[Script Info]
Title: 
[Events]
Format: Layer, Start, End, Style, Name, MarginL, MarginR, MarginV, Effect, Text
Dialogue: 0,0:00:12.49,0:00:15.73,Default,,0000,0000,0000,,Would mathematics exist if people didn't?
Dialogue: 0,0:00:15.73,0:00:19.06,Default,,0000,0000,0000,,Since ancient times, \Nmankind has hotly debated
Dialogue: 0,0:00:19.06,0:00:22.71,Default,,0000,0000,0000,,whether mathematics \Nwas discovered or invented.
Dialogue: 0,0:00:22.71,0:00:27.37,Default,,0000,0000,0000,,Did we create mathematical concepts to\Nhelp us understand the universe around us,
Dialogue: 0,0:00:27.37,0:00:31.52,Default,,0000,0000,0000,,or is math the native language of\Nthe universe itself,
Dialogue: 0,0:00:31.52,0:00:34.73,Default,,0000,0000,0000,,existing whether we find \Nits truths or not?
Dialogue: 0,0:00:34.73,0:00:38.10,Default,,0000,0000,0000,,Are numbers, polygons \Nand equations truly real,
Dialogue: 0,0:00:38.10,0:00:42.68,Default,,0000,0000,0000,,or merely ethereal representations\Nof some theoretical ideal?
Dialogue: 0,0:00:42.68,0:00:46.24,Default,,0000,0000,0000,,The independent reality of math has\Nsome ancient advocates.
Dialogue: 0,0:00:46.24,0:00:49.80,Default,,0000,0000,0000,,The Pythagoreans of 5th Century Greece\Nbelieved numbers were both
Dialogue: 0,0:00:49.80,0:00:53.26,Default,,0000,0000,0000,,living entities and universal principles.
Dialogue: 0,0:00:53.26,0:00:57.57,Default,,0000,0000,0000,,They called the number one, "the monad,"\Nthe generator of all other numbers
Dialogue: 0,0:00:57.57,0:00:59.83,Default,,0000,0000,0000,,and source of all creation.
Dialogue: 0,0:00:59.83,0:01:02.64,Default,,0000,0000,0000,,Numbers were active agents in nature.
Dialogue: 0,0:01:02.64,0:01:05.50,Default,,0000,0000,0000,,Plato argued mathematical \Nconcepts were concrete
Dialogue: 0,0:01:05.50,0:01:10.44,Default,,0000,0000,0000,,and as real as the universe itself,\Nregardless of our knowledge of them.
Dialogue: 0,0:01:10.44,0:01:13.90,Default,,0000,0000,0000,,Euclid, the father of geometry, believed\Nnature itself
Dialogue: 0,0:01:13.90,0:01:17.70,Default,,0000,0000,0000,,was the physical manifestation\Nof mathematical laws.
Dialogue: 0,0:01:17.70,0:01:21.93,Default,,0000,0000,0000,,Others argue that while numbers may\Nor may not exist physically,
Dialogue: 0,0:01:21.93,0:01:25.05,Default,,0000,0000,0000,,mathematical statements definitely don't.
Dialogue: 0,0:01:25.05,0:01:29.59,Default,,0000,0000,0000,,Their truth values are based on rules\Nthat humans created.
Dialogue: 0,0:01:29.59,0:01:32.61,Default,,0000,0000,0000,,Mathematics is thus an invented\Nlogic exercise,
Dialogue: 0,0:01:32.61,0:01:36.36,Default,,0000,0000,0000,,with no existence outside mankind's\Nconscious thought,
Dialogue: 0,0:01:36.36,0:01:40.100,Default,,0000,0000,0000,,a language of abstract relationships\Nbased on patterns discerned by brains,
Dialogue: 0,0:01:40.100,0:01:46.69,Default,,0000,0000,0000,,built to use those patterns to invent\Nuseful but artificial order from chaos.
Dialogue: 0,0:01:46.69,0:01:50.37,Default,,0000,0000,0000,,One proponent of this sort of idea\Nwas Leopold Kronecker,
Dialogue: 0,0:01:50.37,0:01:53.100,Default,,0000,0000,0000,,a professor of mathematics in \N19th century Germany.
Dialogue: 0,0:01:53.100,0:01:56.45,Default,,0000,0000,0000,,His belief is summed up in \Nhis famous statement:
Dialogue: 0,0:01:56.45,0:02:00.96,Default,,0000,0000,0000,,"God created the natural numbers,\Nall else is the work of man."
Dialogue: 0,0:02:00.96,0:02:03.53,Default,,0000,0000,0000,,During mathematician\NDavid Hilbert's lifetime,
Dialogue: 0,0:02:03.53,0:02:07.13,Default,,0000,0000,0000,,there was a push to establish mathematics\Nas a logical construct.
Dialogue: 0,0:02:07.13,0:02:10.50,Default,,0000,0000,0000,,Hilbert attempted to axiomatize all\Nof mathematics,
Dialogue: 0,0:02:10.50,0:02:12.97,Default,,0000,0000,0000,,as Euclid had done with geometry.
Dialogue: 0,0:02:12.97,0:02:17.52,Default,,0000,0000,0000,,He and others who attempted this saw\Nmathematics as a deeply philosophical game
Dialogue: 0,0:02:17.52,0:02:19.70,Default,,0000,0000,0000,,but a game nonetheless.
Dialogue: 0,0:02:19.70,0:02:23.23,Default,,0000,0000,0000,,Henri Poincaré, one of the father's of\Nnon-Euclidean geometry,
Dialogue: 0,0:02:23.23,0:02:26.24,Default,,0000,0000,0000,,believed that the existence of \Nnon-Euclidean geometry,
Dialogue: 0,0:02:26.24,0:02:30.54,Default,,0000,0000,0000,,dealing with the non-flat surfaces of \Nhyperbolic and elliptical curvatures,
Dialogue: 0,0:02:30.54,0:02:35.00,Default,,0000,0000,0000,,proved that Euclidean geometry, the\Nlong standing geometry of flat surfaces,
Dialogue: 0,0:02:35.00,0:02:37.36,Default,,0000,0000,0000,,was not a universal truth,
Dialogue: 0,0:02:37.36,0:02:42.05,Default,,0000,0000,0000,,but rather one outcome of using one\Nparticular set of game rules.
Dialogue: 0,0:02:42.05,0:02:45.86,Default,,0000,0000,0000,,But in 1960, Nobel Physics laureate\NEugene Wigner
Dialogue: 0,0:02:45.86,0:02:50.17,Default,,0000,0000,0000,,coined the phrase, "the unreasonable \Neffectiveness of mathematics,"
Dialogue: 0,0:02:50.17,0:02:53.28,Default,,0000,0000,0000,,pushing strongly for the idea that\Nmathematics is real
Dialogue: 0,0:02:53.28,0:02:55.48,Default,,0000,0000,0000,,and discovered by people.
Dialogue: 0,0:02:55.48,0:02:58.39,Default,,0000,0000,0000,,Wigner pointed out that many purely\Nmathematical theories
Dialogue: 0,0:02:58.39,0:03:03.38,Default,,0000,0000,0000,,developed in a vacuum, often with no view\Ntowards describing any physical phenomena,
Dialogue: 0,0:03:03.38,0:03:05.87,Default,,0000,0000,0000,,have proven decades \Nor even centuries later,
Dialogue: 0,0:03:05.87,0:03:08.34,Default,,0000,0000,0000,,to be the framework necessary to explain
Dialogue: 0,0:03:08.34,0:03:11.44,Default,,0000,0000,0000,,how the universe\Nhas been working all along.
Dialogue: 0,0:03:11.44,0:03:15.69,Default,,0000,0000,0000,,For instance, the number theory of British\Nmathematician Gottfried Hardy,
Dialogue: 0,0:03:15.69,0:03:19.38,Default,,0000,0000,0000,,who had boasted that none of his work\Nwould ever be found useful
Dialogue: 0,0:03:19.38,0:03:21.92,Default,,0000,0000,0000,,in describing any phenomena\Nin the real world,
Dialogue: 0,0:03:21.92,0:03:24.66,Default,,0000,0000,0000,,helped establish cryptography.
Dialogue: 0,0:03:24.66,0:03:26.94,Default,,0000,0000,0000,,Another piece of his purely\Ntheoretical work
Dialogue: 0,0:03:26.94,0:03:30.10,Default,,0000,0000,0000,,became known as the Hardy-Weinberg\Nlaw in genetics,
Dialogue: 0,0:03:30.10,0:03:31.83,Default,,0000,0000,0000,,and won a Nobel prize.
Dialogue: 0,0:03:31.83,0:03:34.43,Default,,0000,0000,0000,,And Fibonacci stumbled \Nupon his famous sequence
Dialogue: 0,0:03:34.43,0:03:38.04,Default,,0000,0000,0000,,while looking at the growth of an \Nidealized rabbit population.
Dialogue: 0,0:03:38.04,0:03:41.55,Default,,0000,0000,0000,,Mankind later found the sequence\Neverywhere in nature,
Dialogue: 0,0:03:41.55,0:03:44.04,Default,,0000,0000,0000,,from sunflower seeds\Nand flower petal arrangements,
Dialogue: 0,0:03:44.04,0:03:45.86,Default,,0000,0000,0000,,to the structure of a pineapple,
Dialogue: 0,0:03:45.86,0:03:48.50,Default,,0000,0000,0000,,even the branching of bronchi\Nin the lungs.
Dialogue: 0,0:03:48.50,0:03:52.70,Default,,0000,0000,0000,,Or there's the non-Euclidean work of\NBernhard Riemann in the 1850s,
Dialogue: 0,0:03:52.70,0:03:57.29,Default,,0000,0000,0000,,which Einstein used in the model for\Ngeneral relativity a century later.
Dialogue: 0,0:03:57.29,0:03:58.71,Default,,0000,0000,0000,,Here's an even bigger jump:
Dialogue: 0,0:03:58.71,0:04:02.93,Default,,0000,0000,0000,,mathematical knot theory, first developed\Naround 1771
Dialogue: 0,0:04:02.93,0:04:05.18,Default,,0000,0000,0000,,to describe the geometry of position,
Dialogue: 0,0:04:05.18,0:04:10.03,Default,,0000,0000,0000,,was used in the late 20th century\Nto explain how DNA unravels itself
Dialogue: 0,0:04:10.03,0:04:12.21,Default,,0000,0000,0000,,during the replication process.
Dialogue: 0,0:04:12.21,0:04:16.16,Default,,0000,0000,0000,,It may even provide key explanations\Nfor string theory.
Dialogue: 0,0:04:16.16,0:04:18.79,Default,,0000,0000,0000,,Some of the most influential \Nmathematicians and scientists
Dialogue: 0,0:04:18.79,0:04:22.47,Default,,0000,0000,0000,,of all of human history\Nhave chimed in on the issue as well,
Dialogue: 0,0:04:22.47,0:04:24.09,Default,,0000,0000,0000,,often in surprising ways.
Dialogue: 0,0:04:24.09,0:04:26.90,Default,,0000,0000,0000,,So, is mathematics an \Ninvention or a discovery?
Dialogue: 0,0:04:26.90,0:04:29.85,Default,,0000,0000,0000,,Artificial construct or\Nuniversal truth?
Dialogue: 0,0:04:29.85,0:04:34.02,Default,,0000,0000,0000,,Human product or\Nnatural, possibly divine, creation?
Dialogue: 0,0:04:34.02,0:04:38.46,Default,,0000,0000,0000,,These questions are so deep the debate\Noften becomes spiritual in nature.
Dialogue: 0,0:04:38.46,0:04:41.55,Default,,0000,0000,0000,,The answer might depend on the specific\Nconcept being looked at,
Dialogue: 0,0:04:41.55,0:04:45.18,Default,,0000,0000,0000,,but it can all feel like a\Ndistorted zen koan.
Dialogue: 0,0:04:45.18,0:04:48.81,Default,,0000,0000,0000,,If there's a number of trees in a forest,\Nbut no one's there to count them,
Dialogue: 0,0:04:48.81,0:04:50.73,Default,,0000,0000,0000,,does that number exist?