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We are living in a giant mathematical structure. Max Tegmark, interview Morgan Freeman’s Through the Wormhole s2e7: How Does the Universe Work? Science 2010
There’s really nothing there at the bottom level except numbers, except math. ibid.
For me Math is a window on our universe. It’s the masterkey to understanding what’s out there. Max Tegmark
I think our entire universe is a giant mathematical structure that we are a part of. Max Tegmark
Each equation … in the book would halve the sales. Stephen Hawking, A Brief History of Time, 1988
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? ibid.
The natural man inevitably rebels against mathematics, a mild form of torture that could only be learned by painful processes of drill. Woodrow Wilson
Everyone needs a basic understanding of calculus. Star Trek: The Next Generation s1e17: When The Bough Breaks, Dr Bernard to young Harry
I perceive the entire universe as a single equation and it’s so simple. Star Trek: The Next Generation s4e19: The Nth Degree, Reginald Barclay
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. Hunting the Hidden Dimension, Discovery Science 2013
It takes endless repetition ... self-similarity. ibid
Mandelbrot replied to his critics with his new book: The Fractal Geometry of Nature. ibid.
Fractal antennas are used in tens of millions of cellphones. ibid.
A healthy heartbeat has a distinctive fractal pattern. ibid.
As a poet and as a mathematician, he would reason well; as a mere mathematician, he could not have reasoned at all. Edgar Allan Poe, The Purloined Letter
Fermat’s Last Theorum. The Goldbach Conjecture. The Riemann Hypothesis. Classification Problem for 4-D Manifold. Horizon: A Mathematical Problem, BBC 1984
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.
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. ibid.
Euclid’s Elements: after the Holy Bible the most widely circulated book in history. ibid.
This calculating table known as Pascal’s Triangle was well known in China more than five hundred years before Pascal was born. ibid.
But it’s only with the Greeks and the method of proof that mathematics becomes more than just a set of specific examples. ibid.
Fermat’s Last Theorum: The problem has a wonderful history. ibid.
Since the nineteenth century Mathematics had been almost abstract. ibid.
Where does mathematics come from? ibid.
Russell’s Paradox concerns set theory. ibid.
Godel’s ... Incompleteness Theorum showed that mathematics would always be incomplete. ibid.
Mathematics seem to permeate Nature ... almost as if God is a master mathematician who has constructed the universe in mathematical forms. Horizon: The Anthropic Principle, BBC 1987
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. ibid.
The Anthropic Principle: The universe was anthropicentric – the hub of all creation was man. ibid.
Galileo’s masterstroke was to discover that what goes on around us depends on mathematical laws. ibid.
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. ibid.
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
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.
So Fermat said he had proof but he never said what it was. ibid.
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.
The problems posed by [Yutaka] Taniyama led to the extraordinary claim that every elliptic curve was really a modular form in disguise. ibid.
Andrew’s trick was to transform the elliptic curves into something called Galois Representations. Which would make counting easier. ibid.
Alan Mathison Turing, mathematician, code-breaker and inventor of the computer was born in London in 1912. Horizon: The Strange Life and Death of Dr Turing, BBC 1992
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. ibid.
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. ibid.
Turing spent more and more time at home working on mathematical biology. ibid.
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. Horizon: Archimedes’ Secret, BBC 2002
He was best known as feared for his weapons of war. ibid.
A book called The Method – it was just like going inside Archimedes’ brain. ibid.
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.