Algebra Quotes - page 2
It has been generally believed that only the complex numbers could legitimately be used as the ground field in discussing quantum-mechanical operators. Over the complex field, Frobenius' theorem is of course not valid; the only division algebra over the complex field is formed by the complex numbers themselves. However, Frobenius' theorem is relevant precisely because the appropriate ground field for much of quantum mechanics is real rather than complex.
Freeman Dyson
Now as to what pertains to these Surd numbers (which, as it were by way of reproach and calumny, having no merit of their own are also styled Irrational, Irregular, and Inexplicable) they are by many denied to be numbers properly speaking, and are wont to be banished from arithmetic to another Science, (which yet is no science) viz. algebra.
Isaac Barrow
...nor have I found occasion to depart from the plan... the rejection of the whole doctrine of series in the establishment of the fundamental parts both of the Differential and Integral Calculus. The method of Lagrange... had taken deep root in elementary works; it was the sacrifice of the clear and indubitable principle of limits to a phantom, the idea that an algebra without limits was purer than one in which that notion was introduced. But, independently of the idea of limits being absolutely necessary even to the proper conception of a convergent series, it must have been obvious enough to Lagrange himself, that all application of the science to concrete magnitude, even in his own system, required the theory of limits.
Augustus De Morgan
My specific... object has been to contain, within the prescribed limits, the whole of the student's course, from the confines of elementary algebra and trigonometry, to the entrance of the highest works on mathematical physics. A learner who has a good knowledge of the subjects just named, and who can master the present treatise, taking up elementary works on conic sections, application of algebra to geometry, and the theory of equations, as he wants them, will, I am perfectly sure, find himself able to conquer the difficulties of anything he may meet with; and need not close any book of Laplace, Lagrange, Legendre, Poisson, Fourier, Cauchy, Gauss, Abel, Hindenburgh and his followers. or of any one of our English mathematicians, under the idea that it is too hard for him.
Augustus De Morgan
I cannot see why it is necessary that every deduction from algebra should be bound to certain conventions incident to an earlier stage of mathematical learning, even supposing them to have been consistently used up to the point in question. I should not care if any one thought this treatise unalgebraical, but should only ask whether the premises were admissible and the conclusions logical.
Augustus De Morgan
By this sinister elision, this slipping from true remorse, the belief that the suffering we have precipitated ought to ennoble us, or at least make us less ignoble from then on, to disguised self-forgiveness, the belief that suffering in some way ennobles life, so that the precipitation of pain comes, by such a cockneyed algebra, to equal the ennoblement, or at any rate the enrichment, of life, by this characteristically twentieth-century retreat from content into form, from meaning into appearance, from ethics into aesthetics, from aqua into unda, I dulled the pain of that accusing death; and hardened myself, to say nothing of it at Bourani. I was still determined to tell Julie, but at the right time and place, when the exchange rate between confession and the sympathy it evoked looked very likely to be high.
John Fowles
I want to see the gardens and palace of the Alcazar where the Moorish Kings used to live. It is as perfect an architecture as the Egyptian, Greek or Gothic and just as beautiful, maybe more beautiful and it is well built for it looks as new as if it had just been done. We have to thanks these Moors for our greatest sciences, they did the big work for us, they started them, Algebra, Chemistry, Astronomy. They are our masters.
Thomas Eakins
[T]he symbols of algebra, when employed in abstruse and complex theoretical investigations, constitute a sort of thought-saving machine, by whose aid a person skilled in its use can solve problems respecting quantities, and dispense with the mental labour of thinking of the quantities denoted by the symbols, except at the beginning and the end of the operation.
William John Macquorn Rankine
I'm a visual thinker, really bad at algebra. There's others that are a pattern thinker. These are the music and math minds. They think in patterns instead of pictures. Then there's another type that's not a visual thinker at all, and they're the ones that memorize all of the sports statistics, all of the weather statistics.
Temple Grandin
It's true that my initial training was in mathematics. However, almost by accident, I happened to take a course from Kenneth Arrow on "Information Economics,” which was so inspiring that I decided to change direction. It seemed to me that economics combined the best of both worlds: the rigor of mathematics with the immediate relevance of a social science. As for how much math I would recommend, I'd say that basic analysis, including measure theory, is certainly very useful. Also, linear algebra and stochastic processes always helps. But beyond that, I don't think a huge mathematical investment is necessary to do economic theory unless you are planning to work in an extremely technical area.
Eric Maskin
The notions she fought with needed more than the simple algebra she'd been grudgingly taught at Lamai Hold. More and more she resented how they had robbed her of this, arguably her one talent, driving her from math and other abstractions by the simple expedient of making them seem boring.
David Brin
By the help of God and with His precious assistance, I say that Algebra is a scientific art. The objects with which it deals are absolute numbers and measurable quantities which, though themselves unknown, are related to "things" which are known, whereby the determination of the unknown quantities is possible.
Omar Khayyám
When I began the following Work, my only object was to extend and explain more fully the Memoir which I read at the public meeting of the Academy of Sciences in the month of April 1787, on the necessity of reforming and completing the Nomenclature of Chemistry. While engaged in this employment, I perceived, better than I had ever done before, the justice of the following maxims of the Abbé de Condillac, in his System of Logic, and some other of his works. "We think only through the medium of words.-Languages are true analytical methods.-Algebra, which is adapted to its purpose in every species of expression, in the most simple, most exact, and best manner possible, is at the same time a language and an analytical method.-The art of reasoning is nothing more than a language well arranged."
Antoine Lavoisier
