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Mathematics:
Beyond the Symbols
Images that come to most people’s
minds when they hear the word “mathematics” are quick
to manifest. There’s the flashback of the old, boring professor
who lectured in a monotone voice straight into the chalkboard
all day while the class was asleep. There’s the inevitable
association with numbers, symbols, computation,
equations and so forth.
Unfortunately, this picture painted in our minds is very incomplete.
Once we peer beyond the equations and symbols we can start to
understand what mathematics really is all about.
It’s not about numbers. It’s not about equations. It’s
not about symbols. Mathematics is about patterns.
Spatial patterns are represented in the field of geometry. Spacial
patterns plus numbers is trigonometry. Patters of motion and change
is calculus.
If I see three dogs, three pencils, and three computers, the pattern
that ties those independent physical objects together in this
situation is threeness. Numbers come about because of
a desire to communicate patterns of physical existence. Alone,
numbers don’t mean anything. We assign a meaning to a the
number seven, for instance, because we want to convey the concept
of sevenness. Numbers obviously have a place in mathematics,
but they don’t make up anywhere near the core of what mathematics
is. Numbers are no more mathematics than sheet music is music.
Both are abstractions. Both require the human brain to decode
them to bring them to life.
When Leibniz and Newton simultaneously and independently invented
calculus in the seventeenth century, our mathematical repertoire
went from being able to represent static patterns (such as measuring
and counting) to dynamic patterns (such as the motion of the planets,
fluid flow, atmospheric conditions, magnetism, electricity, biological
growth, economic activity, and so forth). Suddenly, the opportunity
to engineer the complex systems and technology we take for granted
today, was available. This came from the fundamental ability to
apply an understanding of mathematics to the physical universe.
Mathematics is therefore simply a tool that man uses to help him
understand the world. After all, Leibniz and Newton invented calculus
for the purpose of solving physics problems.
What is the core of mathematics? Pattern recognition.
Agree?
Disagree? Discuss your thoughts here!
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