Mathematics Quotes - page 35
It is significant that we owe the first explicit formulation of the principle of recurrence to the genius of Blaise Pascal... Pascal stated the principle in a tract called The Arithmetic Triangle which appeared in 1654. Yet... the gist of the tract was contained in the correspondence between Pascal and Fermat regarding a problem in gambling, the same correspondence which is now regarded as the nucleus from which developed the theory of probabilities.
It surely is a fitting subject for mystic contemplation that the principle of reasoning by recurrence, which is so basic in pure mathematics, and the theory of probabilities, which is the basis of all deductive sciences, were both conceived while devising a scheme for the division of stakes in an unfinished match of two gamblers.
Blaise Pascal
Among all the studies of natural causes and reasons, light most delights the contemplators; among the great things of mathematics, the certainty of its demonstrations most illustriously elevates the minds of its investigators; perspective must therefore be preferred to all human discourses and disciplines, in the study in which radiant lines are expounded by means of demonstrations and in which the glory is found not only of mathematics, but also physics: it is adorned with the flowers of one and the other.
John Peckham
I have not been able to lay my hands on any notes as to Mathematico-economics that would be of any use to you. I have very indistinct memories of what I used to think on the subject. I never read mathematics now: in fact I have even forgotten how to integrate a good many things.
But I know I had a growing feeling in the later years of my work at the subject that a good mathematical theorem dealing with economic hypotheses was very well unlikely to be good economics: and I went more and more on the rules-(1) Use mathematics as a shorthand language, rather than as an engine of inquiry. (2) Keep to them till you have done. (3) Translate into English. (4) Then illustrate by examples that are important in real life. (5) Burn the mathematics. (6) If you can't succeed in (4), burn (3). This last I do often.
Alfred Marshall
Fifty years ago Kurt Gödel... proved that the world of pure mathematics is inexhaustible. ... I hope that the notion of a final statement of the laws of physics will prove as illusory as the notion of a formal decision process for all mathematics. If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed, I would feel that the Creator had been uncharacteristically lacking in imagination.
Freeman Dyson
Napier also invented a calculating device known as Napier's bones in 1617 and made common use of decimal multiplications and divisions. The device itself does not use logarithms, but rather is a convenient tool to reduce multiplication and division to a sequence of simple addition and subtraction operations. The method employed by Napier's bones was based on Arab mathematics and Fibonacci's Liber Abaci.
John Napier
Several years ago (Reader, Lover of the Mathematics) my Father, of memory always to be revered, made public the use of the Wonderful Canon of Logarithms; but, as he himself mentioned on the seventh and on the last pages of the Logarithms, he was decidedly against committing to types the theory and method of its creation, until he had ascertained the opinion and criticism on the Canon of those who are versed in this kind of learning. But, since his departure from this life, it has been made plain to me by unmistakable proofs, that the most skilled in the mathematical sciences consider this new invention of very great importance, and that nothing more agreeable to them could happen, than if the construction of this Wonderful Canon, or at least so much as might suffice to explain it, go forth into the light for the public benefit.
John Napier
For the things of this world cannot be made known without a knowledge of mathematics. For this is an assured fact in regard to celestial things, since two important sciences of mathematics treat of them, namely theoretical astrology and practical astrology. The first ... gives us definite information as to the number of the heavens and of the stars, whose size can be comprehended by means of instruments, and the shapes of all and their magnitudes and distances from the earth, and the thicknesses and number, and greatness and smallness, ... It likewise treats of the size and shape of the habitable earth ... All this information is secured by means of instruments suitable for these purposes, and by tables and by canons .. For everything works through innate forces shown by lines, angles and figures.
Roger Bacon
The total subject of mathematics is clearly too broad for any one of us. I do not think that any mathematician since Gauss has covered it fully and uniformly, even Hilbert did not, and all of us are of considerably lesser width (quite apart from the question of depth) than Hilbert. It would therefore, be quite unrealistic not to admit, that any address I could possibly give would not be biased towards some areas in mathematics in which I have had some experience, to the detriment of others which may be equally or more important. To be specific, I could not avoid a bias towards those parts of analysis, logics, and certain border areas of the applications of mathematics to other sciences in which I have worked. If your Committee feels that an address which is affected by such imperfections still fits into the program of the Congress, and if the very generous confidence in my ability to deliver continues, I shall be glad to undertake it.
John von Neumann
Cardano was a man of universal interests, and much of his ability must have been inherited from his father, Fazio Cardano... a lawyer... but also deeply steeped in the medical sciences, mathematics, and all kinds of occult lore... he had... a high reputation as a scholar in his native town; even Leonardo da Vinci notes several times that he consulted Messer Fazio on geometric questions... he was appointed as a public lecturer in geometry.
Gerolamo Cardano
...the whole point of studying and teaching mathematics was that it demonstrated how universal truth imposed itself upon the world-rationally, hierarchically, and inescapably. Ideally, the Jesuits believed, the truths of religion would be imposed on the world just like geometrical theorems, leaving no room for avoidance or denial by Protestant or other heretics and leading to the inevitable triumph of the Church.
Amir R. Alexander
The ruling feature of his character was undoubtedly Order. ...He seems not to have destroyed a document of any kind whatever: counterfoils of old cheque-books, notes for tradesmen, circulars, bills, and correspondence of all sorts were carefully preserved in the most complete order... To a high appreciation of order he attributed in a great degree his command of mathematics, and sometimes spoke of mathematics as nothing more than a system of order carried to a considerable extent. In everything he was methodical and orderly, and he had the greatest dread of disorder creeping into the routine work of the Observatory, even in the smallest matters.
George Biddell Airy
He never shirked arithmetical work: the longest and most laborious reductions had no terrors for him, and he was remarkably skilful with the various mathematical expedients for shortening and facilitating arithmetical work of a complex character. This power of handling arithmetic was of great value to him in the Observatory... He regarded it as a duty to finish off his work, whatever it was, and the writer well remembers his comment on the mathematics of one of his old friends, to the effect that "he was too fond of leaving a result in the form of three complex equations with three unknown quantities."
George Biddell Airy
Wallis did not become interested in mathematics till the age of thirty-one, but devoted himself to the subject for the rest of his life. One of the earliest and most important books on algebra ever written in English was his treatise published in 1685. It contains a brief historical sketch of the subject which is unfortunately not entirely accurate, but his treatment of the theory and practice of arithmetic and algebra has made the book a standard work for reference ever since.
John Wallis
There was then no professorship in mathematics and no opening for a mathematician to a career at Cambridge; and so Wallis reluctantly left the university. In 1649 he was appointed to the Savilian chair of geometry at Oxford, where he lived until his death on Oct. 28, 1703. It was there that all his mathematical works were published. Besides those he wrote on theology, logic, and philosophy; and was the first to devise a system for teaching deaf mutes.
John Wallis
In closing, I can only apologize for not having given any positive account of either mathematical truth or mathematical necessity. I can only say that I have not given such an account because I think that the search for such an account is a fundamental mistake. It is not that there is nothing special about mathematics; it is that, in my opinion, the investigation of mathematics must presuppose and not seek to account for the truth of mathematics. But this is the beginning of another paper and not the end of this one.
Hilary Putnam
If a scientist saw a cataclysm coming, say a meteor on collision course for earth in 2050, we wouldn't be saying, "Hallelujah, physics is true, bring it on! Our faith in mathematics is strengthened!” We'd be trying to stop it. Which makes the Christian reaction puzzling. If I actually believed Jesus was coming to end the world, I'd be preparing by stocking up on timber and nails. They were pretty effective last time.
PZ Myers
Now they had to study just as stringently and methodically as the engineers and technicians of the past, if not more so. They had a steep path to climb, had to purify and strengthen their minds by dint of mathematics and scholastic exercises in Aristotelian philosophy. Moreover, they had to learn to renounce all those benefits which previous generations of scholars had considered worth striving for: rapid and easy money-making, celebrity and public honors, the homage of the newspapers, marriages with daughters of bankers and industrialists, a pampered and luxurious style of life.
Hermann Hesse
We wish to see... the typical attitude of the scientist who uses mathematics to understand the world around us. ...In the solution of a problem ...there are typically three phases. The first phase is entirely or almost entirely a matter of physics; the third, a matter of mathematics; and the intermediate phase, a transition from physics to mathematics. The first phase is the formulation of the physical hypothesis or conjecture; the second, its translation into equations; the third, the solution of the equations. Each phase calls for a different kind of work and demands a different attitude.
George Pólya
It's not... something where you say... you've got the fundamental theory of everything, then... [you can] tell me whether... lions are going to eat tigers or something. ...No, you have to run this thing for ...10 steps ...to know ...You say ...run this rule enough times and you will get the whole universe. ...That's what it means to ...have a fundamental theory of physics ...You've got this rule, it's potentially simple... You've kind of reduced the problem of physics to a problem of mathematics... as if you generate the digits of pi.
Stephen Wolfram
I was a solitary, shy, priggish youth. I had no experience of the social pleasures of boyhood and did not miss them. But I liked mathematics, and mathematics was suspect because it has no ethical content. I came also to disagree with the theological opinions of my family, and as I grew up I became increasingly interested in philosophy, of which they profoundly disapproved. Every time the subject came up they repeated with unfailing regularity, 'What is mind? No matter. What is matter? Never mind.' After some fifty or sixty repetitions, this remark ceased to amuse me.
Bertrand Russell
The Laundry is the British Government's secret agency for dealing with "magic.” The use of scare-quotes is deliberate; as Sir Arthur C. Clarke said, "Any sufficiently advanced technology is indistinguishable from magic,” so "magic” is what we deal with. Note that this does not involve potions, pentacles, prayers, eldritch chanting, dressing up in robes and pointy hats, or most (but not all) of the stuff associated with the term in the public mind. No, our magic is computational. The realm of pure mathematics is very real indeed, and the...things...that cast shadows on the walls of Plato's cave can sometimes be made to listen and pay attention if you point a loaded theorem at them. This is, however, a very dangerous process, because most of the shadow-casters are unclear on the distinction between pay attention and free buffet lunch here. My job-applied computational demonologist-comes with a very generous pension scheme, because most of us don't survive to claim it.
Charles Stross
