, Really
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 an curiosity in mathematics or the philosophy of science.
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