Algebra Quotes - page 3
In general the position as regards all such new calculi is this - That one cannot accomplish by them anything that could not be accomplished without them. However, the advantage is, that, provided such a calculus corresponds to the inmost nature of frequent needs, anyone who masters it thoroughly is able - without the unconscious inspiration of genius which no one can command - to solve the respective problems, yea to solve them mechanically in complicated cases in which, without such aid, even genius becomes powerless. Such is the case with the invention of general algebra, with the differential calculus, and in a more limited region with Lagrange's calculus of variations, with my calculus of congruences, and with Mobius's calculus. Such conceptions unite, as it were, into an organic whole countless problems which otherwise would remain isolated and require for their separate solution more or less application of inventive genius.
Carl Friedrich Gauss
It is less than four years since cohomological methods (i. e. methods of Homological Algebra) were introduced into Algebraic Geometry in Serre's fundamental paper[11], and it seems certain that they are to overflow the part of mathematics in the coming years, from the foundations up to the most advanced parts. ... [11] Serre, J. P. Faisceaux algébriques cohérents. Ann. Math. (2), 6, 197–278.
Alexander Grothendieck
We live through myriads of seconds, but there is only one second among all these myriads which brings our whole inner world to the boil; the second in which, as Stendhal described, there suddenly takes place a crystallization in the supersaturated blood; a magical second like that of procreation, and, like it, hidden in the warm interior of one's own body, invisible, intangible, impalpable, a unique experience of mystery. No algebra of the soul can calculate it; no alchemy can divine it. Usually, even for ourselves, it remains unsearchable.
Stefan Zweig
Computer Algebra Systems are NOT the Devil but the new MESSIAH that will take us out of the current utterly trivial phase of human-made mathematics into the much deeper semi-trivial computer-generated phase of future mathematics. Even more important, Computer Algebra Systems will turn out to be much more than just a `tool', since the methodology of computer-assisted and computer-generated research will rule in the future, and will make past mathematics seem like alchemy and astrology, or, at best, theology.
Doron Zeilberger
If there were only some mechanism (like Seurat's proposed system of painting, or the projected Universal Algebra that Gödel believes Leibnitz to have perfected and mislaid) for reasonably and systematically converting into poetry what we see and feel and are! When one reads the verse of people who cannot write poems - people who sometimes have more intelligence, sensibility, and moral discrimination than most of the poets - it is hard not to regard the Muse as a sort of fairy godmother who says to the poet, after her colleagues have showered on him the most disconcerting and ambiguous gifts, "Well, never mind. You're still the only one that can write poetry."
Randall Jarrell
1. The human mind is so constructed that it must see every perception in a time-relation-in an order-and every perception of an object in a space-relation-as outside or beside our perceiving selves.
2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra.
3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry.
Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.
Nicholas Murray Butler
Why not spend that time on art: painting, sculpting, charcoal, pastel, oils? Are words or numbers more important than images? Who decides this? Does algebra move you to tears? Can plural possessives express the feelings in your heart? If you don't learn art now, you will never learn to breathe!
Laurie Halse Anderson
Instead of five hundred thousand average algebra teachers, we need one good algebra teacher. We need that teacher to create software, videotape themselves, answer questions, let your computer or the iPad teach algebra... The hallmark of any good technology is that it destroys jobs.
Michael J. Saylor
What makes the Nightmares on Elm Street universal and forever in their attraction, I think, is simply the dream. The landscape of the mind, the subconscious, the nightmare. Everybody has a nightmare, and everybody apparently has falling dreams, and everybody has the drowning dream, and everybody has certain kinds of sexual manifestation dreams, as well as our stress dreams; I didn't study for the algebra test, I didn't study for my driving test, you know, all those dreams. I still have those dreams, and it's just such an interesting thing that our mind can turn against us, our own mind, you know we all have.
Robert Englund
The unnaturalness of mathematical symbolism is attested to by history. The algebra of the Egyptians, the Babylonians, the Greeks, the Hindus, and the Arabs was what is commonly called rhetorical algebra. ...on the whole they used ordinary rhetoric to describe their mathematical work. Symbolism is a relatively modern invention of the sixteenth and seventeenth centuries...
Morris Kline
By 1700 all of the familiar members of the [number] system... were known. However, opposition to the newer types of numbers was expressed throughout the century. Typical are the objections of... Baron Francis Masères... in 1759 his Dissertation on the Use of the Negative Sign in Algebra... shows how to avoid negative numbers... and especially negative roots, by carefully segregating the types of quadratic equations so that those with negative roots are considered separately; and... the negative roots are to be rejected.
Morris Kline
The famous sixteenth-century algebraist Jerome Cardan called negative roots fictitious, and the founder of modern symbolic algebra, François Viète, discarded negative roots entirely. Descartes, called them false on the ground that they represented numbers less than nothing and so were meaningless.
Morris Kline
