Du Sautoy Quotes

Mathematics has beauty and romance. It's not a boring place to be, the mathematical world. It's an extraordinary place; it's worth spending time there.

One of the most curious consequences of quantum physics is that a particle like an electron can seemingly be in more than one place at the same time until it is observed, at which point there seems to be a random choice made about where the particle is really located. Scientists currently believe that this randomness is genuine, not just caused by a lack of information. Repeat the experiment under the same conditions and you may get a different answer each time.

Much modern art is no longer about the appreciation of an aesthetic and skill by the likes of Rembrandt or Leonardo, but rather the interesting message and perspective that the artist is revealing about our relationship to our world.

The Goldberg Variations is a good example of how symmetry is not just a physical property but pervades many abstract structures.

The knowledge of what we are ignorant of seems to expand faster than our catalogue of breakthroughs.

For any scientist the real challenge is not to stay within the secure garden of the known but to venture out into the wilds of the unknown.

It doesn’t matter how the paint is put on,’ he wrote in describing his method, ‘as long as something is said. Painting is self-discovery. Every good artist paints what he is.

Art does many things, but for me where art is at its best is in providing a window into the way another mind works.

The first algorithm to win its creators a Nobel Prize—originally formulated by two mathematicians, David Gale and Lloyd Shapley, in 1962

The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. Without these, one is wandering about in a dark labyrinth. This

The patterns of tiles created by the Moors are of secondary interest: it is the underlying group of symmetries which preserve aspects of the patterns that defines the geometry of the [Alhambra's] murals.

I also fell in love with Borges. He is a mathematician’s writer. His short stories are like mathematical proofs, delicately constructed and with ideas laced together effortlessly. Each step is taken with precision and watertight logic, yet the narrative is full of surprising twists and turns.

It is Boden’s third form of creativity that is the more mysterious and elusive, and that is transformational creativity. This describes those rare moments that are complete game changers. Every art form has these gear shifts. Think of Picasso and Cubism, Schoenberg and atonality, Joyce and modernism. They are like phase changes, when water suddenly goes from a liquid to a gas.

Viruses like symmetrical shapes because symmetry provides a very simple means for them to multiply, and that is what makes viral diseases so infectious—in fact, that’s what ‘virulent’ means. Traditionally, symmetry has been something people have found aesthetically appealing, whether it is seen in a diamond, a flower or the face of a supermodel. But symmetry isn’t always so desirable. Some of the most deadly viruses on the biological books, from influenza to herpes, from polio to the AIDS virus, are constructed using the shape of an icosahedron. Is

The wave quality of light is the same as that of the electron. The wave determines the probable location of the photon of light when it is detected. The wave character of light is not vibrating stuff like a wave of water but rather a wavelike function encoding information about where you'll find the photon of light once it is detected. Until it reaches the detector plate, like the electron, it is seemingly passing through both slits simultaneously, making its mind up about its location only once it is observed [...]. It's this act of observation that is such a strange feature of quantum physics. Until I ask the detector to pick up where the electron is, the particle should be thought of as probabilistically distributed over space, with a probability described by a mathematical function that has wavelike characteristics. The effect of the two slits on this mathematical wave function alters it in such a way that the electron is forbidden from being located at some points on the detector plate. But when the particle is observed, the die is cast, probabilities disappear, and the particle must decide on a location.

In 1940, the pacifist and mathematician Andre´ Weil, brother of the French philosopher Simone Weil, found himself in prison awaiting trial for desertion. During those months in Rouen prison, Weil produced one of the greatest discoveries of the twentieth century, on solving elliptic curves. He wrote to his wife: ‘My mathematics work is proceeding beyond my wildest hopes, and I am even a bit worried – if it is only in prison that I work so well, will I have to arrange to spend two or three months locked up every year?’ On hearing of his breakthrough, fellow mathematician Henri Cartan wrote back to Weil: ‘We’re not all lucky enough to sit and work undisturbed like you...

It does appear that some parts of our evolutionary process seem inevitable. It is striking that throughout evolutionary history, the eye evolved independently fifty to a hundred times. This is strong evidence for the fact that the different rolls of the dice that have occurred across different species seem to have produced species with eyes regardless of what is going on around them. Lots of other examples illustrate how some features, if they are advantageous, seem to rise to the top of the evolutionary swamp. This is illustrated every time you see the same feature appearing more than once in different parts of the animal kingdom. Dolphins and bats, for example, use echolocation, but they evolved this trait independently at very different points on the evolutionary tree.

Everyone takes the limits of his own vision for the limits of the world. —Arthur Schopenhauer

Galois did not have a clear vision of the possible shapes lurking behind an equation, or of why the language he was developing would help reveal the symmetry of those shapes. Perhaps it was just as well, because the power of the language lay in its ability to create an abstraction – a mathematical description that was independent of any underlying geometry. What Galois could see was that every equation would have its own collection of permutations of the solutions which would preserve the laws relating these solutions, and that analysing the collection of permutations together revealed the secrets of each equation. He called this collection ‘the group’ of permutations associated with the equation. Galois discovered that it was the particular way in which these permutations interacted with each other that indicated whether an equation could be solved or not.

Of course, physics prevents us from dividing things beyond a certain limit, determined by what is called the Planck constant. This is because, according to physicists, it is actually impossible to measure a distance smaller than 10-34m without creating a black hole that would swallow up the measuring device.

If, years later, I do use the slit detector to observe which way the electron went, it will mean that many years earlier the electron must have passed through one slit or the other. But if I don't use the "slit detector," then the electron must have passed through both slits. This is, of course, extremely weird. My actions at the beginning of the twenty-first century can change what happened thousands of years ago when the electron began its journey. It seems that just as there are multiple futures, there are also multiple pasts, and my acts of observation in the present can decide what happened in the past. As much as it challenges any hope of ever really knowing the future, quantum physics asks whether I can ever really know the past. It seems that the past is also in a superposition of possibilities that crystallize only once they are observed.

Some might question whether it makes sense to talk about setting up the experiment and running it again with exactly the same conditions--that it is, in fact, impossible. Locally, you might get the conditions exactly the same, but you have to embed the experiment in the universe, and that has moved on. You can't rewind the wave function of the universe and rerun it. The universe is a one-time-only experiment that includes us as part of its wave function, and there's no going back.

If I keep observing the uranium, which means a little more than keeping my eyes on the pot on my desk and involves something akin to surrounding it with a whole system of Geiger counters, I can freeze it in such a way that it stops emitting radiation. Although Turing first suggested the idea as a theoretical construct, it turns out that it is not just mathematical fiction. Experiments in the last decade have demonstrated the real possibility of using observation to inhibit the progress of a quantum system.

To understand this new frontier, I will have to try to master one of the most difficult and counterintuitive theories ever recorded in the annals of science: quantum physics. Listen to those who have spent their lives immersed in this world and you will have a sense of the challenge we face. After making his groundbreaking discoveries in quantum physics, Werner Heisenberg recalled, "I repeated to myself again and again the question: Can nature possibly be so absurd as it seemed to us in these atomic experiments?" Einstein declared after one discovery, "If it is correct it signifies the end of science." Schrödinger was so shocked by the implications of what he'd cooked up that he admitted, "I do not like it and I am sorry I had anything to do with it." Nevertheless, quantum physics is now one of the most powerful and well-tested pieces of science on the books. Nothing has come close to pushing it off its pedestal as one of the great scientific achievements of the last century. So there is nothing to do but to dive headfirst into this uncertain world. Feynman has some good advice for me as I embark on my quest: "I am going to tell you what nature behaves like. If you will simply admit that maybe she does behave like this, you will find her a delightful, entrancing thing. Do not keep saying to yourself, if you can possibly avoid it, 'But how can it be like that?' because you will get 'down the drain,' into a blind alley from which nobody has yet escaped. Nobody knows how it can be like that.

The scientist does not study Nature because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful. If Nature were not beautiful, it would not be worth knowing, and if Nature were not worth knowing, life would not be worth living.’ One

Humankind now produces in two days the same amount of data it took us from the dawn of civilisation until 2003 to generate.

How do politicians cope with the challenges of predicting or manipulating the future, given that we can have only partial knowledge of the systems being analysed? ‘I think that’s rather a flattering account of what goes on here. With some notable exceptions it’s mostly a bunch of very egotistical people, very ambitious people, who are primarily interested in their own careers.

Marcus du Sautoy, professor of mathematics at Oxford University, was involved in the study of Bakhshali Manuscript. He realises the importance of the text and says[86], ‘Today we take it for granted that the concept of zero is used across the globe and is a key building block of the digital world. But the creation of zero as a number in its own right, which evolved from the placeholder dot symbol found in the Bakhshali manuscript, was one of the greatest breakthroughs in the history of mathematics.

A game,” he wrote, “may be as integral to a culture, as true an object of aesthetic appreciation, as admirable a product of human creativity as a folk art or a style of music; and, as such, it is quite as worthy of study.

Doufejme, že půjdu do důchodu dřív, než někdo něco takového objeví, takže už to nebude moje starost.

Hugh Montgomery věří, že v důsledku jeho konverzace s kvantovým fyzikem Freemanem Dysonem u princetonského čaje jsme ušli pořádný kus cesty směrem ke konečnému důkazu. Tento optimismus je poněkud mírněn doplňující poznámkou:„Důkaz Riemannovy hypotézy je hotov až na jednu velkou mezeru. Bohužel se zdá, že ta mezera je na samém začátku argumentace.“ Montgomery k tomu správně poznamenává, že to není nejlepší místo, na kterém by se měla nacházet mezera v důkazu.

Why do we as humans create art? Why is Richter’s work regarded as art while a book of Dulux colour samples is not?

this equation into the future, it takes a dramatic lurch downward, absurdly predicting complete annihilation of the US population in the middle of October 2028. (Or perhaps the mathematics knows something we don’t!) Graph source: The Mathworks, Inc.

You don't have any need for a creator. Quantum fluctuations mean that we are seeing something appearing from nothing all the time.

A tudós nem azért tanulmányozza a természetet, mert az haszonnal jár, hanem azért, mert a természet gyönyörű. Ha nem volna gyönyörű, nem volna érdemes megismerni, és ha nem volna érdemes megismerni, akkor élni sem volna érdemes.

A prímek listája a szívverés a matematikában, de mintha egy erős koffeinkeverék szabálytalanná tenné ezt a lüktetést.

In the early 1990s a PhD student by the name of Zhihong Xia proved that there is a way to configure five planets such that when you let them go, the combined gravitational pull causes one of the planets to fly off and reach an infinite speed in a finite amount of time.