Keith Devlin Citas

• Like a Shakespearean sonnet that captures the very essence of love, or a painting that brings out the beauty of the human form that is far more than just skin deep, Euler's Equation reaches down into the very depths of existence.

  Keith Devlin

  Essence, Skins, Depth

  "Dr. Euler's Fabulous Formula: Cures Many Mathematical Ills". Book by Paul J. Nahin, 2006.

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• Just as music comes alive in the performance of it, the same is true of mathematics. The symbols on the page have no more to do with mathematics than the notes on a page of music. They simply represent the experience.

  Keith Devlin

  Math, Alive, Pages

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• Mathematical thinking is not the same as doing mathematics - at least not as mathematics is typically presented in our school system. School math typically focuses on learning procedures to solve highly stereotyped problems. Professional mathematicians think a certain way to solve real problems, problems that can arise from the everyday world, or from science, or from within mathematics itself. The key to success in school math is to learn to think inside-the-box. In contrast, a key feature of mathematical thinking is thinking outside-the-box - a valuable ability in today's world.

  Keith Devlin

  Educación, Real, Escuela

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• In fact, the answer to the question "What is mathematics?" has changed several times during the course of history... It was only in the last twenty years or so that a definition of mathematics emerged on which most mathematicians agree: mathematics is the science of patterns.

  Keith Devlin

  Years, History, Twenties

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• There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another.

  Keith Devlin

  Math, Technology, Numbers

  Keith J. Devlin (1988). “Mathematics: the new golden age”, Penguin Books

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• A PhD in Mathematics is three years of guessing it wrong, plus one week of getting it right and writing a dissertation.

  Keith Devlin

  Writing, Years, Three

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• I certainly do care about measuring educational results. But what is an 'educational result?' The twinkling eyes of my students, together with their heartfelt and beautifully expressed mathematical arguments are all the results I need.

  Keith Devlin

  Educational, Eye, Math

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• Calculus works by making visible the infinitesimally small.

  Keith Devlin

  Ontology, Logic, Certainty

  Keith Devlin (2003). “Sets, Functions, and Logic: An Introduction to Abstract Mathematics, Third Edition”, p.7, CRC Press

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• Though the structures and patterns of mathematics reflect the structure of, and resonate in, the human mind every bit as much as do the structures and patterns of music, human beings have developed no mathematical equivalent to a pair of ears. Mathematics can only be "seen" with the "eyes of the mind". It is as if we had no sense of hearing, so that only someone able to sight read music would be able to appreciate its patterns and harmonies.

  Keith Devlin

  Teaching, Eye, Math

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• The human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.

  Keith Devlin

  Zero, Roots, Numbers

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• What makes it possible to learn advanced math fairly quickly is that the human brain is capable of learning to follow a given set of rules without understanding them, and apply them in an intelligent and useful fashion. Given sufficient practice, the brain eventually discovers (or creates) meaning in what began as a meaningless game.

  Keith Devlin

  Education, Fashion, Math

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• I firmly believe that mathematics does not exist outside of humans. It is something we, as a species, invent.

  Keith Devlin

  Believe, Doe, Mathematics

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• We mathematicians are used to the fact that our subject is widely misunderstood, perhaps more than any other subject (except perhaps linguistics).

  Keith Devlin

  Misunderstood, Facts, Used

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• In addition to its use in arithmetic and science, the Hindu-Arabic number system is the only genuinely universal language on Earth, apart perhaps for the Windows operating system, which has achieved the near universal adoption of a conceptually and technologically poor product by the sheer force of market dominance.

  Keith Devlin

  Numbers, Adoption, Use

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• What is mathematics? Ask this question of person chosen at random, and you are likely to receive the answer "Mathematics is the study of number." With a bit of prodding as to what kind of study they mean, you may be able to induce them to come up with the description "the science of numbers." But that is about as far as you will get. And with that you will have obtained a description of mathematics that ceased to be accurate some two and a half thousand years ago!

  Keith Devlin

  Media, Años, Dos

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• The linear-programming was - and is - perhaps the single most important real-life problem.

  Keith Devlin

  Education, Real, Science

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• The completion of a rigorous course in mathematics - it is not even necessary that the student does well in such a course - appears to be an excellent means of sharpening the mind and developing mental skills that are of general benefit.

  Keith Devlin

  Mean, Skills, Mind

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• The whole apparatus of the calculus takes on an entirely different form when developed for the complex numbers.

  Keith Devlin

  Education, Numbers, Statistics

  Keith Devlin (1998). “Mathematics: The New Golden Age”, p.228, Penguin UK

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• Outside observers often assume that the more complicted a piece of mathematics is, the more mathematicians admire it. Nothing could be further from the truth. Mathematicians admire elegance and simplicity above all else, and the ultimate goal in solving a problem is to find the method that does the job in the most efficient manner. Though the major accolades are given to the individual who solves a particular problem first, credit (and gratitude) always goes to those who subsequently find a simpler solution.

  Keith Devlin

  Gratitude, Jobs, Goal

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• De hecho, hoy en día ningún ingeniero eléctrico podría prescindir de los números complejos, y tampoco nadie que trabaje en aerodinámica o dinámica de fluidos.

  Keith Devlin

  Teaching, Math, Aerodynamics

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• For all the time schools devote to the teaching of mathematics, very little (if any) is spent trying to convey just what the subject is about. Instead, the focus is on learning and applying various procedures to solve math problems. That's a bit like explaining soccer by saying it is executing a series of maneuvers to get the ball into the goal. Both accurately describe various key features, but they miss the what and the why of the big picture.

  Keith Devlin

  Soccer, Teaching, School

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• I've never met Hans Rosling, but I just knew him through his many YouTube videos, and they were absolute dynamite.

  Keith Devlin

  Video, Mets, Youtube

  Fuente: www.npr.org

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• In fact, we tend to think things have been getting much worse. In fact, over the last 50 years, almost everything in the world on a global scale has got better. And the way that Hans [ Rosling] did this - it was very good.

  Keith Devlin

  Pensar, Años, Hechos

  Fuente: www.npr.org

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• I saw the first one [video with Hans Rosling ] when he did - I think it was his first one - in 2006, a TED Talk. And for the first time in my life, I thought here's someone who can take statistics that most people regard as dull and boring and bring it alive.

  Keith Devlin

  Pensamiento, Personas, Primeros

  Fuente: www.npr.org

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• Sure, some [teachers] could give the standard limit definitions, but they [the students] clearly did not understand the definitions - and it would be a remarkable student who did, since it took mathematicians a couple of thousand years to sort out the notion of a limit, and I think most of us who call ourselves professional mathematicians really only understand it when we start to teach the stuff, either in graduate school or beyond.

  Keith Devlin

  Teacher, Couple, School

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