What is Math?

Date: 10/04/97 at 01:37:23
From: James J Lake
Subject: What is Math?

Dear Dr. Math:

Is math a science, an art, or some other anomaly?

Date: 10/07/97 at 12:55:41
From: Doctor Ceeks
Subject: Re: What is Math?

Hi,

What a question!

To me, mathematics is a discipline that seeks understanding 
of the patterns and structures of constructs of the human mind.  
Understanding has no end to its depth, and mathematics seeks 
the highest standards of understanding by demanding rigor in its 
foundations and in its development. Rigor is achieved by responsible 
attention to the principles of logic.

In a strict sense, mathematics differs from science, if we accept
that science is the discipline that seeks understanding of the
physical world by means of the scientific method. (The scientific
method is the procedure by which hypotheses are proposed and subjected
to experiments designed to expose weaknesses in the hypotheses.)
The reason mathematics differs from this is because mathematics does
not, in a pure sense, attempt to describe the physical world.  
Mathematical theorems are not tested against nature, but against 
logic.

There may be much in common between mathematics and art, and since
art is also difficult to define, it is difficult to discuss this
relation. Certainly, there are definitions of art that would allow the 
inclusion of mathematics as an art. The creation of mathematics
requires creativity, and I think most mathematicians would agree that
some constructs are more beautiful than others, so that there is an 
aesthetic aspect to mathematics.

In any case, mathematics certainly is a human endeavor involving the
exchange of ideas between human beings. It has been around for
millennia, and shows no signs of abatement.

These ideas are debatable and reflect my own personal opinion. Also,
this response is really too short to explore all the aspects your
question addresses. 

-Doctor Ceeks,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/