Einstein believed that the rules of the universe could always be explained by elegant mathematics. In effect he thought that science could lead to an understanding of God’s design of the universe. Horizon: Einstein’s Unfinished Symphony, BBC 2005
I know lots of people hate maths and think it’s really boring, but I want to show Alan, show everyone in fact, that’s it’s a wonderful exciting subject. Horizon: Alan and Marcus Go Forth And Multiply, Marcus du Sautoy reporting, BBC 2009
These footballers are mathematical geniuses. Intuitively, they’re doing this Maths all the time on the pitch. ibid.
I want Alan to realise that having faith in maths rather than blind optimism will give him a clear, more accurate understanding of the world around him. ibid.
I think we’re all programmed to do maths. I think that we’re almost hardwired to do mathematics. ibid.
It doesn’t matter how many Primes you multiply together, by adding one you’ll either discover a new Prime number or a number that’s divisible by a Prime that’s not on your list. ibid.
There’s something about the permanence of proof. It gives you a hundred per cent certainty. And that proof will be there for ever. This beach will disappear, crumble into sand, but that proof is indestructible. It sort of gives you a little bit of immortality. Like Euclid’s name will somehow live for ever. This proof: it’s the beauty of mathematics. ibid.
Is the universe infinite? Might every event repeat again and again and again ... Is the Earth just one of uncountable copies tumbling through an unending void? Horizon: To Infinity & Beyond, BBC 2010
A google-plex has so many zeros that there is not enough space in the observable universe just to write the number down. ibid.
Graham’s number is so big it even made it into the Guinness Book of Records. ibid.
In an infinite universe anything that is possible has to happen. ibid.
While no-one likes the idea of space coming to an end, the consequences of an infinite universe are even more bewildering. ibid.
For all its intricate mathematics the standard model has flaws. Built into it are a series of theories designed to explain observations that don’t make any sense. Theories that are incomplete and unproven. Horizon: Is Everything We Know About the Universe Wrong? BBC 2010
Big Bang theory says that the universe was created in an explosion. But an explosion would produce a universe that was lumpy and messy. With patches there were at vastly different temperatures from one area to another. The real universe is nothing like this. In all directions the temperature appears to be almost exactly the same. ibid.
The Holographic Principle: which says that all three dimensional objects can be encoded in only two dimensions. Horizon: What is Reality? BBC 2011
But Lenny [Susskind] didn’t stop there. He and other physicists made a truly shocking leap of the imagination: they asked what if the whole of reality is a hologram, projected from our own Event Horizon, the far edges of the universe. ibid.
It seems utterly bizarre that the ultimate nature of reality might be holographic. That at the edge of our universe there might be a shimmering sheet of information that describes the entire universe within ... We are about to put this theory to the test. ibid.
If Max [Tegmark] is right, maths isn’t a language we’ve invented, but a deep structure we are gradually uncovering like archaeologists. An abstract unchanging entity that has no beginning and no end. As we peel back the layers we are discovering the code. Strange as it seems it’s a comforting theory because if the reality is a mathematical object, understanding it might be within our reach. ibid.
These two grand visions of Reality – the mathematical structure and the cosmic hologram represent theoretical thinking at its most imaginative and beautiful. ibid.
It may be that we are standing on the verge of a new version of Reality. Physicists have redefined Reality by close measurement and observation of the material world. They have drilled down to the bottom layer. Discovered that we can change Reality just by looking at it. And begun to sense that information encoded at the edge of our universe could be more important than matter. But in the end Reality is best defined as an intelligent conversation with the Universe. ibid.
Inflation may have started out as a mathematical theory but it has gained acceptance after successful testing against the evidence from the Cosmic Microwave Background. Horizon: How Big is the Universe? BBC 2012
I am convinced that the act of thinking logically cannot possibly be natural to the human mind. If it were, then mathematics would be everybody’s easiest course at school and our species would not have taken several millennia to figure out the scientific method. Neil deGrasse Tyson, The Sky is Not the Limit: Adventures of an Urban Astrophysicist
Newton: he could write the laws of Nature in perfect mathematical sentences. Neil deGrasse Tyson, Cosmos: A Spacetime Odyssey III: When Knowledge Conquered Fear, Fox 2014
Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and simplicity in human thought. Edward Teller, The Pursuit of Simplicity
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater. Albert Einstein, letter 7th January 1943
Development of Western science is based on two great achievements: the invention of the formal logical system (in Euclidean geometry) by the Greek philosophers, and the discovery of the possibility to find out causal relationships by systematic experiment (during the Renaissance). In my opinion, one has not to be astonished that the Chinese sages have not made these steps. The astonishing thing is that these discoveries were made at all. Albert Einstein, letter to US Army Colonel John Singleton Switzer 1953
The theoretician is forced, ever more, to allow himself to be directed by purely mathematical, formal points of view in the search for theories, because the physical experience of the experimenter is not capable of leading us up to the regions of the highest abstraction. Albert Einstein, cited Ideas and Opinions 1954
The core of Science is not a mathematical model – it is intellectual honesty. Sam Harris
The natural world he [Newton] began to realise might unfold from simple rules and patterns. Perhaps Mathematics was at the centre of every question he asked. Genius of Britain: The Scientists Who Changed the World, Channel 4 2012
‘Wren, Hooke and Boyle were all asking the same questions: Were the heavens governed by mathematical laws and could they discover them?’ ibid.
Hooke had spurned the one man with the mathematical talents to help him understand the laws of the universe. ibid.
‘The greatest book ever written in history ... Principia Mathematica.’ ibid. Jim Al-Khalili
The Principia spelled out for the first time the mathematical principles that governed the universe. And the law of gravity that holds all matter in place. ibid.
Philosophy [nature] is written in that great book which ever is before our eyes – I mean the universe – but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth. Galileo Galilei
Arithmetic like language begins in legend. Jacob Bronowski, The Ascent of Man 5/13: Music of the Spheres, BBC 1973
Numbers are the language of Nature. Pythagoras found a basic relation between music harmony and mathematics. ibid.
His [Newton’s] achievements were solitary ... Mathematics: he invented what we know call the Calculus ... Newton kept ‘fluxions’ as his secret tool. Jacob Bronowski, The Ascent of Man 7/13: The Majestic Clockwork
Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry. Bertrand Russell, The Study of Mathematics, 1902