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The full impact of the Lobachevskian method of challenging axioms has probably yet to be felt. It is...

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I think a strong claim can be made that the process of scientific discovery may be regarded as a for...

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Do not try the parallels in that way: I know that way all along. I have measured that bottomless nig...

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The mathematical giant [Gauss], who from his lofty heights embraces in one view the stars and the ab...

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Please give it up. Fear it no less than the sensual passion, because it, too, may take up all your t...

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Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, gra...

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Francis BaconThe Collected Works of Sir Francis Bacon

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, gra...

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Picture of Francis Bacon
Francis BaconThe Collected Works of Sir Francis Bacon

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, gra...

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Picture of Francis Bacon (artist)
Francis Bacon (artist)The Collected Works of Sir Francis Bacon

Histories make men wise; poets, witty; the mathematics, subtle; natural philosophy, deep; moral, gra...

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Picture of Francis Bacon (artist)
Francis Bacon (artist)The Collected Works of Sir Francis Bacon

Language as putative science. - The significance of language for the evolution of culture lies in th...

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[I was advised] to read Jordan's 'Cours d'analyse'; and I shall never forget the astonishment with w...

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A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanen...

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G. H. HardyA Mathematician's Apology

No mathematician should ever allow him to forget that mathematics, more than any other art or scienc...

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G. H. HardyA Mathematician's Apology

[Regarding mathematics,] there are now few studies more generally recognized, for good reasons or ba...

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A mathematician, like a painter or a poet, is a maker of poems. If his patterns are more permanent t...

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G. H. HardyA Mathematician's Apology

Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical id...

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Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; an...

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Reductio ad absurdum, which Euclid loved so much, is one of a mathematician's finest weapons. It is ...

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Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the univer...

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A distinguished writer [Siméon Denis Poisson] has thus stated the fundamental definitions of the sci...

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George BooleAn Investigation of the Laws of Thought

There was yet another disadvantage attaching to the whole of Newton’s physical inquiries, ... the wa...

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One of the first and foremost duties of the teacher is not to give his students the impression that ...

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George PólyaHow to Solve It: A New Aspect of Mathematical Method

Mathematics is the cheapest science. Unlike physics or chemistry, it does not require any expensive ...

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There was a seminar for advanced students in Zürich that I was teaching and von Neumann was in the c...

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I started studying law, but this I could stand just for one semester. I couldn't stand more. Then I ...

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The elegance of a mathematical theorem is directly proportional to the number of independent ideas o...

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George PólyaMathematical Discovery on Understanding

Questions that pertain to the foundations of mathematics, although treated by many in recent times, ...

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It appears that the solution of the problem of time and space is reserved to philosophers who, like ...

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Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquenc...

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As a teacher, Tengo pounded into his students' heads how voraciously mathematics demanded logic. Her...

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How is it that there are so many minds that are incapable of understanding mathematics? ... the skel...

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If we wish to foresee the future of mathematics, our proper course is to study the history and prese...

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The philosophers make still another objection: "What you gain in rigour," they say, "you lose in obj...

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Pure analysis puts at our disposal a multitude of procedures whose infallibility it guarantees; it o...

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One might suppose that reality must be held to at all costs. However, though that may be the moral t...

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Mathematicians deal with large numbers sometimes, but never in their income.

Do you mean ter tell me," he growled at the Dursleys, "that this boy—this boy!—knows nothin' abou'—a...

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J. K. RowlingHarry Potter and the Sorcerer's Stone

the golden eternity is { }

Picture of Jack Kerouac
Jack KerouacThe Scripture of the Golden Eternity

If there is anything that can bind the mind of man to this dreary exile of our earthly home and can ...

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The vast majority of us imagine ourselves as like literature people or math people. But the truth is...

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Whereas Nature does not admit of more than three dimensions ... it may justly seem very improper to ...

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If people do not believe that mathematics is simple, it is only because they do not realize how comp...

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The integrals which we have obtained are not only general expressions which satisfy the differential...

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The deep study of nature is the most fruitful source of mathematical discoveries. By offering to res...

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Primary causes are unknown to us; but are subject to simple and constant laws, which may be discover...

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Joseph FourierThe Analytical Theory of Heat

In my opinion, defining intelligence is much like defining beauty, and I don’t mean that it’s in the...

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It may be appropriate to quote a statement of Poincare, who said (partly in jest no doubt) that ther...

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Mark KacStatistical Independence in Probability Analysis and Number Theory

We're all born with curiosity, but at some point, school usually manages to knock that out of us.

Picture of Max Tegmark
Max TegmarkOur Mathematical Universe: My Quest for the Ultimate Nature of Reality

Mathematics is much more than a language for dealing with the physical world. It is a source of mode...

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Melvin SchwartzPrinciples of Electrodynamics

He walked straight out of college into the waiting arms of the Navy. They gave him an intelligence t...

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The ocean is a Turing machine, the sand is its tape; the water reads the marks in the sand and somet...

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In mathematics, in physics, people are concerned with what you say, not with your certification. But...

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If scientific reasoning were limited to the logical processes of arithmetic, we should not get very ...

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With me, everything turns into mathematics.

But in my opinion, all things in nature occur mathematically.

[About Pierre de Fermat] It cannot be denied that he has had many exceptional ideas, and that he is ...

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It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematic...

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Mathematics as an expression of the human mind reflects the active will, the contemplative reason, a...

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Richard CourantWhat Is Mathematics?: An Elementary Approach to Ideas and Methods

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that ...

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Picture of Richard Courant
Richard CourantWhat Is Mathematics?: An Elementary Approach to Ideas and Methods

It has become almost a cliché to remark that nobody boasts of ignorance of literature, but it is soc...

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No doubt there are some who, when confronted with a line of mathematical symbols, however simply pre...

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Roger PenroseThe Road to Reality: A Complete Guide to the Laws of the Universe

I liked math - that was my favorite subject - and I was very interested in astronomy and in physical...

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The probability of an event is the reason we have to believe that it has taken place, or that it wil...

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If you stop at general math, you're only going to make general math money.

He calculated the number of bricks in the wall, first in twos and then in tens and finally in sixtee...

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The sky is where mathematics and magic become one.

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Tony AbbottThe Forbidden Stone

Eternal truths are ultimately invisible, and you won't find them in material things or natural pheno...

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The Professor never really seemed to care whether we figured out the right answer to a problem. He p...

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Yōko OgawaThe Housekeeper and the Professor

Math has proven the existence of God, because it is absolute and without contradiction; but the devi...

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Yōko OgawaThe Housekeeper and the Professor

But Piglet is so small that he slips into a pocket, where it is very comfortable to feel him when yo...

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The formulation of the problem is often more essential than its solution, which may be merely a matt...

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The study of mathematics is apt to commence in disappointment... We are told that by its aid the sta...

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Mathematics is the science which draws necessary conclusions.

There was a footpath leading across fields to New Southgate, and I used to go there alone to watch t...

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Mathematics, rightly viewed, possesses not only truth, but supreme beauty—a beauty cold and austere,...

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Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner,...

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I never did very well in math - I could never seem to persuade the teacher that I hadn't meant my an...

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Mathematics expresses values that reflect the cosmos, including orderliness, balance, harmony, logic...

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Science attempts to find logic and simplicity in nature. Mathematics attempts to establish order and...

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Business, to be successful, must be based on science, for demand and supply are matters of mathemati...

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