Mathematical Quotes (displaying: 1 - 30 of 150 quotes )
The Matrix has its roots in primitive arcade games,' said the voice-over, 'in early graphics programs and military experimentation with cranial jacks.' On the Sony, a two-dimensional space war faded behind a forest of mathematically generated ferns, demonstrating the spatial possibilities of logarithmic spirals; cold blue military footage burned through, lab animals wired into test systems, helmets feeding into fire control circuits of tanks and war planes. 'Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts... A graphic representation of data abstracted from the banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, receding...
The sciences do not try to explain, they hardly even try to interpret, they mainly make models. By a model is meant a mathematical construct which, with the addition of certain verbal interpretations, describes observed phenomena. The justification of such a mathematical construct is solely and precisely that it is expected to work - that is correctly to describe phenomena from a reasonably wide area. Furthermore, it must satisfy certain esthetic criteria - that is, in relation to how much it describes, it must be rather simple.
Now what is history? It is the centuries of systematic explorations of the riddle of death, with a view to overcoming death. That's why people discover mathematical infinity and electromagnetic waves, that's why they write symphonies. Now, you can't advance in this direction without a certain faith. You can't make such discoveries without spiritual equipment. And the basic elements of this equipment are in the Gospels. What are they? To begin with, love of one's neighbor, which is the supreme form of vital energy. Once it fills the heart of man it has to overflow and spend itself. And then the two basic ideals of modern man—without them he is unthinkable—the idea of free personality and the idea of life as sacrifice.
The art of change-ringing is peculiar to the English, and, like most English peculiarities, unintelligible to the rest of the world. (The change-ringer's) passion- and it is a passion- finds its satisfaction in mathematical completeness and mechanical perfection, and as his bell weaves her way rhythmically up from lead to hinder place and down again, he is filled with the solemn intoxication that comes of intricate ritual faultlessly performed.
But then, the sky! Blue, untainted by a single cloud (the Ancientes had such barbarous tastes given that their poets could have been inspired by such stupid, sloppy, silly-lingering clumps of vapour). I love - and i'm certain that i'm not mistaken if i say we love - skies like this, sterile and flawless! On days like these, the whole world is blown from the same shatterproof, everlasting glass as the glass of the Green Wall and of all our structures. On days like these, you can see to the very blue depths of things, to their unknown surfaces, those marvelous expressions of mathematical equality - which exist in even the most usual and everyday objects.
The Greeks were the first mathematicians who are still ‘real’ to us to-day. Oriental mathematics may be an interesting curiosity, but Greek mathematics is the real thing. The Greeks first spoke a language which modern mathematicians can understand: as Littlewood said to me once, they are not clever schoolboys or ‘scholarship candidates’, but ‘Fellows of another college’. So Greek mathematics is ‘permanent’, more permanent even than Greek literature. Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. ‘Immortality’ may be a silly word, but probably a mathematician has the best chance of whatever it may mean.
What I'm thinking is: here I am, lying under a haystack ... The tiny little place I occupy is so small in relation to the rest of space where I am not and where it's none of my business; and the amount of time which I'll succeed in living is so insignificant by comparison with the eternity where I haven't been and never will be ... And yet in this atom, in this mathematical point, the blood circulates, the brain works and even desires something as well .. What sheer ugliness! What sheer nonsense!
Most people have some appreciation of mathematics, just as most people can enjoy a pleasant tune; and there are probably more people really interested in mathematics than in music. Appearances suggest the contrary, but there are easy explanations. Music can be used to stimulate mass emotion, while mathematics cannot; and musical incapacity is recognized (no doubt rightly) as mildly discreditable, whereas most people are so frightened of the name of mathematics that they are ready, quite unaffectedly, to exaggerate their own mathematical stupidity
Naturally, we are inclined to be so mathematical and calculating that we look upon uncertainty as a bad thing...Certainty is the mark of the common-sense life. To be certain of God means that we are uncertain in all our ways, we do not know what a day may bring forth. This is generally said with a sigh of sadness; it should rather be an expression of breathless expectation.
Immortality is often ridiculous or cruel: few of us would have chosen to be Og or Ananias or Gallio. Even in mathematics, history sometimes plays strange tricks; Rolle figures in the textbooks of elementary calculus as if he had been a mathematician like Newton; Farey is immortal because he failed to understand a theorem which Haros had proved perfectly fourteen years before; the names of five worthy Norwegians still stand in Abel’s Life, just for one act of conscientious imbecility, dutifully performed at the expense of their country’s greatest man. But on the whole the history of science is fair, and this is particularly true in mathematics. No other subject has such clear-cut or unanimously accepted standards, and the men who are remembered are almost always the men who merit it. Mathematical fame, if you have the cash to pay for it, is one of the soundest and steadiest of investments.
Nothing is less applicable to life than a mathematical argument. A proposition expressed in numbers is definitely false or true. In all other relations, the truth is so mingled with the false that often only instinct can help us to decide among virtuous influences, sometimes equally as strong in one direction as in the other.
The peculiarity of the evidence of mathematical truths is, that all the argument is on one side. There are no objections, and no answers to objections. But on every subject on which difference of opinion is possible, the truth depends on a balance to be struck between two sets of confliting reasons. Even in natural philosophy, there is always some other explanation possible of the same facts; some geocentric theory instead of heliocentric, some phlogiston instead of oxygen; and it has to be shown why that other theory cannot be the true on: and until this is shown, and until we know how it is shown, we do not understand the grounds of our opinion. But when we turn to subjects infinitely more complicated, to morals, religion, politics, social relations, and the business of life, three-fourths of the arguments for every disputed opinion consist in dispelling the appearances which favour some opinion different from it.