Arithmetic Quotes - page 3
Of such are the mathematical sciences alone; that is, geometry and arithmetic, in which the Divine intellect indeed knows infinitely more propositions, since it knows all. But with regard to those few which the human intellect does understand, I believe its knowledge equals the Divine in objective certainty, for here it succeeds in understanding necessity, beyond which there can be no greater sureness.
Galileo Galilei
Humans aren't as good as we should be in our capacity to empathize with feelings and thoughts of others, be they humans or other animals on Earth. So maybe part of our formal education should be training in empathy. Imagine how different the world would be if, in fact, that were 'reading, writing, arithmetic, empathy.'
Neil deGrasse Tyson
An important point is that the p-adic field, or respectively the real or complex field, corresponding to a prime ideal, plays exactly the role, in arithmetic, that the field of power series in the neighborhood of a point plays in the theory of functions: that is why one calls it a local field.
André Weil
He left in his Optics, the earliest surviving table of angles of refraction from air to water. ...This table, quoted and requoted until modern times, has been admired... A closer glance at it, however, suggests that there was less experimentation involved in it than originally was thought, for the values of the angles of refraction form an arithmetic progression of second order... As in other portions of Greek Science, confidence in mathematics was here greater than that in the evidence of the senses, although the value corresponding to 60° agrees remarkably well with experience.
Ptolemy
Arithmetic and geometry, according to Plato, are the two wings of the mathematician. The object indeed of all mathematical questions, is to determine the ratios of numbers, or of magnitudes ; and it may even be said, to continue the comparison of the ancient philosopher, that arithmetic is the mathematician's right wing; for it is an incontestable truth, that geometrical determinations would, for the most part, present nothing satisfactory to the mind, if the ratios thus determined could not be reduced to numerical ratios. This justifies the common practice, which we shall here follow, of beginning with arithmetic.
Jacques Ozanam
![This art is music. It stands quite apart from all the others. In it we do not recognize the copy, the repetition, of any Idea of the inner nature of the world. Yet it is such a great and exceedingly fine art, its effect on man's innermost nature is so powerful, and it is so completely and profoundly understood by him in his innermost being as an entirely universal language, whose distinctness surpasses even that of the world of perception itself, that in it we certainly have to look for more than that exercitium arithmeticae occultum nescientis se numerare animi [exercise in arithmetic in which the mind does not know it is counting] which Leibniz took it to be. (Arthur Schopenhauer)](https://cdn.quotesdtb.com/img/quotes_images_webp/91/arthur-schopenhauer-apart-arithmetic-476191.webp)
Others ... are in the habit of teaching that religion and philosophy are really the same thing. Such a statement, however, appears to be true only in the sense in which Francis I is supposed to have said in a very conciliatory tone with reference to Charles V: ‘what my brother Charles wants is also what I want', namely Milan. Others again do not stand on such ceremony, but talk bluntly of a Christian philosophy, which is much the same as if we were to speak of a Christian arithmetic, and this would be stretching a point. Moreover, epithets taken from such dogmas are obviously unbecoming of philosophy, for it is devoted to the attempt of the faculty of reason to solve by its own means and independently of all authority the problem of existence.
Arthur Schopenhauer
[M]athematics is not a popular subject... The reason for this is to be found in the common superstition that [it] is but a continuation... of the fine art of arithmetic, of juggling with numbers. [We] combat that superstition, by offering, instead of formulas, figures that may be looked at and that may easily be supplemented by models which the reader may construct. This book... bring[s] about a greater enjoyment of mathematics, by making it easier... to penetrate the essence of mathematics without... a laborious course of studies.
David Hilbert
I would teach the world how the Greeks proved, more than 2,000 years ago, that there are infinitely many prime numbers. In my mind, this discovery is the beginning of mathematics – when humankind realised that, by pure thought alone, it could prove eternal truths of the universe.
Prime numbers are the indivisible numbers, numbers that can be divided only by themselves and one. They are the most important numbers in mathematics, because every number is built by multiplying prime numbers together – for example, 60 = 2 x 2 x 3 x 5. They are like the atoms of arithmetic, the hydrogen and oxygen of the world of numbers.
Marcus du Sautoy
This ideography is a "formula language", that is, a lingua characterica, a language written with special symbols, "for pure thought", that is, free from rhetorical embellishments, "modeled upon that of arithmetic", that is, constructed from specific symbols that are manipulated according to definite rules.
Gottlob Frege
I hope I may claim in the present work to have made it probable that the laws of arithmetic are analytic judgments and consequently a priori. Arithmetic thus becomes simply a development of logic, and every proposition of arithmetic a law of logic, albeit a derivative one. To apply arithmetic in the physical sciences is to bring logic to bear on observed facts; calculation becomes deduction.
Gottlob Frege
In the early days of the computer revolution computer designers and numerical analysts worked closely together and indeed were often the same people. Now there is a regrettable tendency for numerical analysts to opt out of any responsibility for the design of the arithmetic facilities and a failure to influence the more basic features of software. It is often said that the use of computers for scientific work represents a small part of the market and numerical analysts have resigned themselves to accepting facilities "designed" for other purposes and making the best of them. [...] One of the main virtues of an electronic computer from the point of view of the numerical analyst is its ability to "do arithmetic fast."
James H. Wilkinson
Whether in number theory, or space-time cosmology, Gödel's method was to advance the formalization of the system under consideration and then test it to destruction upon the ‘strange loops' it generated (paradoxes of self-reference and time-travel). In each case, the system was shown to permit cases that it could not consistently absorb, opening it to an interminable process of revision, or technical improvement. It thus defined dynamic intelligence, or the logic of evolutionary imperfection, with an adequacy that was both sufficient and necessarily inconclusive. What it did not do was trash the very possibility of arithmetic, mathematical logic, or cosmic history - except insofar as these were falsely identified with idols of finality or closure.
Nick Land
Modern mind has become more and more calculating. The calculative exactness of practical life which the money economy has brought about corresponds to the ideal of natural science: to transform the world into an arithmetic problem, to fix every part of the world by mathematical formulas. Only money economy has filled the days of so many people with weighing, calculating, with numerical determinations, with a reduction of qualitative values to quantitative ones.
Georg Simmel
An ancient writer said that arithmetic and geometry are the wings of mathematics; I believe one can say without speaking metaphorically that these two sciences are the foundation and essence of all the sciences which deal with quantity. Not only are they the foundation, they are also, as it were, the capstones; for, whenever a result has been arrived at, in order to use that result, it is necessary to translate it into numbers or into lines; to translate it into numbers requires the aid of arithmetic, to translate it into lines necessitates the use of geometry.
Joseph Louis Lagrange
I'm afraid I'm not very good at Latin, said the superintendent. On the other hand I sometimes think about arithmetic; and in particular about one number – the number One. But I will admit that it is also the most incomprehensible number in the world. Beyond this particular dimension I know only one thing which is supernatural, even though it may well be the reality that affects mortal men most deeply; and that is Time. And when one comes to think about this strange place I was telling you about, the world that is only One, and its connection with the only supernatural thing we know, Time, then everything ceases to be higher or lower than anything else, larger or smaller.
Halldór Laxness
Vladimir Voevodsky and his collaborators have provided us with a very interesting candidate-category of motives: a category (of sheaves relative to an extraordinarily fine Grothendieck-style topology on the category of schemes) which in some intuitive sense "softens algebraic geometry” so as to allow for a good notion of homotopy in an algebro-geometric setup and is sufficiently directly connected to concrete algebraic geometry to have already yielded some extraordinary applications. The quest for a full theory of motives is a potent driving force in complex analysis, algebraic geometry, automorphic representation theory, the study of L functions, and arithmetic. It will continue to be so throughout the current century.
Barry Mazur
