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  • Would mathematics exist if people didn't?

  • Since ancient times, mankind has hotly debated

  • whether mathematics was discovered or invented.

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

  • or is math the native language of the universe itself,

  • existing whether we find its truths or not?

  • Are numbers, polygons and equations truly real,

  • or merely ethereal representations of some theoretical ideal?

  • The independent reality of math has some ancient advocates.

  • The Pythagoreans of 5th Century Greece believed numbers were both

  • living entities and universal principles.

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

  • and source of all creation.

  • Numbers were active agents in nature.

  • Plato argued mathematical concepts were concrete

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

  • Euclid, the father of geometry, believed nature itself

  • was the physical manifestation of mathematical laws.

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

  • mathematical statements definitely don't.

  • Their truth values are based on rules that humans created.

  • Mathematics is thus an invented logic exercise,

  • with no existence outside mankind's conscious thought,

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

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

  • One proponent of this sort of idea was Leopold Kronecker,

  • a professor of mathematics in 19th century Germany.

  • His belief is summed up in his famous statement:

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

  • During mathematician David Hilbert's lifetime,

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

  • Hilbert attempted to axiomatize all of mathematics,

  • as Euclid had done with geometry.

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

  • but a game nonetheless.

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

  • believed that the existence of non-Euclidean geometry,

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

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

  • was not a universal truth,

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

  • But in 1960, Nobel Physics laureate Eugene Wigner

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

  • pushing strongly for the idea that mathematics is real

  • and discovered by people.

  • Wigner pointed out that many purely mathematical theories

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

  • have proven decades or even centuries later,

  • to be the framework necessary to explain

  • how the universe has been working all along.

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

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

  • in describing any phenomena in the real world,

  • helped establish cryptography.

  • Another piece of his purely theoretical work

  • became known as the Hardy-Weinberg law in genetics,

  • and won a Nobel prize.

  • And Fibonacci stumbled upon his famous sequence

  • while looking at the growth of an idealized rabbit population.

  • Mankind later found the sequence everywhere in nature,

  • from sunflower seeds and flower petal arrangements,

  • to the structure of a pineapple,

  • even the branching of bronchi in the lungs.

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

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

  • Here's an even bigger jump:

  • mathematical knot theory, first developed around 1771

  • to describe the geometry of position,

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

  • during the replication process.

  • It may even provide key explanations for string theory.

  • Some of the most influential mathematicians and scientists

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

  • often in surprising ways.

  • So, is mathematics an invention or a discovery?

  • Artificial construct or universal truth?

  • Human product or natural, possibly divine, creation?

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

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

  • but it can all feel like a distorted zen koan.

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

  • does that number exist?

Would mathematics exist if people didn't?

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B2 US TED-Ed mathematics geometry mathematical mankind universe

【TED-Ed】Is math discovered or invented? - Jeff Dekofsky

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    稲葉白兎 posted on 2015/03/09
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