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Objects Quotes

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Objects Quotes

“The object of mathematics is the honor of the human spirit.”

Humans Spirit Objects Honor Mathematics Math Human Spirit

Author:Carl Gustav Jacob Jacobi

“I always believe in going hard at everything, whether it is Latin or mathematics, boxing or football, but at the same time I want to keep the sense of proportion. It is never worth while to absolutely exhaust one's self or to take big chances unless for an adequate object. I want you to keep in training the faculties which would make you, if the need arose, able to put your last ounce of pluck and strength into a contest. But I do not want you to squander these qualities.”

Source: A Bully Father: Theodore Roosevelt's Letters to His Children

“Let me also remind you that zero, like all of mathematics, is fictional and an idealization. It is impossible to reach absolute zero temperature or to get perfect vacuum. Luckily, mathematics is a fairyland where ideal and fictional objects are possible.”

Perfect Impossible Objects Ideals Let Me Absolutes Mathematics Zero Temperature Vacuums

Author:Doron Zeilberger

“At the other end of the spectrum is, for example, graph theory, where the basic object, a graph, can be immediately comprehended. One will not get anywhere in graph theory by sitting in an armchair and trying to understand graphs better. Neither is it particularly necessary to read much of the literature before tackling a problem: it is of course helpful to be aware of some of the most important techniques, but the interesting problems tend to be open precisely because the established techniques cannot easily be applied.”

Trying Important Ends Problem Courses Literature Interesting Example Objects Theory Sitting Mathematics Technique Helpful Spectrum Tackling Armchairs Graphs

Author:Timothy Gowers

“The science of the church is neglected for the study of geometry, and they lose sight of Heaven while they are employed in measuring the earth. Euclid is perpetually in their hands. Aristotle and Theophrastus are the objects of their admiration; and they express an uncommon reverence for the works of Galen. Their errors are derived from the abuse of the arts and sciences of the infidels, and they corrupt the simplicity of the gospel by the refinements of human reason.”

Source: Delphi Complete Works of Edward Gibbon (Illustrated)

“The goal of a definition is to introduce a mathematical object. The goal of a theorem is to state some of its properties, or interrelations between various objects. The goal of a proof is to make such a statement convincing by presenting a reasoning subdivided into small steps each of which is justified as an "elementary" convincing argument.”

States Goal Steps Objects Argument Mathematics Property Definitions Various Proof Statements Mathematical Reasoning Introducing Justified Convincing Presenting Theorems Small Steps

Author:IU?. I. Manin

“As we speak of poetical beauty, so ought we to speak of mathematical beauty and medical beauty. But we do not do so; and that reason is that we know well what is the object of mathematics, and that it consists in proofs, and what is the object of medicine, and that it consists in healing. But we do not know in what grace consists, which is the object of poetry.”

Knows Wells Reason Poetry Speak Healing Beauty Grace Objects Poet Ought Mathematics Medicine Proof Medical Mathematical Poetry Is Mathematical Beauty

Book:Thoughts, Letters & Minor Works

Source: Thoughts, Letters & Minor Works

“[Mathematics is] purely intellectual, a pure theory of forms, which has for its objects not the combination of quantities or their images, the numbers, but things of thought to which there could correspond effective objects or relations, even though such a correspondence is not necessary.”

Form Numbers Objects Theory Pure Intellectual Relation Mathematics Combination Quantity Correspondence

Author:Hermann Hankel

“In mathematics ... we find two tendencies present. On the one hand, the tendency towards abstraction seeks to crystallise the logical relations inherent in the maze of materials ... being studied, and to correlate the material in a systematic and orderly manner. On the other hand, the tendency towards intuitive understanding fosters a more immediate grasp of the objects one studies, a live rapport with them, so to speak, which stresses the concrete meaning of their relations.”

Two Hands Speak Understanding Study Objects Materials Stress Relation Mathematics Tendencies Logical Concrete Inherent Abstraction Intuitive Systematic Orderly Mazes Rapport

Author:David Hilbert

“. . . the membership relation for sets can often be replaced by the composition operation for functions. This leads to an alternative foundation for Mathematics upon categories -- specifically, on the category of all functions. Now much of Mathematics is dynamic, in that it deals with morphisms of an object into another object of the same kind. Such morphisms (like functions) form categories, and so the approach via categories fits well with the objective of organizing and understanding Mathematics. That, in truth, should be the goal of a proper philosophy of Mathematics.”

“We can hardly imagine a state of mind in which all material objects were regarded as symbols of spirtual truths or episodes in sacred history. Yet, unless we make this effort of imagination, Medieval art is largely incomprehensible.”

Mind Art States Imagination Effort Imagine Objects Materials Art Is Mathematics Sacred Symbols State Of Mind Episodes Medieval

Author:Kenneth Clark