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Math Quotes

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Math Quotes

“Tengo's lectures took on uncommon warmth, and the students found themselves swept up in his eloquence. He taught them how to practically and effectively solve mathematical problems while simultaneously presenting a spectacular display of the romance concealed in the questions it posed. Tengo saw admiration in the eyes of several of his female students, and he realized that he was seducing these seventeen- or eighteen-year-olds through mathematics. His eloquence was a kind of intellectual foreplay. Mathematical functions stroked their backs; theorems sent warm breath into their ears.”

“The customary units of measurement? They have practical applications, but learning them is mostly done through rote memorization— There aren’t any proofs or critical evaluations regarding REASONS why a foot equals twelve inches There are only facts to memorize, but not puzzles to solve, With algebra—YES! There isn’t just memorization— There is the rearrangement of jigsaw pieces— jigsaw pieces that you can solve, not just memorize!”

“Subjects such as history have less of that problem solving relationship. Because history is driven by human nature, one cannot merely hypothesize what happened; one must, unfortunately, resort to memorization. To analyze history, one must memorize a fact, but STEM enables students to analyze the logic behind a STEM occurrence or phenomenon throughout. STEM is a subject of problem solving. STEM is problem solving.”

“Dear Rick, I've never thought math was a miracle. The things we study simply are. They were the rules of the universe before we were here to understand them. They operate the world behind the curtain, whether we look behind it or not. The rules are already there. Music is a miracle. It adds something to the world that didn't have to be here. Language is a miracle. Every sentence ever spoken and every song ever sung is a new invention. Not only do they add something new to the world, they transmit thoughts and emotions that would otherwise be locked within one person. I hear a song and feel something a composer felt 200 years ago. I read your letter and hear your voice saying the words. I feel you in the room with me. That's the miracle.”

“Always preoccupied with his profound researches, the great Newton showed in the ordinary-affairs of life an absence of mind which has become proverbial. It is related that one day, wishing to find the number of seconds necessary for the boiling of an egg, he perceived, after waiting a minute, that he held the egg in his hand, and had placed his seconds watch (an instrument of great value on account of its mathematical precision) to boil! This absence of mind reminds one of the mathematician Ampere, who one day, as he was going to his course of lectures, noticed a little pebble on the road; he picked it up, and examined with admiration the mottled veins. All at once the lecture which he ought to be attending to returned to his mind; he drew out his watch; perceiving that the hour approached, he hastily doubled his pace, carefully placed the pebble in his pocket, and threw his watch over the parapet of the Pont des Arts.”

“الفلسفة مكتوبة في الكتاب الأكبر، كتاب الكون، والذي يواجهنا مفتوحا بشكل دائم لأعيننا، ولكن هذا الكتاب لا يمكن فهمه قبل أن نتعلم لغته أولا ثم نقرأه بعد ذلك، والكون مكتوب بلغة الرياضيات، وصفاتها كالدوائر، المثلثات، الأشكال الهندسية الأخرى التي بدونها يستحيل على البشر فهم كلمة واحدة من هذا الكتاب، من دون تلك اللغة سوف نتخبط في متاهة مظلمة!”

“Einstein, twenty-six years old, only three years away from crude privation, still a patent examiner, published in the Annalen der Physik in 1905 five papers on entirely different subjects. Three of them were among the greatest in the history of physics. One, very simple, gave the quantum explanation of the photoelectric effect—it was this work for which, sixteen years later, he was awarded the Nobel prize. Another dealt with the phenomenon of Brownian motion, the apparently erratic movement of tiny particles suspended in a liquid: Einstein showed that these movements satisfied a clear statistical law. This was like a conjuring trick, easy when explained: before it, decent scientists could still doubt the concrete existence of atoms and molecules: this paper was as near to a direct proof of their concreteness as a theoretician could give. The third paper was the special theory of relativity, which quietly amalgamated space, time, and matter into one fundamental unity. This last paper contains no references and quotes to authority. All of them are written in a style unlike any other theoretical physicist's. They contain very little mathematics. There is a good deal of verbal commentary. The conclusions, the bizarre conclusions, emerge as though with the greatest of ease: the reasoning is unbreakable. It looks as though he had reached the conclusions by pure thought, unaided, without listening to the opinions of others. To a surprisingly large extent, that is precisely what he had done.”

“This success permits us to hope that after thirty or forty years of observation on the new Planet [Neptune], we may employ it, in its turn, for the discovery of the one following it in its order of distances from the Sun. Thus, at least, we should unhappily soon fall among bodies invisible by reason of their immense distance, but whose orbits might yet be traced in a succession of ages, with the greatest exactness, by the theory of Secular Inequalities. [Following the success of the confirmation of the existence of the planet Neptune, he considered the possibility of the discovery of a yet further planet.]”

“Biot, who assisted Laplace in revising it [The Mécanique Céleste] for the press, says that Laplace himself was frequently unable to recover the details in the chain of reasoning, and if satisfied that the conclusions were correct, he was content to insert the constantly recurring formula, 'Il est àisé avoir' [it is easy to see].”

“Je me rends parfaitement compte du desagreable effet que produit sur la majorite de l'humanité, tout ce qui se rapporte, même au plus faible dègré, á des calculs ou raisonnements mathematiques. I am well aware of the disagreeable effect produced on the majority of humanity, by whatever relates, even at the slightest degree to calculations or mathematical reasonings.”

“A goal of this book has been to tear down in some small part these barriers to understanding by attempting to shatter the “divinity of arithmetic,” through showing that even the methods, which we now take most for granted, were not given to us from on high, but were actually the result of centuries of scientific efforts on the part of our predecessors. p. 269”

“Luck is not some esoteric, godlike phenomenon. Luck is countable but undefinable. Luck easily can be explained by a number of factors acting in favour of a person. These factors' behaviour could be statistically proved, and the probability of such a result is possible. So, it is not an unexplainable event. Actually, the miracle would be if these events (luck) are not in presence in our life. So, make your luck!"”

“Conventional wisdom nor scientific, mathematical prove of randomness in life could do nothing to deter human's curiosity for the unknown, however small the chance of a positive outcome maybe.”

“In my opinion, defining intelligence is much like defining beauty, and I don’t mean that it’s in the eye of the beholder. To illustrate, let’s say that you are the only beholder, and your word is final. Would you be able to choose the 1000 most beautiful women in the country? And if that sounds impossible, consider this: Say you’re now looking at your picks. Could you compare them to each other and say which one is more beautiful? For example, who is more beautiful— Katie Holmes or Angelina Jolie? How about Angelina Jolie or Catherine Zeta-Jones? I think intelligence is like this. So many factors are involved that attempts to measure it are useless. Not that IQ tests are useless. Far from it. Good tests work: They measure a variety of mental abilities, and the best tests do it well. But they don’t measure intelligence itself.”

“Is it possible that the Pentateuch could not have been written by uninspired men? that the assistance of God was necessary to produce these books? Is it possible that Galilei ascertained the mechanical principles of 'Virtual Velocity,' the laws of falling bodies and of all motion; that Copernicus ascertained the true position of the earth and accounted for all celestial phenomena; that Kepler discovered his three laws—discoveries of such importance that the 8th of May, 1618, may be called the birth-day of modern science; that Newton gave to the world the Method of Fluxions, the Theory of Universal Gravitation, and the Decomposition of Light; that Euclid, Cavalieri, Descartes, and Leibniz, almost completed the science of mathematics; that all the discoveries in optics, hydrostatics, pneumatics and chemistry, the experiments, discoveries, and inventions of Galvani, Volta, Franklin and Morse, of Trevithick, Watt and Fulton and of all the pioneers of progress—that all this was accomplished by uninspired men, while the writer of the Pentateuch was directed and inspired by an infinite God? Is it possible that the codes of China, India, Egypt, Greece and Rome were made by man, and that the laws recorded in the Pentateuch were alone given by God? Is it possible that Æschylus and Shakespeare, Burns, and Beranger, Goethe and Schiller, and all the poets of the world, and all their wondrous tragedies and songs are but the work of men, while no intelligence except the infinite God could be the author of the Pentateuch? Is it possible that of all the books that crowd the libraries of the world, the books of science, fiction, history and song, that all save only one, have been produced by man? Is it possible that of all these, the bible only is the work of God?”

“Euclid's Elements has been for nearly twenty-two centuries the encouragement and guide of that scientific thought which is one thing with the progress of man from a worse to a better state. The encouragement; for it contained a body of knowledge that was really known and could be relied on, and that moreover was growing in extent and application. For even at the time this book was written—shortly after the foundation of the Alexandrian Museum—Mathematics was no longer the merely ideal science of the Platonic school, but had started on her career of conquest over the whole world of Phenomena. The guide; for the aim of every scientific student of every subject was to bring his knowledge of that subject into a form as perfect as that which geometry had attained. Far up on the great mountain of Truth, which all the sciences hope to scale, the foremost of that sacred sisterhood was seen, beckoning for the rest to follow her.”