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    "segs": [ {
      "utf8": "Would mathematics exist if people didn't?"
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    "segs": [ {
      "utf8": "Since ancient times, \nmankind has hotly debated"
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    "segs": [ {
      "utf8": "whether mathematics \nwas discovered or invented."
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    "segs": [ {
      "utf8": "Did we create mathematical concepts to\nhelp us understand the universe around us,"
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    "segs": [ {
      "utf8": "or is math the native language of\nthe universe itself,"
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  }, {
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    "segs": [ {
      "utf8": "existing whether we find \nits truths or not?"
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    "segs": [ {
      "utf8": "Are numbers, polygons \nand equations truly real,"
    } ]
  }, {
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    "segs": [ {
      "utf8": "or merely ethereal representations\nof some theoretical ideal?"
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    "segs": [ {
      "utf8": "The independent reality of math has\nsome ancient advocates."
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    "segs": [ {
      "utf8": "The Pythagoreans of 5th Century Greece\nbelieved numbers were both"
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    "segs": [ {
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    } ]
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    "segs": [ {
      "utf8": "They called the number one, \"the monad,\"\nthe generator of all other numbers"
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  }, {
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    "segs": [ {
      "utf8": "and source of all creation."
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    "segs": [ {
      "utf8": "Numbers were active agents in nature."
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    "segs": [ {
      "utf8": "Plato argued mathematical \nconcepts were concrete"
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    "segs": [ {
      "utf8": "and as real as the universe itself,\nregardless of our knowledge of them."
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    "segs": [ {
      "utf8": "Euclid, the father of geometry, believed\nnature itself"
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    "segs": [ {
      "utf8": "was the physical manifestation\nof mathematical laws."
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    "segs": [ {
      "utf8": "Others argue that while numbers may\nor may not exist physically,"
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  }, {
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    "segs": [ {
      "utf8": "mathematical statements definitely don't."
    } ]
  }, {
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    "segs": [ {
      "utf8": "Their truth values are based on rules\nthat humans created."
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  }, {
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    "segs": [ {
      "utf8": "Mathematics is thus an invented\nlogic exercise,"
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    "segs": [ {
      "utf8": "with no existence outside mankind's\nconscious thought,"
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  }, {
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    "segs": [ {
      "utf8": "a language of abstract relationships\nbased on patterns discerned by brains,"
    } ]
  }, {
    "tStartMs": 100997,
    "dDurationMs": 5697,
    "segs": [ {
      "utf8": "built to use those patterns to invent\nuseful but artificial order from chaos."
    } ]
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    "segs": [ {
      "utf8": "One proponent of this sort of idea\nwas Leopold Kronecker,"
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    "segs": [ {
      "utf8": "a professor of mathematics in \n19th century Germany."
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    "segs": [ {
      "utf8": "His belief is summed up in \nhis famous statement:"
    } ]
  }, {
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    "dDurationMs": 4509,
    "segs": [ {
      "utf8": "\"God created the natural numbers,\nall else is the work of man.\""
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  }, {
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    "segs": [ {
      "utf8": "During mathematician\nDavid Hilbert's lifetime,"
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    "segs": [ {
      "utf8": "there was a push to establish mathematics\nas a logical construct."
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    "segs": [ {
      "utf8": "Hilbert attempted to axiomatize all\nof mathematics,"
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    "segs": [ {
      "utf8": "as Euclid had done with geometry."
    } ]
  }, {
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    "segs": [ {
      "utf8": "He and others who attempted this saw\nmathematics as a deeply philosophical game"
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    "segs": [ {
      "utf8": "but a game nonetheless."
    } ]
  }, {
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    "segs": [ {
      "utf8": "Henri Poincaré, one of the father's of\nnon-Euclidean geometry,"
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    "tStartMs": 143231,
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    "segs": [ {
      "utf8": "believed that the existence of \nnon-Euclidean geometry,"
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  }, {
    "tStartMs": 146238,
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    "segs": [ {
      "utf8": "dealing with the non-flat surfaces of \nhyperbolic and elliptical curvatures,"
    } ]
  }, {
    "tStartMs": 150535,
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      "utf8": "proved that Euclidean geometry, the\nlong standing geometry of flat surfaces,"
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  }, {
    "tStartMs": 155001,
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      "utf8": "was not a universal truth,"
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  }, {
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    "segs": [ {
      "utf8": "but rather one outcome of using one\nparticular set of game rules."
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  }, {
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    "segs": [ {
      "utf8": "But in 1960, Nobel Physics laureate\nEugene Wigner"
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  }, {
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    "segs": [ {
      "utf8": "coined the phrase, \"the unreasonable \neffectiveness of mathematics,\""
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  }, {
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    "segs": [ {
      "utf8": "pushing strongly for the idea that\nmathematics is real"
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      "utf8": "and discovered by people."
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      "utf8": "Wigner pointed out that many purely\nmathematical theories"
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  }, {
    "tStartMs": 183379,
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    "segs": [ {
      "utf8": "have proven decades \nor even centuries later,"
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  }, {
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      "utf8": "to be the framework necessary to explain"
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    "segs": [ {
      "utf8": "how the universe\nhas been working all along."
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    "segs": [ {
      "utf8": "For instance, the number theory of British\nmathematician Gottfried Hardy,"
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    "segs": [ {
      "utf8": "who had boasted that none of his work\nwould ever be found useful"
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      "utf8": "in describing any phenomena\nin the real world,"
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  }, {
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    "segs": [ {
      "utf8": "helped establish cryptography."
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  }, {
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    "dDurationMs": 2278,
    "segs": [ {
      "utf8": "Another piece of his purely\ntheoretical work"
    } ]
  }, {
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    "segs": [ {
      "utf8": "became known as the Hardy-Weinberg\nlaw in genetics,"
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  }, {
    "tStartMs": 210095,
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    "segs": [ {
      "utf8": "and won a Nobel prize."
    } ]
  }, {
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    "dDurationMs": 2592,
    "segs": [ {
      "utf8": "And Fibonacci stumbled \nupon his famous sequence"
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  }, {
    "tStartMs": 214426,
    "dDurationMs": 3614,
    "segs": [ {
      "utf8": "while looking at the growth of an \nidealized rabbit population."
    } ]
  }, {
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    "segs": [ {
      "utf8": "Mankind later found the sequence\neverywhere in nature,"
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  }, {
    "tStartMs": 221548,
    "dDurationMs": 2488,
    "segs": [ {
      "utf8": "from sunflower seeds\nand flower petal arrangements,"
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  }, {
    "tStartMs": 224036,
    "dDurationMs": 1821,
    "segs": [ {
      "utf8": "to the structure of a pineapple,"
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  }, {
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    "dDurationMs": 2640,
    "segs": [ {
      "utf8": "even the branching of bronchi\nin the lungs."
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  }, {
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    "segs": [ {
      "utf8": "Or there's the non-Euclidean work of\nBernhard Riemann in the 1850s,"
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  }, {
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    "segs": [ {
      "utf8": "which Einstein used in the model for\ngeneral relativity a century later."
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  }, {
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    "dDurationMs": 1416,
    "segs": [ {
      "utf8": "Here's an even bigger jump:"
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  }, {
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    "segs": [ {
      "utf8": "mathematical knot theory, first developed\naround 1771"
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  }, {
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    "segs": [ {
      "utf8": "to describe the geometry of position,"
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  }, {
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    "dDurationMs": 4848,
    "segs": [ {
      "utf8": "was used in the late 20th century\nto explain how DNA unravels itself"
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  }, {
    "tStartMs": 250033,
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      "utf8": "during the replication process."
    } ]
  }, {
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    "segs": [ {
      "utf8": "It may even provide key explanations\nfor string theory."
    } ]
  }, {
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    "segs": [ {
      "utf8": "Some of the most influential \nmathematicians and scientists"
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  }, {
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    "segs": [ {
      "utf8": "of all of human history\nhave chimed in on the issue as well,"
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    "tStartMs": 262472,
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    "segs": [ {
      "utf8": "often in surprising ways."
    } ]
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      "utf8": "So, is mathematics an \ninvention or a discovery?"
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  }, {
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    "segs": [ {
      "utf8": "Artificial construct or\nuniversal truth?"
    } ]
  }, {
    "tStartMs": 269851,
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    "segs": [ {
      "utf8": "Human product or\nnatural, possibly divine, creation?"
    } ]
  }, {
    "tStartMs": 274017,
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    "segs": [ {
      "utf8": "These questions are so deep the debate\noften becomes spiritual in nature."
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    "segs": [ {
      "utf8": "The answer might depend on the specific\nconcept being looked at,"
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  }, {
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    "segs": [ {
      "utf8": "but it can all feel like a\ndistorted zen koan."
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    "segs": [ {
      "utf8": "If there's a number of trees in a forest,\nbut no one's there to count them,"
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    "dDurationMs": 1920,
    "segs": [ {
      "utf8": "does that number exist?"
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