Short Mathematical Quotes & Sayings

They [the mathematicians of the Enlightenment] defined their terms vaguely and used their methods loosely, and the logic of their arguments was made to fit the dictates of their intuition. In short, they broke all the laws of rigor and of mathematical decorum. The veritable orgy which followed the introduction of the infinitesimals ... was but a natural reaction. Intuition had too long been held imprisoned by the severe rigor of the Greeks. Now it broke loose, and there were no Euclids to keep its romantic flight in check. — Tobias Dantzig

His [Thomas Edison] method was inefficient in the extreme, for an immense ground had to be covered to get anything at all unless blind chance intervened and, at first, I was almost a sorry witness of his doings, knowing that just a little theory and calculation would have saved him 90 per cent of the labor. But he had a veritable contempt for book learning and mathematical knowledge, trusting himself entirely to his inventor's instinct and practical American sense. In view of this, the truly prodigious amount of his actual accomplishments is little short of a miracle. — Nikola Tesla

The mathematical life of a mathematician is short. Work rarely improves after the age of twenty-five or thirty. If little has been accomplished by then, little will ever be accomplished. — Alfred Adler

Paul closed his eyes and turned his face to the sun. In spite of everything, it was hard not to take solace from the warmth flooding onto his skin. He stretched the muscles in his arms, his shoulders, his back -- and it felt like he was reaching out from the "self" in his virtual skull to all his mathematical flesh, imprinting the nebulous data with meaning; binding it all together, staking some kind of claim. He felt the stirrings of an erection. Existence was beginning to seduce him. He let himself surrender for a moment to a visceral sense of identity which drowned out all his pale mental images of optical processors, all his abstract reflections on the software's approximations and short-cuts. This body didn't want to evaporate. This body didn't want to bale out. It didn't much care that there was another -- "more real" -- version of itself elsewhere. It wanted to retain its wholeness. It wanted to endure. — Greg Egan

We shed as we pick up, like travellers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. You do not suppose, my lady, that if all of Archimedes had been hiding in the great library of Alexandria, we would be at a loss for a corkscrew? — Tom Stoppard

To make a long story short, Cantorian set theory helps unify and clarify math in the sense that all mathematical entities can now be understood as fundamentally the same kind of thing-a set. — David Foster Wallace

We shed as we pick up, like travelers who must carry everything in their arms, and what we let fall will be picked up by those behind. The procession is very long and life is very short. We die on the march. But there is nothing outside the march so nothing can be lost to it. The missing plays of Sophocles will turn up piece by piece, or be written again in another language. Ancient cures for diseases will reveal themselves once more. Mathematical discoveries glimpsed and lost to view will have their time again. — Tom Stoppard

[...] confusing time with its mathematical progression, as the old do, to whom all the past is not a diminishing road but, instead, a huge meadow which no winter ever touches. — William Faulkner

The fact that such objective and enduring knowledge exists (and moreover, belongs to all of us) is nothing short of a miracle. It suggests that mathematical concepts exist in a world separate from the physical and mental worlds — Edward Frenkel

In short, I do not write for mathematicians, nor as a mathematician, but as an economist wishing to convince other economists that their science can only be satisfactorily treated on an explicitly mathematical basis. — William Stanley Jevons

In all human transactions, the highest degree of assurance to which we can arrive, short of the evidence of our own senses, is that of probability. The most that can be asserted is, that the narrative is more likely to be true than false; and it may be in the highest degree more likely, but still be short of absolute mathematical certainty. Yet this very probability may be so great as to satisfy the mind of the most cautious, and enforce the assent of the most reluctant and unbelieving. If it is such as usually satisfies reasonable men, in matters of ordinary transaction, it is all which the greatest sceptic has a right to require; for it is by such evidence alone that our rights are determined, in the civil tribunals; and on no other evidence do they proceed, even in capital cases. — Simon Greenleaf

..the following parable may be useful. Long ago, when shepherds wanted to see if two herds of sheep were isomorphic, they would look for an explicit isomorphism. In other words, they would line up both herds and try to match each sheep in one herd with a sheep in the other. But one day, along came a shepherd who invented decategorification. She realized one could take each herd and 'count' it, setting up an isomorphism between it and some set of 'numbers', which were nonsense words like 'one, two, three, . . . ' specially designed for this purpose. By comparing the resulting numbers, she could show that two herds were isomorphic without explicitly establishing an isomorphism! In short, by decategorifying the category of finite sets, the set of natural numbers was invented. According to this parable, decategorification started out as a stroke of mathematical genius. Only later did it become a matter of dumb habit, which we are now struggling to overcome by means of categorification. — John Baez

The ecological complexities of existence overwhelm the human mind, even though some of that richness is an integral part of man's own nature. It is only by isolating some little part of that existence for a short time that it can be momentarily grasped: we learn only from samples. By separating primary from secondary qualities, by making mathematical description the test of truth, by utilizing only a part of the human self to explore only a part of its environment, the new science successfully turned the most significant attributes of life into purely secondary phenomena, ticketed for replacement by the machine. Thus living organisms, in their most typical functions and purposes, became superfluous. — Lewis Mumford

The miracle of man is not how far he has sunk but how magnificently he has risen. We are known among the stars by our poems, not our corpses. No creature who began as a mathematical improbability, who was selected through millions of years of unprecedented environmental hardship and change for ruggedness, ruthlessness, cunning, and adaptability, and who in the short ten thousand years of what we may call civilization has achieved such wonders as we find about us, may be regarded as a creature without promise. — Robert Ardrey

Because of mathematics precise, formal character, mathematical arguments remain sound even when they are long and complex. In contast, common sense arguments can generally be trusted only if they remain short; even moderately long nonmathematical arguments rapidly becomes farfetched an dubious. — Jacob T. Schwartz