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Mathematicians (page 13)
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"Juggling is sometimes called the art of controlling patterns, controlling patterns in time and space"
Ronald Graham, Mathematician
"A lot of the high-level sports are really in your mind"
Ronald Graham, Mathematician
"Mathematics is as old as Man"
Stefan Banach, Mathematician
"One of the basic things about a string is that it can vibrate in many different shapes or forms, which gives music its beauty"
Edward Witten, Mathematician
"If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways"
Edward Witten, Mathematician
"Even before string theory, especially as physics developed in the 20th century, it turned out that the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle"
Edward Witten, Mathematician
"As of now, string theorists have no explanation of why there are three large dimensions as well as time, and the other dimensions are microscopic. Proposals about that have been all over the map"
Edward Witten, Mathematician
"String theory is an attempt at a deeper description of nature by thinking of an elementary particle not as a little point but as a little loop of vibrating string"
Edward Witten, Mathematician
"Quantum mechanics brought an unexpected fuzziness into physics because of quantum uncertainty, the Heisenberg uncertainty principle"
Edward Witten, Mathematician
"As far as extra dimensions are concerned, very tiny extra dimensions wouldn't be perceived in everyday life, just as atoms aren't: we see many atoms together but we don't see atoms individually"
Edward Witten, Mathematician
"Technically, you need the extra dimensions. At first people didn't like them too much, but they've got a big benefit, which is that the ability of string theory to describe all the elementary particles and their forces along with gravity depends on using the extra dimensions"
Edward Witten, Mathematician
"There was a long history of speculation that in quantum gravity, unlike Einstein's classical theory, it might be possible for the topology of spacetime to change"
Edward Witten, Mathematician
"Spreading out the particle into a string is a step in the direction of making everything we're familiar with fuzzy. You enter a completely new world where things aren't at all what you're used to"
Edward Witten, Mathematician
"So when you ask me how string theory might be tested, I can tell you what's likely to happen at accelerators or some parts of the theory that are likely to be tested"
Edward Witten, Mathematician
"It's indeed surprising that replacing the elementary particle with a string leads to such a big change in things. I'm tempted to say that it has to do with the fuzziness it introduces"
Edward Witten, Mathematician
"I do engineering, not religion"
Daniel J. Bernstein, Mathematician
"In general, the Internet was not designed to accommodate deliberate failures to communicate"
Daniel J. Bernstein, Mathematician
"I have discovered that there are two types of command interfaces in the world of computing: good interfaces and user interfaces"
Daniel J. Bernstein, Mathematician
"The average user doesn't give a damn what happens, as long as (1) it works and (2) it's fast"
Daniel J. Bernstein, Mathematician
"I won't be satisfied until I've put the entire security industry out of work"
Daniel J. Bernstein, Mathematician
"To unfold the secret laws and relations of those high faculties of thought, by which all beyond the merely perceptive knowledge of the world and of ourselves is attained or matured, is a object which does not stand in need of commendation to a rational mind"
George Boole, Mathematician
"Of the many forms of false culture, a premature converse with abstractions is perhaps the most likely to prove fatal to the growth of a masculine vigour of intellect"
George Boole, Mathematician
"What most experimenters take for granted before they begin their experiments is infinitely more interesting than any results to which their experiments lead"
Norbert Wiener, Mathematician
"It is not of the essence of mathematics to be conversant with the ideas of number and quantity"
George Boole, Mathematician
"Probability is expectation founded upon partial knowledge. A perfect acquaintance with all the circumstances affecting the occurrence of an event would change expectation into certainty, and leave nether room nor demand for a theory of probabilities"
George Boole, Mathematician
"To live effectively is to live with adequate information"
Norbert Wiener, Mathematician
"The idea that information can be stored in a changing world without an overwhelming depreciation of its value is false. It is scarcely less false than the more plausible claim that after a war we may take our existing weapons, fill their barrels with information"
Norbert Wiener, Mathematician
"Progress imposes not only new possibilities for the future but new restrictions"
Norbert Wiener, Mathematician
"I visualize a time when we will be to robots what dogs are to humans, and I'm rooting for the machines"
Claude Shannon, Mathematician
"I just wondered how things were put together"
Claude Shannon, Mathematician
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