Reply #57: Thats a nice definition [View All]

[sweetheart]

I agree, that only in graduate school was i introduced to the philosophy
of mathematics, what i should have been exposed to from the very outset.
As indeed, to know whether a symbol represents knowledge, one must
as well know what knowledge is.

I was recently trying to calculate what the opimal 3 dimensional
rectangular container size to hold the most spheres, with the problem
already defined as "the knowledge" i wished to obtain. I ended up on
the web studying sphere packing algorithms, which were impractical
for a simple container, and i then went and made a model out of card
board and put marbles in it.

I would use this definition for maths:
Mathematics is a system of manipulating symbols to represent knowledge.

Some correlaries:
Mathematical results are certain
Mathematics is objective
Mathematics is wedded to classic logic
Mathematics is independent of sense experience

I really wish i had been exposed more to the root of what knowledge
was, in early maths, as what i really discuss in the poll is
"applied maths", and sadly, the deeper interest is glossed over.