Thursday 16 March 2017

PURE MATHEMATICS IS, IN ITS WAY, THE POETRYOF LOGICAL IDEAS

Meta Knowledge/ Knowledge Calculus - classification of Action Research

Pure mathematics is, in its way, the poetry of logical ideas.
Albert Einstein

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The most painful thing about mathematics is how far away you are from being able to use it after you have learned it. James Newman



I must study politics and war that my sons may have liberty to study mathematics and philosophy. John Adams

Today's scientists have substituted mathematics for experiments, and they wander off through equation after equation, and eventually build a structure which has no relation to reality. Nikola Tesla


Mathematics knows no races or geographic boundaries; for mathematics, the cultural world is one country. David Hilbert


God used beautiful mathematics in creating the world. Paul Dirac


Mathematics is a game played according to certain simple rules with meaningless marks on paper. David Hilbert 

Guided only by their feeling for symmetry, simplicity, and generality, and an indefinable sense of the fitness of things, creative mathematicians now, as in the past, are inspired by the art of mathematics rather than by any prospect of ultimate usefulness. E. T. Bell



Angling may be said to be so like the mathematics that it can never be fully learned. Izaak Walton

A lot of music is mathematics. It's balance. Mel Brooks

Beauty is the first test: there is no permanent place in the world for ugly mathematics. G. H. Hardy



The object of pure physics is the unfolding of the laws of the intelligible world; the object of pure mathematics that of unfolding the laws of human intelligence. James Joseph Sylvester


'Obvious' is the most dangerous word in mathematics. E. T. Bell


I had an excellent math and physics teacher in high school named T.C. Patel, and in the university, I had truly dedicated professors in both physics and mathematics who gave me a sound foundation with which to pursue graduate studies. Venkatraman Ramakrishnan


To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as they are usually believed to be. Leonhard Euler



The science of operations, as derived from mathematics more especially, is a science of itself, and has its own abstract truth and value. Ada Lovelace


Mathematics cannot handle physical quantities like density that literally go to infinity. Gregory Benford


There should be no such thing as boring mathematics. Edsger Dijkstra


In mathematics the art of proposing a question must be held of higher value than solving it. Georg Cantor

It may be true, that men, who are mere mathematicians, have certain specific shortcomings, but that is not the fault of mathematics, for it is equally true of every other exclusive occupation. Carl Friedrich Gauss

As a graduate student I studied mathematics fairly broadly, and I was fortunate enough, besides developing the idea which led to 'Non-Cooperative Games,' also to make a nice discovery relating to manifolds and real algebraic varieties. John Forbes Nash, Jr.


I can observe the game theory is applied very much in economics. Generally, it would be wise to get into the mathematics as much as seems reasonable because the economists who use more mathematics are somehow more respected than those who use less. That's the trend. John Forbes Nash, Jr.

The Universal Zulu Nation stands to acknowledge wisdom, understanding, freedom, justice, and equality, peace, unity, love, and having fun, work, overcoming the negative through the positive, science, mathematics, faith, facts, and the wonders of God, whether we call him Allah, Jehovah, Yahweh, or Jah. Afrika Bambaataa

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Richard Courant

The problem is that no ethical system has ever achieved consensus. Ethical systems are completely unlike mathematics or science. This is a source of concern. Daniel Dennett

For the things of this world cannot be made known without a knowledge of mathematics. Roger Bacon

I could never accept findings based almost exclusively on mathematics. It ain't ignorance that causes all the trouble in this world. It's the things people know that ain't so. Edwin Armstrong

As far as the laws of mathematics refer to reality, they are not certain, and as far as they are certain, they do not refer to reality. Albert Einstein


May not music be described as the mathematics of the sense, mathematics as music of the reason? The musician feels mathematics, the mathematician thinks music: music the dream, mathematics the working life. James Joseph Sylvester Life, Music, Mathematics

The essence of mathematics lies in its freedom. Georg Cantor

At 20, I realized that I could not possibly adjust to a feminine role as conceived by my father and asked him permission to engage in a professional career. In eight months I filled my gaps in Latin, Greek and mathematics, graduated from high school, and entered medical school in Turin. Rita Levi-Montalcini

Without mathematics, there's nothing you can do. Everything around you is mathematics. Everything around you is numbers. Shakuntala Devi

Even when I was studying mathematics, physics, and computer science, it always seemed that the problem of consciousness was about the most interesting problem out there for science to come to grips with. David Chalmers


We in science are spoiled by the success of mathematics. Mathematics is the study of problems so simple that they have good solutions. Whitfield Diffie

One of the things that ultimately led me to leave mathematics and go into political science was thinking I could prevent nuclear war. Paul Wolfowitz


It is not of the essence of mathematics to be conversant with the ideas of number and quantity. George Boole


The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry. Bertrand Russell


The art of doing mathematics consists in finding that special case which contains all the germs of generality. David Hilbert


If a man's wit be wandering, let him study the mathematics. Francis Bacon

All science requires mathematics. The knowledge of mathematical things is almost innate in us. This is the easiest of sciences, a fact which is obvious in that no one's brain rejects it; for laymen and people who are utterly illiterate know how to count and reckon. Roger Bacon

The traditional mathematician recognizes and appreciates mathematical elegance when he sees it. I propose to go one step further, and to consider elegance an essential ingredient of mathematics: if it is clumsy, it is not mathematics. Edsger Dijkstra


Mathematics allows for no hypocrisy and no vagueness. Stendhal


In mathematics we have long since drawn the rein, and given over a hopeless race. Charles Babbage
 


If I were again beginning my studies, I would follow the advice of Plato and start with mathematics. Galileo Galilei

We are servants rather than masters in mathematics. Charles Hermite
It is generally recognised that women are better than men at languages, personal relations and multi-tasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics. Stephen Hawking
What makes this story so remarkable is that throughout my early childhood I had ongoing learning difficulties, particularly in mathematics. I struggled to learn the multiplication table, and no matter how hard I tried, I simply couldn't remember 6 times 7 or 7 times 8. Andrew Lo
 

There's something mathematically satisfying about music: notes fit together and harmony and all that. And mathematics has to do with abstractions and making connections. Tom Lehrer
I wasn't actually very naturally good at economics. My brain doesn't work very well, in terms of mathematics. Brit Marling

Modern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it. Camille Paglia


As mathematics had been my best subject at school, my parents proposed - and I accepted - studies at the University of Lund in mathematics, statistics, and economics. The choice of the latter subject is said to be due to the fact that at the age of five years, I was very fond of calculating the cost of the various cakes my mother used to bake. Bertil Ohlin


Modern bodybuilding is ritual, religion, sport, art, and science, awash in Western chemistry and mathematics. Defying nature, it surpasses it. Camille Paglia
 

Aerodynamics is mathematics for those who haven't learned to do calculus. In my case, too, for one who hasn't learned to add or multiply, at least the first time. Richard Bach
 

Mathematics is written for mathematicians. Nicolaus Copernicus
 

At the risk of being forgotten completely by the media, I went to college and pursued a passion that had nothing to do with acting: mathematics. Danica McKellar 

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth. Marston Morse
 

Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth. Marston Morse
 

The definition of a good mathematical problem is the mathematics it generates rather than the problem itself. Andrew Wiles
 

My interests started about in science and in mathematics; I always thought I was going to be a mathematician. David Chalmers

I find all of my performances come down to mathematics in a sense - how do you approach the problem of this character? Sometimes I crack that problem, sometimes I don't. Brad Pitt

I appreciate and enjoy mathematics and science and all that side of things. I definitely have that side of me even though I'm not by any means an expert, but I love reading about physics and math and that kind of stuff. I wish I knew more than I did. I mean, I read books written for laymen, not textbooks or anything. Chris Parnell
 

I was always told that I was good in mathematics, and I guess my grades and standardized test scores supported that. My worst subjects were those that generally involved a lot of reading - English and history. So, having good test scores in math and mediocre ones in reading, I was naturally advised to major in engineering in college. Henry Petroski

I won some genetic lottery. I always happened to be strangely good at mathematics in my head. I just popped out weird. Rodney Brooks


The correct statement of the laws of physics involves some very unfamiliar ideas which require advanced mathematics for their description. Therefore, one needs a considerable amount of preparatory training even to learn what the words mean. Richard P. Feynman


I got my mathematics degree because I wanted to teach deaf children math. Nyle DiMarco


I won some genetic lottery. I always happened to be strangely good at mathematics in my head. I just popped out weird. Rodney Brooks


By a combination of formal training and self study, the latter continuing systematically well into the 1940s, I was able to gain a broad base of knowledge in economics and political science, together with reasonable skills in advanced mathematics, symbolic logic, and mathematical statistics. Herbert A. Simon


I would not dare to say that there is a direct relation between mathematics and madness, but there is no doubt that great mathematicians suffer from maniacal characteristics, delirium, and symptoms of schizophrenia. John Forbes Nash, Jr.


It is now quite lawful for a Catholic woman to avoid pregnancy by a resort to mathematics, though she is still forbidden to resort to physics or chemistry. H. L. Mencken

When we were making the law, when we were writing the literature and the mathematics the grandfarthers of Blair and little Bush were scratching around in caves. Mohammed Saeed al-Sahaf
Everyone knows what a curve is, until he has studied enough mathematics to become confused through the countless number of possible exceptions. Felix Klein
God exists since mathematics is consistent, and the Devil exists since we cannot prove it. Andre Weil
Programming is one of the most difficult branches of applied mathematics; the poorer mathematicians had better remain pure mathematicians. Edsger Dijkstra
When we were making the law, when we were writing the literature and the mathematics the grandfarthers of Blair and little Bush were scratching around in caves. Mohammed Saeed al-Sahaf

I chose to deal with the science of cryptography. Cryptography began in mathematics. Codes were developed, even from Caesar's time, based on number theory and mathematical principles. I decided to use those principles and designed a work that is encoded. James Sanborn

It has become almost a cliche to remark that nobody boasts of ignorance of literature, but it is socially acceptable to boast ignorance of science and proudly claim incompetence in mathematics. Richard Dawkins

The problem is that modern fundamental physics is so far from you and me. The mathematics has become so much more complicated that you need at least 10 years to understand it. Fundamental physics has advanced so far from the understanding of most people that there is really a big disconnect. Yuri Milner

The broader the chess player you are, the easier it is to be competitive, and the same seems to be true of mathematics - if you can find links between different branches of mathematics, it can help you resolve problems. In both mathematics and chess, you study existing theory and use that to go forward. Viswanathan Anand

In my family, as in most middle-class Indian families I knew when I was growing up, science and mathematics were held in awe. Aravind Adiga

Things like the financial markets - a proper grounding in mathematics could help the common man. I believe that if people are more familiar with mathematical concepts... it can help deal with modern life, which is increasingly complex. Viswanathan Anand

I was performing at a New Jersey high school, and I asked a class of 2,000 students, 'How many of you love mathematics?' and only one hand went up. And that was the hand of the maths teacher! Shakuntala Devi

I still remember asking my high school guidance teacher for permission to take a second year of algebra instead of a fifth year of Latin. She looked down her nose at me and sneered, 'What lady would take mathematics instead of Latin?' Nancy Roman

Mathematics takes us into the region of absolute necessity, to which not only the actual word, but every possible word, must conform. Bertrand Russell

I stayed away from mathematics not so much because I knew it would be hard work as because of the amount of time I knew it would take, hours spent in a field where I was not a natural. Carl Sandburg

I was so pleased to be at university to do physics and mathematics. John Henry Carver

When Europeans first came to Africa, they considered the architecture very disorganized and thus primitive. It never occurred to them that the Africans might have been using a form of mathematics that they hadn't even discovered yet. Ron Eglash

No matter what engineering field you're in, you learn the same basic science and mathematics. And then maybe you learn a little bit about how to apply it. Noam Chomsky

It is the perennial youthfulness of mathematics itself which marks it off with a disconcerting immortality from the other sciences. E. T. Bell

What affected me most profoundly was the realization that the sciences of cryptography and mathematics are very elegant, pure sciences. I found that the ends for which these pure sciences are used are less elegant. James Sanborn

In some parts of life, like mathematics and science, yeah, I was a genius. I would top all the top scores you could ever measure it by. Steve Wozniak

Thus, in a sense, mathematics has been most advanced by those who distinguished themselves by intuition rather than by rigorous proofs. Felix Klein

The mistakes and unresolved difficulties of the past in mathematics have always been the opportunities of its future. E. T. Bell

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. G. H. Hardy

I am interested in mathematics only as a creative art. G. H. Hardy

Pure mathematics is on the whole distinctly more useful than applied. For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics. G. H. Hardy

Many of our young people spend four years getting very expensive college degrees. But our universities fail them and the nation if they continue to graduate students with expertise in biochemistry, mathematics or history without teaching them to think about what problems are important and why. Heather Wilson

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