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★ Maths & Mathematics

Maths & Mathematics: see Geometry & Computers & Artificial Intelligence & Physics & Science & Space & Universe & Cosmology & Figures & Finite & Infinite & Numbers & Data & Code & Information & Art & Music & School & Knowledge & Games & Particle & Quantum Physics & Measurement & Anthropic Principle & Logic & Simulation Theory & Laws of Science

Max Tegmark - Stephen Hawking - Woodrow Wilson - Star Trek: The Next Generation TV - Hunting the Hidden Dimension TV - Edgar Allan Poe - BBC Horizon TV - Neil deGrasse Tyson - Edward Teller - Albert Einstein - Sam Harris - Genius of Britain: The Scientists Who Changed the World TV - Galileo Galilei - Jacob Bronowski TV - Bertrand Russell - Brian Greene - Roger Penrose - Paul Dirac - Maimonides - Copenhagen 2002 - Jim Al-Khalili TV - Morgan Freeman TV - Marcus du Sautoy TV - James Burke TV - Peter Capaldi TV & Leonardo da Vinci - Alan Greenspan - Michio Kaku - Lenny Susskind - James Jeans - Christian Goldbach - Nature Magazine - Jean DieuDonne - John von Neumann & Oscar Morgenstern - Raymond Smullyan - John Maynard Smith - John Nash - Sylvia Nasar - Zipporah Levinson - S Capell - Andrew Wiles - Stendhal - Stephen Hawking - Maurice Allais - Hannah Arendt - F M Cornford - Paul Davies - Robert Musil - Great Scientists TV - The Genius of George Boole TV - John Williams - Paul Cohen - Norbert Wiener - Adam Curtis TV - Dangerous Knowledge TV - Matthew Collings TV - Slave to the Algorithm 2018 -   

 

 

115,428.  We are living in a giant mathematical structure.  (Universe & Maths & Simulation Theory)  Max Tegmark, interview Morgan Freeman’s Through the Wormhole s2e7: How Does the Universe Work?

  

115,429.  There’s really nothing there at the bottom level except numbers, except math.  (Universe & Maths & Simulation Theory)  ibid.

 

 

80,697.  For me Math is a window on our universe.  It’s the masterkey to understanding what’s out there.  (Mathematics & Anthropic Principle & Simulation Theory)  Professor Max Tegmark

 

 

2,715.  I think our entire universe is a giant mathematical structure that we are a part of.  (Universe & Mathematics & Anthropic Principle & Simulation Theory)  Professor Max Tegmark

 

 

2,740.  Each equation … in the book would halve the sales.  (Universe & Mathematics)  Stephen Hawking, A Brief History of Time 1988

 

2,742.  What is it that breathes fire into the equations and makes a universe for them to describe? … Why does the universe go to all the bother of existing?  (Universe & Mathematics)  ibid.

 

 

98,585.  The natural man inevitably rebels against mathematics, a mild form of torture that could only be learned by painful processes of drill.  Woodrow Wilson

 

 

24,213.  Everyone needs a basic understanding of calculus.  (Star Trek: The Next Generation & Mathematics)  Star Trek: The Next Generation: When The Bough Breaks s1e17, Dr Bernard to young Harry

 

 

24,380.  I perceive the entire universe as a single equation and it’s so simple.  (Star Trek: The Next Generation & Universe & Simulation Theory)  Star Trek: The Next Generation: The Nth Degree s4e19, Reginald Barclay

 

 

73,562.  You can find it in the rain forest.  On the frontiers of medical research.  In the movies.  And it’s all over the world of wireless communications.  One of Nature’s biggest design secrets has finally been revealed.  It’s an odd looking shape you may never have heard of but it’s everywhere around you – the jagged repeating form called a fractal.  (Geometry & Nature & Mathematics)  Hunting the Hidden Dimension, Discovery Science 2013

 

73,563.  It takes endless repetition ... self-similarity.  (Geometry & Nature & Mathematics)  ibid

 

73,564.  Mandelbrot replied to his critics with his new book: The Fractal Geometry of Nature.  (Geometry & Nature & Mathematics)  ibid.

 

73,565.  Fractal antennas are used in tens of millions of cellphones.  (Geometry & Nature & Mathematics & Mobile Phone)  ibid.

 

73,566.  A healthy heartbeat has a distinctive fractal pattern.  (Geometry & Nature & Mathematics & Heart)  ibid.                     

 

 

2,321.  As a poet and as a mathematician, he would reason well; as a mere mathematician, he could not have reasoned at all.  (Reason & Poetry & Mathematics)  Edgar Allan Poe, The Purloined Letter 

 

 

80,709.  Fermat’s Last Theorum.  The Goldbach Conjecture.  The Riemann Hypothesis.  Classification Problem For 4-D Manifold.  Horizon: A Mathematical Problem, BBC 1984   

 

80,710.  Solve any of these problems and you will achieve instant fame among the world’s mathematicians.  They are the classical unsolved problems of pure mathematics.  And they have resisted solution by the world’s greatest mathematical minds.  But why bother?  There’s no obvious practical benefit to be had for mankind.  These are completely abstract problems.  By mathematicians for mathematicians.  Studied for their own intrinsic interest.  ibid.

 

80,711.  Numbers are the fabric of mathematics.  But not all numbers are the same.  There are numbers and there are Prime Numbers .... They crop up at random getting larger as the numbers get rarer.  (Mathematics & Numbers)  ibid.

 

80,712.  Euclid’s Elements: after the Holy Bible the most widely circulated book in history.  (Mathematics & Book)  ibid.

 

80,713.  This calculating table known as Pascal’s Triangle was well known in China more than five hundred years before Pascal was born.  ibid.

 

80,714.  But it’s only with the Greeks and the method of proof that mathematics becomes more than just a set of specific examples.  ibid.

 

80,715.  Fermat’s Last Theorum: The problem has a wonderful history.  ibid.

 

80,716.  Since the nineteenth century Mathematics had been almost abstract.  ibid.

 

80,717.  Where does mathematics come from?  ibid.

 

80,718.  Russell’s Paradox concerns set theory.  ibid.

 

80,719.  Godel’s ... Incompleteness Theorum showed that mathematics would always be incomplete.  ibid.

 

 

2,790.  Mathematics seem to permeate Nature ... almost as if God is a master mathematician who has constructed the universe in mathematical forms.  (Science & Nature & Mathematics & Astronomy & Anthropic Theory & Simulation Theory)  Horizon: The Anthropic Principle, BBC 1987

 

2,791.  This universe we live in: scientists have discovered some remarkably strange things about it.  So strange they are having to use the most disturbing principles to describe what’s going on.  (Universe & Astronomy & Cosmology & Laws & Anthropic Principle & Simulation Theory & Mathematics)  ibid.  

 

2,792.  The Anthropic Principle: The universe was anthropicentric – the hub of all creation was man.  (Universe & Life & Astronomy & Cosmology & Anthropic Principle & Simulation Theory & Mathematics)  ibid.

 

2,793.  Galileo’s masterstroke was to discover that what goes on around us depends on mathematical laws.  (Universe & Astronomy & Mathematics & Cosmology & Laws & Anthropic Principle & Galileo & Simulation Theory)  ibid.

 

2,794.  So what are we?  A statistical accident.  Where are we?  Nowhere special.  Where are we going?  Into oblivion.  A meaningless hiccup in the blank procession of matter through time.  It’s a tatty destiny.  (Universe & Astronomy & Cosmology & Meaning of Life & Simulation Theory & Mathematics)  ibid.  

 

 

80,731.  This is the story of one man’s obsession with the world’s greatest mathematical problem.  For seven years Professor Andrew Wiles worked in complete secrecy creating the calculation of the century.  It was a calculation that brought him fame and regret.  Horizon: Fermat’s Last Theorem, BBC 1996   

 

80,732.  This tiny note is the world’s hardest mathematical problem.  It’s been unsolved for centuries.  Yet it begins with an equation so simple that children know it off by heart; the square on the hypotenuse is equal to the sum of the squares of the other two sides.  ibid.

 

80,733.  So Fermat said he had proof but he never said what it was.  ibid.

 

80,734.  What he didn’t realise was that on the other side of the world elliptic curves and Fermat’s Last Theorem were becoming inextricably linked.  ibid.

 

80,735.  The problems posed by [Yutaka] Taniyama led to the extraordinary claim that every elliptic curve was really a modular form in disguise.  ibid.

 

80,736.  Andrew’s trick was to transform the elliptic curves into something called Galois Representations.  Which would make counting easier.  ibid.

 

 

7,518.  Alan Mathison Turing, mathematician, code-breaker and inventor of the computer was born in London in 1912.  (Computer & Mathematics)  Horizon: The Strange Life and Death of Dr Turing, BBC 1992

 

2,343.  Turing’s paper described how any logical process could be broken down into its simplest possible components – precise sequential steps that could in principle be carried out by a machine.  With his new definition of method as machine he was able to formulate a logical paradox which rapidly disposed of Gilbert’s question.  (Logic & Computers & Mathematics)  ibid.

 

7,519.  He went on to imagine a universal machine which could read and execute the instructions set of any single Turing machine and therefore perform all logical tasks ... He had in effect formulated the idea of the stored programmed computer.  (Computer & Mathematics)  ibid.

 

80,720.  Turing spent more and more time at home working on mathematical biology.  ibid. 

 

 

80,727.  The buyer a billionaire who wouldn’t reveal his identity.  But instead of hiding it away he put the precious manuscript into the hands of those who could unlock its secrets.  But interpreting Archimedes’ manuscript proved to be more difficult than anyone imagined.  (Mathematics & Manuscript)  Horizon: Archimedes’ Secret, BBC 2002

 

80,728.  He was best known as feared for his weapons of war.  ibid.

 

80,729.  A book called The Method – it was just like going inside Archimedes’ brain.  ibid.

 

80,730.  Working out volumes using infinite slicing suggested that Archimedes was taking the first step towards a vital branch of mathematics known as Calculus, 1,800 years before it was invented.  ibid.

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