“Pure mathematics is on the whole distinctly more useful than applied. […] For what is useful above all is technique, and mathematical technique is taught mainly through pure mathematics.”

— G. H. Hardy, book A Mathematician's Apology

A Mathematician's Apology (1941)

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G. H. Hardy20

British mathematician 1877–1947

George Frederick James Temple (1901–1992) British mathematician

100 Years of Mathematics: a Personal Viewpoint (1981)

“The use of practically any computing technique itself raises a number of mathematical problems. There is thus a very considerable impact of computation on mathematics itself, and this may be expected to influence mathematical research to an increasing degree.”

George Forsythe (1917–1972) Stanford University computer scientist

George Forsythe (1958) cited in: Computers and people Vol 23. (1974). p. 11 Pagina 11

“The manner in which mathematical theories are applied does not depend on preconceived ideas; it is a purposeful technique depending on, and changing with, experience.”

William Feller (1906–1970) Croatian-American mathematician

Introduction, The Nature of Probability Theory, p. 2 - 3.
An Introduction To Probability Theory And Its Applications (Third Edition)

“Pure mathematics is useless to ordinary people, but useful to those who wish to understand Absolute Truth, God or Infinity. Applied maths is useful in our daily life.”

Mwanandeke Kindembo (1996) Congolese author

“Pure mathematics is religion.”

Novalis book Blüthenstaub

Reine Mathematik ist Religion.
Blüthenstaub (1798), Unsequenced

“What has taught us to know the true profound analogies, those the eyes do not see but reason divines?
It is the mathematical spirit, which disdains matter to cling only to pure form.”

Henri Poincaré book The Value of Science

Source: The Value of Science (1905), Ch. 5: Analysis and Physics
Context: All laws are... deduced from experiment; but to enunciate them, a special language is needful... ordinary language is too poor...
This... is one reason why the physicist can not do without mathematics; it furnishes him the only language he can speak. And a well-made language is no indifferent thing;
... the analyst, who pursues a purely esthetic aim, helps create, just by that, a language more fit to satisfy the physicist.
... law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise...
In a word, to get the law from experiment, it is necessary to generalize... But how generalize?... in this choice what shall guide us?
It can only be analogy.... What has taught us to know the true profound analogies, those the eyes do not see but reason divines?
It is the mathematical spirit, which disdains matter to cling only to pure form.<!--pp.76-77