FOM: What is mathematics?
Miguel A. Lerma
mlerma at math.northwestern.edu
Fri Feb 15 10:53:35 EST 2002
Gordon Fisher wrote:
> So I propose that a proposition that _mathematics_ as a
> whole be defined as the study of formal structures, or the
> like, or that it be confined to "proving", is to be too narrow.
I agree. Proofs may be an important part of mathematical activity
but not essential in defining mathematics. They play more or less
the same role as experiments in physics, a necessary activity for
verifying hypothesis and finding new facts, but not essential in
the definition of the science.
I think the main characteristic of mathematics is abstraction.
Mathematical reasoning is an activity in which no material
features (or any mentions to the real world) are involved.
I find particularly enlightening the distinction between
mathematics and physics: a formula is physics if it involves
units, otherwise it is mathematics. So "2 meters + 2 meters =
4 meters" is physics, "2 + 2 = 4" is mathematics.
Miguel A. Lerma
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