“The more abstract is form, the more clear and direct is its appeal. In any composition the material side may be more or less omitted in proportion as the forms used are more or less material, and for them substituted pure abstractions, or largely dematerialized objects. The more an artist uses these abstracted forms, the deeper and more confidently will he advance into the kingdom of the abstract. And after him will follow the gazer at his pictures, who also will have gradually acquired a greater familiarity with the language of that kingdom.
Must we then abandon utterly all material objects and paint solely in abstractions? The problem of harmonizing the appeal of the material and the non-material shows us the answer to this question. As every word spoken rouses an inner vibration, so likewise does every object represented. To deprive oneself of this possibility is to limit one's powers of expression. That is at any rate the case at present. But besides this answer to the question, there is another, and one which art can always employ to any question beginning with "must": There is no "must" in art, because art is free.”

— Wassily Kandinsky

VI. The language of Form and Colour
1910 - 1915, Concerning the Spiritual in Art, 1911

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Wassily Kandinsky 68

Russian painter 1866–1944

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“The more freely abstract the form becomes, the purer, and also the more primitive it sounds. Therefore, in a composition in which corporeal elements are more or less superfluous, they can be more or less omitted and replaced by purely abstract forms, or by corporeal forms that have been completely abstracted... Here we are confronted by the question: Must we not then renounce the object altogether, throw it to the winds and instead lay bare the purely abstract? This is a question that naturally arises, the answer to which is at once indicated by an analysis of the concordance of the two elements of form (the objective and the abstract). Just as every word spoken (tree, sky, man) awakens an inner vibration, so too does every pictorially represented object. To deprive oneself of the possibility of this calling up vibrations would be to narrow one's arsenal of expressive means. At least, that is how it is today. But apart from today's answer, the above question receives the eternal answer to every question in art that begins with 'must.”

Wassily Kandinsky (1866–1944) Russian painter

There is no 'must' in art, which is forever free.
Quote from: Kandinsky: Complete Writings on Art, eds. Kenneth C. Lindsay and Peter Vergo, 2 Vols. (transl. Peter Vergo); Boston: G.K. Hall & Co., (1982), p. 195; as cited in: Samet, Jennifer Sachs. Painterly Representation in New York, 1945-1975. Dissertation, The City University of New York, 2010. p. 25
1910 - 1915

“And from the point of view of art there are no concrete or abstract forms, but only forms which are more or less convincing lies. That those lies are necessary to our mental selves is beyond any doubt, as it is through them that we form our aesthetic point of view of life.”

Pablo Picasso (1881–1973) Spanish painter, sculptor, printmaker, ceramicist, and stage designer

Paris 1923
As quoted by Marius de Zayas, in 'The Arts', New York, May 1923
Quotes, 1920's, "Picasso Speaks," 1923

“What is conserved, in modern physics, is not any particular substance or material but only much more abstract entities such as energy, momentum, and electric charge. The permanent aspects of reality are not particular materials or structures but rather the possible forms of structures and the rules for their transformation.”

Frank Wilczek (1951) physicist

Source: Longing for the Harmonies: Themes and Variations from Modern Physics (1987), Ch.8 The Weak Interaction

“the Cubists in Paris made me see that there was also a possibility of suppressing the natural aspect of form. I continued my research by abstracting the form and purifying the colour more and more. While working, I arrived at suppressing the closed effect of abstract form, expressing myself exclusively by means of the straight line in rectangular opposition; thus by rectangular planes of colour with white, grey and black. At that time, I encountered artists with approximately the same spirit, First Van der Leck, who, though still figurative, painted in compact planes of pure colour. My more or less cubist technique - in consequence still more or less picturesque - underwent the influence of his exact technique. Shortly afterwards I had the pleasure of making the acquaintance of Van Doesburg. Full of vitality and zeal for the already international movement that was called 'abstract', and most sincerely appreciative of my work, he came to ask me to collaborate in a review he intended to publish, and which he [Theo van Doesburg] was to call 'De Stijl.”

Piet Mondrian (1872–1944) Peintre Néerlandais

I was happy with an opportunity to publish my ideas on art, which I was engaged in writing down: I saw the possibility of contacts with similar efforts.
Quote of Mondrian c 1931, in 'De Stijl' (last number), p. 48; as cited in De Stijl 1917-1931 - The Dutch Contribution to Modern Art, by H.L.C. Jaffé http://www.dbnl.org/tekst/jaff001stij01_01/jaff001stij01_01.pdf; J.M. Meulenhoff, Amsterdam 1956, pp. 44-45
published in the memorial number of 'De Stijl', after the death of Theo Van Doesburg in 1931
1930's

“Maps have been a successful form of representation for centuries by making the world understandable through systematic abstraction that retains the iconicity of space depicting space. Advances in methods and technologies are blurring the lines among maps and other forms of visual representation and pushing the bounds of “map” as a concept toward both more realistic and more abstract depiction. As a result, there are a variety of unanswered questions about the attributes and implications of “maps.””

Alan MacEachren (1952) American geographer

Source: Research challenges in geovisualization (2001), p. 6-7

“These universal means of expression were discovered in modern painting by a logical and gradual progress toward ever more abstract form and color. Once the solution was discovered, there followed the exact representation of relations alone, that is to say, of the essential and fundamental element in any plastic emotion of the beautiful.”

Piet Mondrian (1872–1944) Peintre Néerlandais

1910's, Natural Reality and Abstract Reality', 1919

“We speak of concrete and not 'abstract painting', because we have finished with the period of research and speculative experience. In their search for purity artists were obliged to abstract from 'natural forms' in which the plastic elements were hidden, in order to eliminate natural forms and to replace them with 'artistic forms'. To-day the idea of 'artistic form' is as obsolete as the idea of 'natural form'. We establish the period of pure painting by constructing 'spiritual form.”

Theo van Doesburg (1883–1931) Dutch architect, painter, draughtsman and writer

Creative spirit becomes concrete.
Quote on 'Concrete art', in: 'Comments on the basic of concrete painting', Paris, January 1930; 'Art Concret', April 1930, pp. 2–4
1926 – 1931

“We are mainly interested in the processes… not… in presenting mathematics in its most abstract form. …we will often begin with concrete forms and then exhibit the process of abstraction.”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)

“We speak of concrete and not abstract painting because nothing is more concrete, more real then a line, a colour, a surface. A woman, a tree, a cow; are these concrete elements in a painting? No. A woman, a tree and a cow are concrete only in nature; in painting they are abstract, illusionistic, vague and speculative. However, a plane is a plane, a line is a line and no more or no less than that. 'Concrete paintin.”

Theo van Doesburg (1883–1931) Dutch architect, painter, draughtsman and writer

Spirit has arrived at the age of maturity...
Quote in 'Comments on the basic of concrete painting', Paris, January 1930, in 'Art Concret', April 1930, pp. 2–4
1926 – 1931

“It is the same with art. Art will become the product of another duality in man: the product of a cultivated externality and of an inwardness deepened and more conscious. As a pure representation of the human mind, art will express itself in an aesthetically purified, that is to say, abstract form.”

Piet Mondrian (1872–1944) Peintre Néerlandais

1910's, Natural Reality and Abstract Reality', 1919

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Wassily Kandinsky 68

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