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Home > Dictionary of Science Quotations > Scientist Names Index C > Richard Courant Quotes

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Richard Courant
(8 Jan 1888 - 27 Jan 1972)

German-American mathematician.


Science Quotes by Richard Courant (6 quotes)

For scholars and laymen alike it is not philosophy but active experience in mathematics itself that can alone answer the question: What is mathematics?
— Richard Courant
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), xiii.
Science quotes on:  |  Activity (101)  |  Answer (210)  |  Experience (288)  |  Itself (7)  |  Layman (13)  |  Mathematics (597)  |  Philosophy (217)  |  Question (327)  |  Scholar (31)

It becomes the urgent duty of mathematicians, therefore, to meditate about the essence of mathematics, its motivations and goals and the ideas that must bind divergent interests together.
— Richard Courant
In 'Mathematics in the Modern World', Scientific American (Sep 1964) 211, No. 3, 42. Collected in Ronald J. Comer and Morris Kline, Mathematics in the Modern World: Readings from Scientific American (1988), 20.
Science quotes on:  |  Binding (8)  |  Divergence (4)  |  Duty (57)  |  Essence (43)  |  Idea (457)  |  Interest (182)  |  Mathematician (178)  |  Mathematics (597)  |  Mediation (3)  |  Motivation (24)  |  Together (60)  |  Urgency (8)

Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.
— Richard Courant
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), x.
Science quotes on:  |  Activity (101)  |  Aesthetics (4)  |  Analysis (124)  |  Antithesis (5)  |  Aspect (43)  |  Basic (56)  |  Constitution (27)  |  Construction (70)  |  Contemplation (37)  |  Desire (114)  |  Difference (214)  |  Element (137)  |  Emphasis (15)  |  Expression (85)  |  Force (208)  |  Generality (23)  |  Human Mind (53)  |  Individuality (12)  |  Interplay (5)  |  Intuition (41)  |  Logic (190)  |  Mathematics (597)  |  Perfection (75)  |  Reason (343)  |  Reflection (52)  |  Struggle (66)  |  Supreme (26)  |  Synthesis (40)  |  Tradition (43)  |  Usefulness (71)  |  Value (188)  |  Will (29)

Since the seventeenth century, physical intuition has served as a vital source for mathematical porblems and methods. Recent trends and fashions have, however, weakened the connection between mathematics and physics; mathematicians, turning away from their roots of mathematics in intuition, have concentrated on refinement and emphasized the postulated side of mathematics, and at other times have overlooked the unity of their science with physics and other fields. In many cases, physicists have ceased to appreciate the attitudes of mathematicians. This rift is unquestionably a serious threat to science as a whole; the broad stream of scientific development may split into smaller and smaller rivulets and dry out. It seems therefore important to direct our efforts towards reuniting divergent trends by classifying the common features and interconnections of many distinct and diverse scientific facts.
— Richard Courant
As co-author with David Hilbert, in Methods of Mathematical Physics (1937, 1989), Preface, v.
Science quotes on:  |  17th Century (10)  |  Appreciation (20)  |  Attitude (51)  |  Ceasing (2)  |  Classification (79)  |  Common (96)  |  Concentration (14)  |  Connection (87)  |  Directing (5)  |  Distinct (31)  |  Divergence (4)  |  Diverse (8)  |  Effort (106)  |  Emphasis (15)  |  Fact (628)  |  Fashion (26)  |  Feature (36)  |  Importance (186)  |  Interconnection (7)  |  Intuition (41)  |  Mathematician (178)  |  Mathematics (597)  |  Method (159)  |  Overlooking (3)  |  Physicist (132)  |  Physics (304)  |  Postulate (23)  |  Problem (382)  |  Recent (24)  |  Refinement (12)  |  Rift (2)  |  Root (48)  |  Science (1741)  |  Serious (40)  |  Serving (4)  |  Source (75)  |  Threat (26)  |  Trend (16)  |  Turning (5)  |  Unity (43)  |  Unquestionably (2)  |  Vital (34)  |  Weakening (2)  |  Whole (130)

The fact that the proof of a theorem consists in the application of certain simple rules of logic does not dispose of the creative element in mathematics, which lies in the choice of the possibilities to be examined.
— Richard Courant
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), 15.
Science quotes on:  |  Choice (72)  |  Creative (46)  |  Fact (628)  |  Logic (190)  |  Mathematics (597)  |  Possibility (101)  |  Proof (192)  |  Rule (140)  |  Simple (123)  |  Theorem (47)

The question of the origin of the hypothesis belongs to a domain in which no very general rules can be given; experiment, analogy and constructive intuition play their part here. But once the correct hypothesis is formulated, the principle of mathematical induction is often sufficient to provide the proof.
— Richard Courant
As co-author with Herbert Robbins, in What Is Mathematics?: An Elementary Approach to Ideas and Methods (1941, 1996), 15.
Science quotes on:  |  Analogy (46)  |  Constructive (3)  |  Correct (56)  |  Experiment (548)  |  Formulate (10)  |  General (99)  |  Hypothesis (231)  |  Induction (45)  |  Intuition (41)  |  Mathematics (597)  |  Origin (78)  |  Principle (232)  |  Proof (192)  |  Provide (49)  |  Question (327)  |  Rule (140)  |  Sufficient (30)


See also:

Carl Sagan Thumbnail In science it often happens that scientists say, 'You know that's a really good argument; my position is mistaken,' and then they would actually change their minds and you never hear that old view from them again. They really do it. It doesn't happen as often as it should, because scientists are human and change is sometimes painful. But it happens every day. I cannot recall the last time something like that happened in politics or religion. (1987) -- Carl Sagan
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