“Mathematics rightly viewed possesses not only truth but supreme beauty.”

— Bertrand Russell

1900s, "The Study of Mathematics" (November 1907)
Context: Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.

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Bertrand Russell 562

logician, one of the first analytic philosophers and politi… 1872–1970

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“Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of highest excellence, is to be found in mathematics as surely as in poetry. What is best in mathematics deserves not merely to be learnt as a task, but to be assimilated as a part of daily thought, and brought again and again before the mind with ever-renewed encouragement.”

Bertrand Russell (1872–1970) logician, one of the first analytic philosophers and political activist

1900s, "The Study of Mathematics" (November 1907)

“The beauty of mathematics only shows itself to more patient followers.”

Maryam Mirzakhani (1977–2017) Iranian mathematician

Source: http://www.theguardian.com/science/2014/aug/13/interview-maryam-mirzakhani-fields-medal-winner-mathematician

“You can only possess beauty through understanding it.”

John Ruskin (1819–1900) English writer and art critic

“To emphasize only the beautiful seems to me to be like a mathematical system that only concerns itself with positive numbers.”

Paul Klee (1879–1940) German Swiss painter

Diary entry (March 1906), # 759, in The Diaries of Paul Klee, 1898-1918; University of California Press, 1968
1903 - 1910

“The truth is that the mathematical sciences are growing in complete security and harmony. The ideas of Dedekind, Poincare, and Hilbert have been systematically developed with great success, without any conflict in the results. It is only from the philosophical point of view that objections have been raised. They bear on certain ways of reasoning peculiar to analysis and set theory. These modes of reasoning were first systematically applied in giving a rigorous form to the methods of the calculus. [According to them, ] the objects of a theory are viewed as elements of a totality such that one can reason as follows: For each property expressible using the notions of the theory, it is [an] objectively determinate [fact] whether there is or there is not an element of the totality which possesses this property. Similarly, it follows from this point of view that either all the elements of a set possess a given property, or there is at least one element which does not possess it”

Paul Bernays (1888–1977) Swiss mathematician

Paul Bernays, Platonism in mathematics http://sites.google.com/site/ancientaroma2/book_platonism.pdf (1935)

“You cannot possess the truth, you can only search for it.”

Albert Jacquard (1925–2013) French biologist

La vérité ne se possède pas, elle se cherche.
[Albert Jacquard, Petite philosophie à l'usage des non-philosophes, Quebec Livres, 1997, 2920596179].

“It was not so much that I was doing mathematics, but rather that mathematics had taken possession of me.”

Stanislaw Ulam (1909–1984) Polish-American mathematician

Source: Adventures of a Mathematician - Third Edition (1991), Chapter 3, Travels Abroad, p. 52

“Only he who possesses a personal religion, an original view of infinity, can be an artist.”

Karl Wilhelm Friedrich Schlegel (1772–1829) German poet, critic and scholar

Nur derjenige kann ein Künstler seyn, welcher eine eigne Religion, eine originelle Ansicht des Unendlichen hat.
“Selected Ideas (1799-1800)”, Dialogue on Poetry and Literary Aphorisms, Ernst Behler and Roman Struc, trans. (Pennsylvania University Press:1968) #13

“Science and mathematics… have added little to our understanding of such things as Truth, Beauty, and Justice. There may be definite limits to the applicability of the scientific method.”

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

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

“Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.”

David Deutsch book The Fabric of Reality

The Fabric of Reality (1997)

“Mathematics rightly viewed possesses not only truth but supreme beauty.”

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