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Would mathematics exist if people didn't?

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Since ancient times, 
mankind has hotly debated

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whether mathematics 
was discovered or invented.

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Did we create mathematical concepts to
help us understand the universe around us,

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or is math the native language of
the universe itself,

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existing whether we find 
its truths or not?

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Are numbers, polygons 
and equations truly real,

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or merely ethereal representations
of some theoretical ideal?

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The independent reality of math has
some ancient advocates.

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The Pythagoreans of 5th Century Greece
believed numbers were both

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living entities and universal principles.

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They called the number one, "the monad,"
the generator of all other numbers

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and source of all creation.

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Numbers were active agents in nature.

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Plato argued mathematical 
concepts were concrete

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and as real as the universe itself,
regardless of our knowledge of them.

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Euclid, the father of geometry, believed
nature itself

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was the physical manifestation
of mathematical laws.

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Others argue that while numbers may
or may not exist physically,

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mathematical statements definitely don't.

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Their truth values are based on rules
that humans created.

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Mathematics is thus an invented
logic exercise,

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with no existence outside mankind's
conscious thought,

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a language of abstract relationships
based on patterns discerned by brains,

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built to use those patterns to invent
useful but artificial order from chaos.

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One proponent of this sort of idea
was Leopold Kronecker,

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a professor of mathematics in 
19th century Germany.

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His belief is summed up in 
his famous statement:

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"God created the natural numbers,
all else is the work of man."

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During mathematician
David Hilbert's lifetime,

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there was a push to establish mathematics
as a logical construct.

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Hilbert attempted to axiomatize all
of mathematics,

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as Euclid had done with geometry.

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He and others who attempted this saw
mathematics as a deeply philosophical game

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but a game nonetheless.

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Henri Poincaré, one of the father's of
non-Euclidean geometry,

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believed that the existence of 
non-Euclidean geometry,

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dealing with the non-flat surfaces of 
hyperbolic and elliptical curvatures,

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proved that Euclidean geometry, the
long standing geometry of flat surfaces,

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was not a universal truth,

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but rather one outcome of using one
particular set of game rules.

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But in 1960, Nobel Physics laureate
Eugene Wigner

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coined the phrase, "the unreasonable 
effectiveness of mathematics,"

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pushing strongly for the idea that
mathematics is real

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and discovered by people.

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Wigner pointed out that many purely
mathematical theories

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developed in a vacuum, often with no view
towards describing any physical phenomena,

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have proven decades 
or even centuries later,

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to be the framework necessary to explain

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how the universe
has been working all along.

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For instance, the number theory of British
mathematician Gottfried Hardy,

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who had boasted that none of his work
would ever be found useful

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in describing any phenomena
in the real world,

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helped establish cryptography.

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Another piece of his purely
theoretical work

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became known as the Hardy-Weinberg
law in genetics,

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and won a Nobel prize.

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And Fibonacci stumbled 
upon his famous sequence

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while looking at the growth of an 
idealized rabbit population.

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Mankind later found the sequence
everywhere in nature,

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from sunflower seeds
and flower petal arrangements,

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to the structure of a pineapple,

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even the branching of bronchi
in the lungs.

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Or there's the non-Euclidean work of
Bernhard Riemann in the 1850s,

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which Einstein used in the model for
general relativity a century later.

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Here's an even bigger jump:

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mathematical knot theory, first developed
around 1771

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to describe the geometry of position,

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was used in the late 20th century
to explain how DNA unravels itself

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during the replication process.

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It may even provide key explanations
for string theory.

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Some of the most influential 
mathematicians and scientists

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of all of human history
have chimed in on the issue as well,

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often in surprising ways.

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So, is mathematics an 
invention or a discovery?

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Artificial construct or
universal truth?

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Human product or
natural, possibly divine, creation?

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These questions are so deep the debate
often becomes spiritual in nature.

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The answer might depend on the specific
concept being looked at,

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but it can all feel like a
distorted zen koan.

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If there's a number of trees in a forest,
but no one's there to count them,

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does that number exist?