History Of Mathematics Quotes

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.

Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...

To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples. ~ Jonathan Black

In short, the idea dawns that the one universal principle which possibly ... between force and structure, the embodiment of the Principle of Least Action and the (unknown) force, which in mathematics is known as the attractor which pulls ... in the direction of the most optimal and relatively stable self-organized criticality, could very well be the Golden Ratio dynamic. the universal principle which as the balance between finiteness and infinity, stability and flexibility underlies self-similar fractal forms emerging at the 'edge of chaos' indeed seems to be the Golden Ratio Spiral. ~ Marja De Vries

The Golden Mean was considered a fundamental constant by the Egyptians and the fundamental division of the whole into two parts. ~ Richard Heath

Thousands of years ago the ancients had an advanced mathematical understanding of universe that is revealed in many sources. There is a consistent link to knowledge of the golden mean, but the way in which the ancients were able to formulate and use this information speaks of a technical grasp of the subject that exceeds what we know about it in the present day. ~ Alison Charlotte Primrose

Since ancient times artists and architects have seen in the golden mean the most aesthetically satisfying geometric ratio. ~ Stephen M. Barr

We therefore find that the triangles and rectangles herein described, enclose a large majority of the temples and cathedrals of the Greek and Gothic masters, for we have seen that the rectangle of the Egyptian triangle is a perfect generative medium, its ratio of five in width to eight in length 'encouraging impressions of contrast between horizontal and vertical lines' or spaces; and the same practically may be said of the Pythagorean triangle ~ Samuel Colman

This relationship, often called the Golden mean, has been discovered and rediscovered at various times in history as a unique proportion believed to have both aesthetic and mystic significance. That the Egyptians knew of it and used it seems certain. ~ John Pile

Some of the greatest mathematical minds of all ages, from Pythagoras and Euclid in ancient Greece, through the medieval Italian mathematician Leonardo of Pisa and the Renaissance astronomer Johannes Kepler, to present-day scientific figures such as Oxford physicist Roger Penrose, have spent endless hours over this simple ratio and its properties. But the fascination with the Golden Ratio is not confined just to mathematicians. Biologists, artists, musicians, historians, architects, psychologists, and even mystics have pondered and debated the basis of its ubiquity and appeal. In fact, it is probably fair to say that the Golden Ratio has inspired thinkers of all disciplines like no other number in the history of mathematics. ~ Mario Livio

The golden section was discovered by the Egyptians, and has been used in art and architecture, most commonly, during the classical ages of Egypt and Greece. ~ Steven L. Griffing

The attempt to apply rational arithmetic to a problem in geometry resulted in the first crisis in the history of mathematics. The two relatively simple problems
the determination of the diagonal of a square and that of the circumference of a circle
revealed the existence of new mathematical beings for which no place could be found within the rational domain. ~ David Van Dantzig

A straight line is said to have been cut in extreme and mean ratio when, as the whole line is to the greater segment, so is the greater to the lesser. ~ Euclid

Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc ... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus. ~ Abraham Robinson

The history of pi is only a small part of the history of mathematics, which itself is but a mirror of the history of man. That history is full of patterns and tendencies whose frequency and similarity is too striking to be dismissed as accidental. Like the laws of quantum mechanics, and in the final analysis, of all nature, the laws of history are evidently statistical in character. But what those laws are, nobody knows. Only a few scraps are evident. And of these is that the Heisels of Cleveland are more numerous than the Archimedes of Syracuse. ~ Petr Beckmann

The impulse to all movement and all form is given by [the golden ratio], since it is the proportion that summarizes in itself the additive and the geometric, or logarithmic, series. ~ Schwaller De Lubicz

The conclusion that the Egyptians of the Old Kingdom were acquainted with both the Fibonacci series and the Golden Section, says Stecchini, is so startling in relation to current assumptions about the level of Egyptian mathematics that it could hardly have been accepted on the basis of Herodotus' statement alone, or on the fact that the phi [golden] proportion happens to be incorporated in the Great Pyramid.

But the many measurements made by Professor Jean Philippe Lauer, says Stecchini, definitely prove the occurrence of the Golden Section throughout the architecture of the Old Kingdom.... Schwaller de Lubicz also found graphic evidence that the pharonic Egyptians had worked out a direct relation between pi and phi in that pi = phi^2 x 6/5. ~ Peter Tompkins

Central to all these interlinked themes was that curious irrational, phi, the Golden Section. Schwaller de Lubicz believed that if ancient Egypt possessed knowledge of ultimate causes, that knowledge would be written into their temples not in explicit texts but in harmony, proportion, myth and symbol. ~ John Anthony West

The golden ratio, as well as the Great Pyramid as an expression of it, is an important key to our universe containing the Earth and the Moon. ... The ratio between the Earth and the Moon is in fact the basis for the mathematical concept of 'squaring the circle' ... ~ Willem Witteveen

The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That's an incredible role for one number to play, but then again this one number has played an incredible role in human history and the universe at large. ~ H.E. Huntley

While twentieth-century physicists were not able to identify any convincing mathematical constants underlying the fine structure, partly because such thinking has normally not been encouraged, a revolutionary suggestion was recently made by the Czech physicist Raji Heyrovska, who deduced that the fine structure constant, ...really is defined by the [golden] ratio .... ~ Carl Johan Calleman

The Golden Proportion, sometimes called the Divine Proportion, has come down to us from the beginning of creation. The harmony of this ancient proportion, built into the very structure of creation, can be unlocked with the 'key' ... 528, opening to us its marvelous beauty. Plato called it the most binding of all mathematical relations, and the key to the physics of the cosmos. ~ Bonnie Gaunt

That this blind and aging man forged ahead with such gusto is a remarkable lesson, a tale for the ages. Euler's courage, determination, and utter unwillingness to be beaten serves, in the truest sense of the word, as an inspiration for mathematician and non-mathematician alike. The long history of mathematics provides no finer example of the triumph of the human spirit. ~ William Dunham

The Ark of the Covenant is a Golden Rectangle because its rectangular shape is in the proportions of the Golden Ratio. ~ Donald Frazer

The main duty of the historian of mathematics, as well as his fondest privilege, is to explain the humanity of mathematics, to illustrate its greatness, beauty and dignity, and to describe how the incessant efforts and accumulated genius of many generations have built up that magnificent monument, the object of our most legitimate pride as men, and of our wonder, humility and thankfulness, as individuals. The study of the history of mathematics will not make better mathematicians but gentler ones, it will enrich their minds, mellow their hearts, and bring out their finer qualities. ~ George Sarton

The only event in the history of our species that compares with this one is Genesis. And this is a new kind of Genesis, the Genesis of our species into conscious awareness. ~ Gary Zukav

The path of waiting and listening forgoes certainty and exposes us to a sense of tentative unknowing, which is often uncomfortable at best.

This may only be tolerable when we have developed some degree of trust in the inherent healing capacity built into the human system and the power of interpersonal receptivity to animate the process.

For most of us, this trust arrives because we have experienced it ourselves and can now embody it for others.

As this deep learning proceeds in us, we may be able to rest more easily into the waiting because the unknowing is increasingly being held within our expanding window of tolerance.

As we are able to work in this way, I believe our people get a felt sense of our profound and enduring respect for their inherent wisdom, something that is likely a unique and healing experience given their history of traumatic relationships.

I don't believe I have found any offering that is more empowering than respect. ~ Bonnie Badenoch

Time of course has showed the question up in all its young illogic. We can justify any apologia simply by calling life a successive rejection of personalities. No apologia I s any more than a romance - half a fiction - in which all the successive identities are taken on and rejected by the writer as a function of linear time are treated as separate characters. The writing itself even constitutes another rejection, another "character" added to the past. So we do sell our souls: paying them away to history in little installments. It isn't so much to pay for eyes clear enough to see past the fiction of continuity, the fiction of cause and effect, the fiction of a humanized history endowed with "reason. ~ Thomas Pynchon

A morsel of genuine history is a thing so rare as to be always valuable. ~ Thomas Jefferson

Why do we need to be pardoned? What are we to be pardoned for? For not dying of hunger? For not accepting humbly the historic burden of disdain and abandonment? For having risen up in arms after we found all other paths closed? For not heeding the Chiapas penal code, one of the most absurd and repressive in history? For showing the rest of the country and the whole world that human dignity still exists even among the world's poorest peoples? For having made careful preparations before we began our uprising? For bringing guns to battle instead of bows and arrows? For being Mexicans? For being mainly indigenous? For calling on the Mexican people to fight by whatever means possible for what belongs to them? For fighting for liberty, democracy and justice? For not following the example of previous guerrilla armies? For refusing to surrender? For refusing to sell ourselves out? Who should we ask for pardon, and who can grant it? Those who for many years glutted themselves at a table of plenty while we sat with death so often, we finally stopped fearing it? Those who filled our pockets and our souls with empty promises and words? Or should we ask pardon from the dead, our dead, who died "natural" deaths of "natural causes" like measles, whooping cough, break-bone fever, cholera, typhus, mononucleosis, tetanus, pneumonia, malaria and other lovely gastrointestinal and pulmonary diseases? Our dead, so very dead, so democratically dead from sorrow because no one did anything, because t ~ Subcomandante Marcos

The spirit of elder days found a dwelling here, and we delighted to trace its footsteps. ~ Mary Shelley

As a student of the game, it is a dream come true to align myself with a brand that has a rich history in sports. Like most kids, I grew up idolizing Michael Jordan and continue to work relentlessly to reach his iconic status on the court. I'm truly motivated to take my career to the next level as a member of Team Jordan, ~ Maya Moore

Contempt for theory, art, history, and for man as an end in himself, which is contained in an abstract form in the Jewish religion, is the real, conscious standpoint, the virtue of the man of money. The species-relation itself, the relation between man and woman, etc., becomes an object of trade! The woman is bought and sold. ~ Karl Marx

What he didn't say, because it was too heavy a burden for any man to bear, was that Aden was already a leader who was on his way to greatness. If he didn't lose his way, if he didn't break under the strain, he'd become a man who would be written of in history. To make it, he needed someone to walk with him, to hold him when things became too hard, and to fight for his right to his own happiness. Aden needed love more than anyone Walker had ever met. ~ Nalini Singh

We must be the great arsenal of democracy. ~ Franklin D. Roosevelt

Slavery as an institution that degraded man to a thing has never died out. In some periods of history it has flourished: many civilizations have climbed to power and glory on the backs of slaves. In other times slaves have dwindled in number and economic importance. But never has slavery disappeared. ~ Milton Meltzer

In a very real sense, the Constitution is our compact with history ... [but] the Constitution can maintain that compact and serve as the lodestar of our political system only if its terms are binding on us. To the extent we depart from the document's language and rely instead on generalities that we see written between the lines, we rob the Constitution of its binding force and give free reign to the fashions and passions of the day. ~ Alex Kozinski

How do you quantify love? Can you weigh it, measure it, pin it down with equations? If the sum of all experiences is really just the interaction of a finite soup of chemicals copulating in nerve endings, how did this even dare articulate the infinite?
Mathematicians will tell you there are different types of infinities. Some are countable, some are not. We can love someone more and more; we can stop loving. But we can never guess how much all this is. Love has no units. ~ Sean J Halford

During bull markets, everyone believes that he is committed to stocks for the long term. Unfortunately, history also tells us that during bear markets, you can hardly give stocks away. Most investors are simply not capable of withstanding the vicissitudes of an all-stock investment strategy. The ~ William J. Bernstein

The whole history of life is a record of cycles. ~ Ellsworth Huntington

History books report one war after another. 'History' is the dates of wars, who won and who lost. But in truth, no one ever wins a war. Someone obtained the spoils, but no one wins.

'Intermediate Guide To Meditation ~ Kriyananda

What a knot of history one mistake can become. ~ Barbara Kingsolver

But he had expressed to Mme. du Chatelet the hope that a way out might lie in applying philosophy to history, and endeavoring to trace, beneath the flux of political events, the history of the human mind. 'Only philosophers should write history,' he said. 'In all nations, history is disfigured by fable, till at last philosophy comes to enlighten man; and when it does finally arrive in the midst of darkness, it finds the human mind so blinded centuries of error, that it can hardly undeceive it; it finds ceremonies, facts and monuments, heaped up to prove lies.' 'History,' he concludes, 'is after all nothing but a pack of tricks which we play upon the dead;' we transform the past to suit our wishes for the future, and in the upshot 'history proves that anything can be proved by history. ~ Will Durant

I grew up thinking the only scriptures on earth were those inspired by the Hebrew prophets of the Old Testament, the words and letters of Jesus and his apostles, and the scriptures of the Restoration. But how could the God I believed was the loving God of all the earth not speak somehow to everyone else? For years I wrestled with this idea. Having now read the Chinese classics, certainly Confucius, but others as well, I believe I have found the scriptural infusion God gave the Chinese nation. Mencius is my favorite, I must admit, and I do not hesitate to call what he bestowed upon the world scripture--some of the most optimistic, holy writing the world has. ~ S. Michael Wilcox

Can you name a single one of the great fundamental and original intellectual achievements which have raise man in the scale of civilization that may be credited to the Anglo-Saxon? The art of letters, of poetry, of music, of sculpture, of painting, of the drama, of architecture; the science of mathematics, of astronomy, of philosophy, of logic, of physics, of chemistry, the use of the metals and principles of mechanics, were all invented or discovered by darker and what we now call inferior races and nations. ~ James Weldon Johnson

All our ancient history, as one of our wits remarked, is no more than accepted fiction. ~ Voltaire

today we read of Don Quixote with a bitter taste in the mouth, it is
almost an ordeal, which would make us seem very strange and incomprehensible
to the author and his contemporaries, – they read it with a clear
conscience as the funniest of books, it made them nearly laugh themselves
to death).To see suffering does you good, to make suffer, better still – that
On the Genealogy of Morality
42
48 See below, Supplementary material, pp. 153–4.
49 See below, Supplementary material, pp. 137–9, pp. 140–1, pp. 143–4.
50 Don Quixote, Book II, chs 31–7.
is a hard proposition, but an ancient, powerful, human-all-too-human
proposition to which, by the way, even the apes might subscribe: as people
say, in thinking up bizarre cruelties they anticipate and, as it were, act out
a 'demonstration' of what man will do. No cruelty, no feast: that is what
the oldest and longest period in human history teaches us – and punishment,
too, has such very strong festive aspects! – ~ Friedrich Nietzsche

Science and mathematics [are] much more compelling and exciting than the doctrines of pseudoscience, whose practitioners were condemned as early as the fifth century B.C. by the Ionian philosopher Heraclitus as 'night walkers, magicians, priests of Bacchus, priestesses of the wine-vat, mystery-mongers.' But science is more intricate and subtle, reveals a much richer universe, and powerfully evokes our sense of wonder. And it has the additional and important virtue-to whatever extent the word has any meaning-of being true. ~ Carl Sagan

How did Biot arrive at the partial differential equation? [the heat conduction equation] ... Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals. ~ Clifford A. Truesdell

about everything, about the whole history of the world and all its racism and the unfairness of all of it. ~ Nicola Yoon

One of the painfully sobering realizations that come from reading history is the utter incompetence that is possible among leaders of whole nations and empires - and the blind faith that such leaders can nevertheless inspire among the people who are enthralled by their words or their posturing. ~ Thomas Sowell

Real science studies and makes accessible that knowledge which people at that period of history think important, and real art transfers this truth from the domain of knowledge to the domain of feelings. ~ Leo Tolstoy

The essence of Hilbert's program was to find a decision process that would operate on symbols in a purely mechanical fashion, without requiring any understanding of their meaning. Since mathematics was reduced to a collection of marks on paper, the decision process should concern itself only with the marks and not with the fallible human intuitions out of which the marks were reduced. In spite of the prolonged efforts of Hilbert and his disciples, the Entscheidungsproblem was never solved. Success was achieved only in highly restricted domains of mathematics, excluding all the deeper and more interesting concepts. Hilbert never gave up hope, but as the years went by his program became an exercise in formal logic having little connection with real mathematics. Finally, when Hilbert was seventy years old, Kurt Godel proved by a brilliant analysis that the Entscheindungsproblem as Hilbert formulated it cannot be solved.

Godel proved that in any formulation of mathematics, including the rules of ordinary arithmetic, a formal process for separating statements into true and false cannot exist. He proved the stronger result which is now known as Godel's theorem, that in any formalization of mathematics including the rules of ordinary arithmetic there are meaningful arithmetical statements that cannot be proved true or false. Godel's theorem shows conclusively that in pure mathematics reductionism does not work. To decide whether a mathematical statement is true, it is not ~ Freeman Dyson

I do enjoy history. That's one of the things that I love about acting is you get a chance to really dive into history and develop a real personal opinion about it. ~ Andre Holland

Within a decade or two, all Holocaust survivors will likely have passed away so a ticking clock is in effect in this battle between the truth and lies. Keep in mind even those survivors born in a concentration camp during WW2 would be at least 71 years-of-age when this book (the one you are reading now) was released. Those survivors old enough to clearly recall the events of that nightmare will, of course, be older and have much less time left. As the memory of the Holocaust begins to fade away, it will become easier to deny the genocide even occurred unless those of us who are truthseekers are able to embrace the memory of the genocide and educate others do the same. What's needed in this propaganda war is for the true stories of Holocaust survivors – as well as those of the Nazi perpetrators, their associates and others who witnessed the genocide – to be told loudly and clearly so that there will never, ever be room for doubt in generations to come. After all, nothing is more powerful, credible or damning than eyewitness accounts. ~ James Morcan

Our history is a material history, not just a succession of thoughts or speech acts. ~ Andrew Shryock

I want a laitywho know their creed so well, that they can
give an account of it, who know so much of history that
they can defend it. ~ John Henry Newman

The student of history knows no more refreshing recreation than that of nailing liars, like vermin, to the wall. ~ Frederick Rolfe

Throughout history, the word "war" has meant one thing to human beings: loss of life. The word "peace" has always meant security and love within a person's soul. ~ A.H. Metwally

May it not be that, just as we have to have faith in Him, God has to have faith in us and, considering the history of the human race so far, may it not be that 'faith' is even more difficult for Him than it is for us? ~ W. H. Auden