“Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.”

— Henri Poincaré, book Science and Hypothesis

Les mathématiciens n'étudient pas des objets, mais des relations entre les objets ; il leur est donc indifférent de remplacer ces objets par d'autres, pourvu que les relations ne changent pas. La matière ne leur importe pas, la forme seule les intéresse.
Source: Science and Hypothesis (1901), Ch. II: Dover abridged edition (1952), p. 20

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these…" by Henri Poincaré?

Henri Poincaré49

French mathematician, physicist, engineer, and philosopher … 1854–1912

Related quotes

“Sex itself only exists in relation to procreation. That's one of the reasons why I sometimes object — and it's just a theoretical objection, but it's worth thinking about — to the whole notion that one calls what people of the same sex do "sexual relations." As a matter of fact, they have precisely turned their back on sexual relations, in order to engage in acts of mutual pleasure that have nothing whatsoever to do with sexuality.”

Alan Keyes (1950) American politician

National Federation of Republican Assemblies, NYC, August 31, 2004. http://renewamerica.us/archives/speeches/04_08_31nfra.htm. <br class="br">2009

“Now what is science? …it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations. …it is in relations alone that objectivity must be sought. …it is relations alone which can be regarded as objective.
External objects… are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation.”

Henri Poincaré book The Value of Science

Source: The Value of Science (1905), Ch. 11: Science and Reality

“Unmediated concepts … veil the relations between objects. … They are, therefore, objects of knowledge, but the object which is known through them is not the capitalist system of production itself, but the ideology of its ruling class.”

György Lukács book History and Class Consciousness

Source: History and Class Consciousness (1968), pp. 13-14

“I am interested in sculpture that manipulates the viewer into a specific relation with both space and time. Time, on two levels; one narratively and cinematically as a matter of the passage through the work, and the other as a literal elongation of the moment. This has to do with form and colour and the propensity of colour to induce reverie. Consequently, I hope, an elongation of time. Space is as complex, the space contained in an objectmust be bigger than the object which contains it. My aim is to separate the object from its object-hood.”

Anish Kapoor (1954) British contemporary artist of Indian birth

Anish Kapoor in conversation with Heidi Reitmaier, July 2007 in "Anish Kapoor" by Royal Academy Organization.

“Although people seem to be unaware of it today, the development of the faculty of attention forms the real object and almost the sole interest of studies.”

Simone Weil (1909–1943) French philosopher, Christian mystic, and social activist

Waiting on God (1950), Reflections on the Right Use of School Studies with a View to the Love of God

“Mind and matter brought down to the essential, to the consciousness and its object, form a natural whole, and the difficulty does not consist in uniting but in separating them.”

Alfred Binet (1857–1911) French psychologist and inventor of the first usable intelligence test

Source: The Mind and the Brain, 1907, p. 184

“The most important motivation for the research work that resulted in the relational model was the objective of providing a sharp and clear boundary between the logical and physical aspects of database management.”

E. F. Codd (1923–2003) computer scientist

Relational Database: A Practical Foundation for Productivity (1982)

“The cultural obsession with the art object is slowly disappearing and being replaced by what might be called "systems consciousness." Actually, this shifts from the direct shaping of matter to a concern for organizing quantities of energy and information. Seen another way, it is a refocusing of aesthetic awareness – based on future scientific-technological evolution – on matter-energy information exchanges and away from the invention of solid artefacts. These new systems prompt us not to look at the skin of objects, but at those meaningful relations within and between their visible boundaries.”

Jack Burnham (1931) American art historian

Source: Beyond Modern Sculpture, 1968, p. 369-70

“Between two absolutely different spheres, as between subject and object, there is no causality, no correctness, and no expression; there is, at most, an aesthetic relation”

Friedrich Nietzsche (1844–1900) German philosopher, poet, composer, cultural critic, and classical philologist

On Truth and Lie in an Extra-Moral Sense (1873)
Context: Between two absolutely different spheres, as between subject and object, there is no causality, no correctness, and no expression; there is, at most, an aesthetic relation: I mean, a suggestive transference, a stammering translation into a completely foreign tongue — for which I there is required, in any case, a freely inventive intermediate sphere and mediating force. "Appearance" is a word that contains many temptations, which is why I avoid it as much as possible. For it is not true that the essence of things "appears" in the empirical world. A painter without hands who wished to express in song the picture before his mind would, by means of this substitution of spheres, still reveal more about the essence of things than does the empirical world. Even the relationship of a nerve stimulus to the generated image is not a necessary one. But when the same image has been generated millions of times and has been handed down for many generations and finally appears on the same occasion every time for all mankind, then it acquires at last the same meaning for men it would have if it were the sole necessary image and if the relationship of the original nerve stimulus to the generated image were a strictly causal one. In the same manner, an eternally repeated dream would certainly be felt and judged to be reality. But the hardening and congealing of a metaphor guarantees absolutely nothing concerning its necessity and exclusive justification.

“Love is an affection which carries the attention of the mind beyond itself, and is the sense of a relation to some fellow creature as to its object.”

Adam Ferguson book An Essay on the History of Civil Society

PART I, SECTION II.
An Essay on the History of Civil Society (1767)

“Mathematicians do not study objects, but the relations between objects; to them it is a matter of indifference if these objects are replaced by others, provided that the relations do not change. Matter does not engage their attention, they are interested in form alone.”

Help us to complete the source, original and additional information

Henri Poincaré49

Related quotes

Related topics