TedTest

From the Ted Talk by Jeff Dekofsky: Is math discovered or invented?

Unscramble the Blue Letters

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 luggaane of the universe itself, existing whether we find its ttruhs or not? Are numbers, polngyos and enuiaqots truly real, or merely ethereal representations of some theoretical ideal? The iepnndedent reality of math has some ancient advocates. The Pythagoreans of 5th Century Greece blieveed numbers were both living entities and universal principles. They clelad the number one, "the monad," the getaonerr of all other numbers and sorcue of all creation. Numbers were acitve agents in nature. Plato argued mathematical concepts were cntercoe and as real as the usrvneie itself, regardless of our kwneldoge of them. Euclid, the father of geometry, believed nature itself was the physical mieotsafntain of mathematical laws. Others augre that while numbers may or may not exist phsillycay, mathematical statements definitely don't. Their truth values are based on rules that humans created. Mathematics is thus an invented logic eirecxse, with no existence outside mankind's conscious thought, a language of arstcabt relationships based on patterns discerned by brnias, built to use those patterns to invent useful but artificial order from chaos. One proponent of this sort of idea was Leopold Kronecker, a posefsorr of mathematics in 19th century Germany. His blieef is summed up in his famous statement: "God caeetrd the natural nemurbs, all else is the work of man." During mathematician dvaid 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 aptmeettd 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 hrpeboilyc and eiclpailtl curvatures, proved that Euclidean geometry, the long standing goertemy of flat surfaces, was not a universal truth, but rather one outcome of using one particular set of game rules. But in 1960, Nobel piyshcs laureate Eugene Wigner coined the phrase, "the unreasonable effectiveness of mthmaetaics," pushing sltnrgoy 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 innsctae, 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 senceque while looking at the growth of an idealized rabbit population. Mankind later found the sequence everywhere in nature, from swnleuofr seeds and flower petal arrangements, to the structure of a pineapple, even the brhnicnag 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: mtematahacil knot theory, first developed around 1771 to describe the geometry of position, was used in the late 20th century to exailpn 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 hmuan hstrioy have chimed in on the issue as well, often in surprising ways. So, is mathematics an invention or a diecsorvy? Artificial construct or unveisarl 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 cunot them, does that number esixt?

Open Cloze

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 ________ of the universe itself, existing whether we find its ______ or not? Are numbers, ________ and _________ truly real, or merely ethereal representations of some theoretical ideal? The ___________ reality of math has some ancient advocates. The Pythagoreans of 5th Century Greece ________ numbers were both living entities and universal principles. They ______ the number one, "the monad," the _________ of all other numbers and ______ of all creation. Numbers were ______ agents in nature. Plato argued mathematical concepts were ________ and as real as the ________ itself, regardless of our _________ of them. Euclid, the father of geometry, believed nature itself was the physical _____________ of mathematical laws. Others _____ that while numbers may or may not exist __________, mathematical statements definitely don't. Their truth values are based on rules that humans created. Mathematics is thus an invented logic ________, with no existence outside mankind's conscious thought, a language of ________ relationships based on patterns discerned by ______, built to use those patterns to invent useful but artificial order from chaos. One proponent of this sort of idea was Leopold Kronecker, a _________ of mathematics in 19th century Germany. His ______ is summed up in his famous statement: "God _______ the natural _______, all else is the work of man." During mathematician _____ 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 _________ 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 __________ and __________ curvatures, proved that Euclidean geometry, the long standing ________ of flat surfaces, was not a universal truth, but rather one outcome of using one particular set of game rules. But in 1960, Nobel _______ laureate Eugene Wigner coined the phrase, "the unreasonable effectiveness of ___________," pushing ________ 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 ________, 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 ________ while looking at the growth of an idealized rabbit population. Mankind later found the sequence everywhere in nature, from _________ seeds and flower petal arrangements, to the structure of a pineapple, even the _________ 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: ____________ knot theory, first developed around 1771 to describe the geometry of position, was used in the late 20th century to _______ 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 _____ _______ have chimed in on the issue as well, often in surprising ways. So, is mathematics an invention or a _________? Artificial construct or _________ 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 _____ them, does that number _____?

Solution

knowledge
universal
sunflower
generator
language
numbers
exist
active
argue
universe
called
geometry
believed
mathematical
brains
manifestation
branching
history
physics
human
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mathematics
elliptical
david
professor
count
discovery
polygons
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created
attempted
explain
belief

Original Text

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?

Frequently Occurring Word Combinations

ngrams of length 2

collocation	frequency
mathematical concepts	2

Important Words

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