Quotes by Mathematician of the Authors - Page 56

Most economists, when modeling market behavior, tend to sweep major fluctuations under the rug and assume they are anomalies. What I have found is that major rises and falls in prices are actually inevitable.
Benoit Mandelbrot / Mathematician
Behavior
Inevitable
Modeling
Assume
Economists
Falls
Major
Prices
Rises
Rug
Sweep
Tend
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A science or an art may be said to be "useful" if its development increases, even indirectly, the material well-being and comfort of men, it promotes happiness, using that word in a crude and commonplace way.
G. H. Hardy / Mathematician
Art
Men
Science
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A formal and consistent theory of inductive processes cannot represent the operation of every human mind in detail; it will represent an ideal mind, but it will help the actual mind to approximate that ideal.
Harold Jeffreys / Mathematician
Details
Helping
Mind
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Perhaps the central problem we face in all of computer science is how we are to get to the situation where we build on top of the work of others rather than redoing so much of it in a trivially different way.
Richard Hamming / Mathematician
Science
Differences
Hard Work
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In many cases, mathematics is an escape from reality. The mathematician finds his own monastic niche and happiness in pursuits that are disconnected from external affairs. Some practice it as if using a drug.
Stanislaw Ulam / Mathematician
Mathematical
Mathematics
Reality
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In its evolution from a more primitive nervous system, the brain, as an organ with ten or more billion neurons and many more connections between them must have changed and grown as a result of many accidents.
Stanislaw Ulam / Mathematician
Brain
Connections
Neurons
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Mathematics is entirely free in its development, and its concepts are only linked by the necessity of being consistent, and are co-ordinated with concepts introduced previously by means of precise definitions.
Georg Cantor / Mathematician
Development
Math
Mean
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The dot was introduced as a symbol for multiplication by Leibniz. On July 29, 1698, he wrote in a letter to Johann Bernoulli: "I do not like X as a symbol for multiplication, as it is easily confounded with x.
Gottfried Leibniz / Mathematician
Dots
July
Letters
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It can have its effect only through the intervention of God, inasmuch as in the ideas of God a monad rightly demands that God, in regulating the rest from the beginning of things, should have regard to itself.
Gottfried Leibniz / Mathematician
Intervention
Regard
Beginning
Effect
Rest
Inasmuch
Monad
Rightly
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It is unnecessary to understand electromagnetic theory before wiring a lamp or to study physics in order to repair a pump. We count on our fingers and give no heed to the proliferating implications of the act.
James R Newman / Mathematician
Giving
Lamps
Order
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How can you construct a morality if there's no morality inherent in the way things are? You might be able to delude yourself into thinking you had 'created' a morality, but that's all it would be, an illusion.
John Lennox / Mathematician
Might
Thinking
Would Be
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Science, as well as technology, will in the near and in the farther future increasingly turn from problems of intensity, substance, and energy, to problems of structure, organization, information, and control.
John Von Neumann / Mathematician
Technology
Energy
Organization
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I like to think of mathematicians as forming a nation of our own without distinctions of geographical origin, race, creed, sex, age or even time... all dedicated to the most beautiful of the arts and sciences.
Julia Robinson / Mathematician
Art
Beautiful
Sex
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No matter how much we enjoy following the lives of the rich and famous, we know the world is affected more deeply by quiet, even invisible acts of integrity, kindness, and generosity, than by fame and fortune.
Karl Pearson / Mathematician
Kindness
Generosity
Integrity
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When I got to Princeton I made a point of attending the Philosophy Club and listening to the lectures, but I didn't get involved in any discussions in those clubs. I guess after the first year, I dropped that.
Stephen Cole Kleene / Mathematician
Attending
Clubs
Lectures
Listening
Philosophy
Princeton
Years
Discussions
Dropped
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I still remember the realization in college at Flinders University in Australia that mathematics was not just an abstract game of symbols but could be used as a tool to analyze and understand the modern world.
Terence Tao / Mathematician
Abstract
Australia
College
Mathematics
Modern World
Realization
Remember
Symbols
University
Used
Understand
Analyze
Game
Could
Still
Tool
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Our reasonings are grounded upon two great principles, that of contradiction, in virtue of which we judge false that which involves a contradiction, and true that which is opposed or contradictory to the false.
Gottfried Leibniz / Mathematician
Science
Judging
Two
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In symbols one observes an advantage in discovery which is greatest when they express the exact nature of a thing briefly and, as it were, picture it; then indeed the labor of thought is wonderfully diminished.
Gottfried Leibniz / Mathematician
Nature
Science
Math
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If one looks at the different problems of the integral calculus which arise naturally when one wishes to go deep into the different parts of physics, it is impossible not to be struck by the analogies existing.
Henri Poincare / Mathematician
Arise
Calculus
Different
Impossible
Looks
Physics
Wish
Naturally
Analogy
Different Parts
Existing
Integral
Parts
Struck
Wishes
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Mathematics is not the rigid and rigidity-producing schema that the layman thinks it is; rather, in it we find ourselves at that meeting point of constraint and freedom that is the very essence of human nature.
Hermann Weyl / Mathematician
Essence
Math
Thinking
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Mathematics has been called the science of the infinite. Indeed, the mathematician invents finite constructions by which questions are decided that by their very nature refer to the infinite. This is his glory.
Hermann Weyl / Mathematician
Construction
Glory
Infinite
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It is indubitable that a 50-year-old mathematician knows the mathematics he learned at 20 or 30, but has only notions, often rather vague, of the mathematics of his epoch, i.e. the period of time when he is 50.
Jean Dieudonne / Mathematician
Mathematics
Periods
Years
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I know that if I could really understand mental illness, then it would be appropriate to make a big career shift. I would become a therapist and a leader in terms of mental illness. But I'm not in the position.
John Forbes Nash / Mathematician
Careers
Leader
Would Be
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Moreover, broad plans commensurate with our national purpose and resources would bring conviction of our power to every soldier in the front line, to the nations associated with us in the war, and to the enemy.
Kelly Miller / Mathematician
War
Conviction
Enemy
Nations
Plans
Resources
Soldier
Associated
Broad
Front Line
Moreover
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If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you dont quite know what problems are worth working on.
Richard Hamming / Mathematician
Doors
Office
Years
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Math education has changed over the years. In the 19th century, they taught spherical trigonometry because one of the biggest applications of mathematics was navigating the ocean. This is no longer so relevant.
Terence Tao / Mathematician
Education
Ocean
Changed
Math
Relevant
Taught
Years
Applications
Biggest
Over
Longer
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These disturbing phenomena [Extra Sensory Perception] seem to deny all our scientific ideas. How we should like to discredit them! Unfortunately the statistical evidence, at least for telepathy, is overwhelming.
Alan Turing / Mathematician
Science
Ideas
Perception
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I shall risk nothing on an attempt to prove the transcendence of p. If others undertake this enterprise, no one will be happier than I in their success. But believe me, it will not fail to cost them some effort.
Charles Hermite / Mathematician
Believe
Effort
Risk
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No other question has ever moved so profoundly the spirit of man; no other idea has so fruitfully stimulated his intellect; yet no other concept stands in greater need of clarification than that of the infinite.
David Hilbert / Mathematician
Men
Clarification
Greater
Ideas
Infinite
Intellect
Moved
Needs
Spirit
Idea
Concept
Profoundly
Question
Stands
Stimulated
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For my part, it is difficult for me to say what I owe to Ramanujan - his originality has been a constant source of suggestion to me ever since I knew him, and his death is one of the worst blows I have ever had.
G. H. Hardy / Mathematician
Blow
Ramanujan
Suggestions
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The topdog may win the game of force. But not the moral issue - and when that dawns upon him and his allies, change of consciousness sets in, and demoralization starts thawing the frozen heart. The game is over.
Johan Galtung / Mathematician
Games
Heart
Winning
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If you have the door to your office closed, you get more work done today and tomorrow, and you are more productive than most. But ten years later somehow, you don't quite know what problems are worth working on.
Richard Hamming / Mathematician
Office
Productive
Ten
Tomorrow
Work Today Tomorrow
Closed
Door
Later
Problems
Somehow
Ten Years
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It wouild be very discouraging if somewhere down the line you could ask a computer if the Riemann hypothesis is correct and it said, 'Yes, it is true, but you won't be able to understand the proof.' John Horgan.
Ronald Graham / Mathematician
Able
Lines
Understanding
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I'm an agnostic. Sometimes I muse deeply on the forces that are for me invisible. When I am almost close to the idea of God, I feel immediately estranged by the horrors of this world, which he seems to tolerate.
Stanislaw Ulam / Mathematician
Agnostic
Ideas
World
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Into this, for good or ill, is woven every belief of every man who has speech of his fellows. A awful privilege, and an awful responsibility, that we should help to create the world in which posterity will live.
William Kingdon Clifford / Mathematician
Belief
Every Man
Fellows
Ill
Posterity
Privilege
Responsibility
Woven
Good Man World
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A powerful attraction exists, therefore, to the promotion of a study and of duties of all others engrossing the time most completely, and which is less benefited than most others by any acquaintance with science.
Charles Babbage / Mathematician
Acquaintance
Attraction
Powerful
Promotion
Study
Duties
Exists
Therefore
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We never have a full demonstration, although there is always an underlying reason for the truth, even if it is only perfectly understood by God, who alone penetrated the infinite series in one stroke of the mind.
Gottfried Leibniz / Mathematician
Infinite
Mind
Reason
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Mathematics is not a deductive science - that's a cliché. When you try to prove a theorem, you don't just list the hypotheses, and then start to reason. What you do is trial and error, experimentation, guesswork.
Paul Halmos / Mathematician
Science
Errors
Math
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If children really want to learn something, and have the opportunity to learn it in use, they do so even if the teaching is poor. For example many learn difficult video games with no professional teaching at all!
Seymour Papert / Mathematician
Opportunity
Children
Teaching
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In like manner, if I let myself believe anything on insufficient evidence, there may be no great harm done by the mere belief; it may be true after all, or I may never have occasion to exhibit it in outward acts.
William Kingdon Clifford / Mathematician
Belief
Evidence
Harm
Insufficient
Mere
Acts
Great Myself Believe
Be True
Exhibit
Manner
Occasion
Outward
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Routine is the god of every social system; it is the seventh heaven of business, the essential component in the success of every factory, the ideal of every statesman. The social machine should run like clockwork.
Alfred North Whitehead / Mathematician
Running
Essentials
Heaven
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The main importance of Francis Bacon's influence does not lie in any peculiar theory of inductive reasoning which he happened to express, but in the revolt against second-hand information of which he was a leader.
Alfred North Whitehead / Mathematician
Hands
Leader
Lying
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I'm sure that some of them will be very hard and I'll have a sense of achievement again, but nothing will mean the same to me - there's no other problem in mathematics that could hold me the way that this one did.
Andrew Wiles / Mathematician
Achievement
Hold
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We are so presumptuous that we wish to be known to all the world, even to those who come after us; and we are so vain that the esteem of five or six persons immediately around us is enough to amuse and satisfy us.
Blaise Pascal / Mathematician
Vanity
Wish
World
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I cannot forgive Descartes. In all his philosophy he would have been quite willing to dispense with God. But he had to make Him give a fillip to set the world in motion; beyond this, he has no further need of God.
Blaise Pascal / Mathematician
Giving
Needs
Philosophy
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Mathematicians do not study objects, but relations among objects; they are indifferent to the replacement of objects by others as long the relations don't change. Matter is not important, only form interests them.
Henri Poincare / Mathematician
Important
Long
Teaching
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Why is it that showers and even storms seem to come by chance, so that many people think it quite natural to pray for rain or fine weather, though they would consider it ridiculous to ask for an eclipse by prayer.
Henri Poincare / Mathematician
Science
Prayer
Rain
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The richness of human life is that we have many lives, we live the events that do not happen (and some that cannot) as vividly as those that do, and if thereby we die a thousand deaths, that is the price we pay...
Jacob Bronowski / Mathematician
Events
Life Is
Pay
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The moon... is a mass, akin to the mass of the earth, attracts the waters by a magnetic force, not because they are liquid, but because they possess earthy substance, and so share in the movements of a heavy body.
Johannes Kepler / Mathematician
Moon
Substance
Water
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Either human intelligence ultimately owes its origin to mindless matter; or there is a Creator. It is strange that some people claim that it is their intelligence that leads them to prefer the first to the second.
John Lennox / Mathematician
Firsts
Matter
People
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