TODAY IN SCIENCE HISTORY ®  •  TODAYINSCI ®
Celebrating 24 Years on the Web
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “The Columbia is lost; there are no survivors.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index W > Karl Weierstrass, Quotes

Thumbnail of  Karl Weierstrass, (source)
Karl Weierstrass,
(31 Oct 1815 - 19 Feb 1897)

German mathematician.


Science Quotes by Karl Weierstrass, (2 quotes)

It is true that a mathematician who is not somewhat of a poet, will never be a perfect mathematician.
— Karl Weierstrass,
From letter to Sofia Kovalevskaya (27 Aug 1883), as quoted by Mittag-Leffler in Compte Rendu du Deuxième Congrès International des Mathématiciens Tenu à Paris du 6 au 12 Août 1900 (1902), 149. In Robert Edoward Moritz, Memorabilia Mathematica; Or, The Philomath's Quotation-book (1914), 121. From the original German, “Es ist wahr, ein Mathematiker, der nicht etwas Poet ist, wird nimmer ein vollkommener Mathematiker sein.” Also seen translated as, “No mathematician can be a complete mathematician unless he is also something of a poet”, in, for example, E.T. Bell, Men of Mathematics (1937), 432.
Science quotes on:  |  Mathematician (407)  |  Never (1089)  |  Perfect (223)  |  Poet (97)  |  Will (2350)

The more I meditate on the principles of the theory of functions—and I do this unremittingly the stronger becomes my conviction that the foundations upon which these must be built are the truths of Algebra…
— Karl Weierstrass,
From Letter (3 Oct 1875), to Professor Schwartz. As quoted and translated in Ernst Hairer and Gerhard Wanner, Analysis by Its History (2008), 177. From the original German in Mathematische Werke (1875, 1895), Vol. 2, 235, “Je mehr ich über die Principien der Functionentheorie nachdenke—und ich thue dies unablässig—, um so fester wird meine Überzeugung, dass diese auf dem Fundamente algebraischer Wahrheiten aufgebaut werden muss…”
Science quotes on:  |  Algebra (117)  |  Conviction (100)  |  Foundation (177)  |  Function (235)  |  Meditate (4)  |  Principle (530)  |  Theory (1015)  |  Truth (1109)



Quotes by others about Karl Weierstrass, (8)

Men of science belong to two different types—the logical and the intuitive. Science owes its progress to both forms of minds. Mathematics, although a purely logical structure, nevertheless makes use of intuition. Among the mathematicians there are intuitives and logicians, analysts and geometricians. Hermite and Weierstrass were intuitives. Riemann and Bertrand, logicians. The discoveries of intuition have always to be developed by logic.
In Man the Unknown (1935), 123.
Science quotes on:  |  Analyst (8)  |  Belong (168)  |  Joseph Bertrand (6)  |  Both (496)  |  Develop (278)  |  Different (595)  |  Discovery (837)  |  Form (976)  |  Geometrician (6)  |  Charles Hermite (10)  |  Intuition (82)  |  Intuitive (14)  |  Logic (311)  |  Logician (18)  |  Mathematician (407)  |  Mathematics (1395)  |  Men Of Science (147)  |  Mind (1377)  |  Nevertheless (90)  |  Owe (71)  |  Progress (492)  |  Pure (299)  |  Purely (111)  |  Bernhard Riemann (7)  |  Structure (365)  |  Two (936)  |  Type (171)  |  Use (771)

It is not surprising, in view of the polydynamic constitution of the genuinely mathematical mind, that many of the major heros of the science, men like Desargues and Pascal, Descartes and Leibnitz, Newton, Gauss and Bolzano, Helmholtz and Clifford, Riemann and Salmon and Plücker and Poincaré, have attained to high distinction in other fields not only of science but of philosophy and letters too. And when we reflect that the very greatest mathematical achievements have been due, not alone to the peering, microscopic, histologic vision of men like Weierstrass, illuminating the hidden recesses, the minute and intimate structure of logical reality, but to the larger vision also of men like Klein who survey the kingdoms of geometry and analysis for the endless variety of things that flourish there, as the eye of Darwin ranged over the flora and fauna of the world, or as a commercial monarch contemplates its industry, or as a statesman beholds an empire; when we reflect not only that the Calculus of Probability is a creation of mathematics but that the master mathematician is constantly required to exercise judgment—judgment, that is, in matters not admitting of certainty—balancing probabilities not yet reduced nor even reducible perhaps to calculation; when we reflect that he is called upon to exercise a function analogous to that of the comparative anatomist like Cuvier, comparing theories and doctrines of every degree of similarity and dissimilarity of structure; when, finally, we reflect that he seldom deals with a single idea at a tune, but is for the most part engaged in wielding organized hosts of them, as a general wields at once the division of an army or as a great civil administrator directs from his central office diverse and scattered but related groups of interests and operations; then, I say, the current opinion that devotion to mathematics unfits the devotee for practical affairs should be known for false on a priori grounds. And one should be thus prepared to find that as a fact Gaspard Monge, creator of descriptive geometry, author of the classic Applications de l’analyse à la géométrie; Lazare Carnot, author of the celebrated works, Géométrie de position, and Réflections sur la Métaphysique du Calcul infinitesimal; Fourier, immortal creator of the Théorie analytique de la chaleur; Arago, rightful inheritor of Monge’s chair of geometry; Poncelet, creator of pure projective geometry; one should not be surprised, I say, to find that these and other mathematicians in a land sagacious enough to invoke their aid, rendered, alike in peace and in war, eminent public service.
In Lectures on Science, Philosophy and Art (1908), 32-33.
Science quotes on:  |  A Priori (26)  |  Achievement (187)  |  Administrator (11)  |  Admit (49)  |  Affair (29)  |  Aid (101)  |  Alike (60)  |  Alone (324)  |  Analogous (7)  |  Analysis (244)  |  Anatomist (24)  |  Application (257)  |  François Arago (15)  |  Army (35)  |  Attain (126)  |  Author (175)  |  Balance (82)  |  Behold (19)  |  Bernhard Bolzano (2)  |  Calculation (134)  |  Calculus (65)  |  Call (781)  |  Lazare-Nicolas-Marguerite Carnot (4)  |  Celebrated (2)  |  Central (81)  |  Certainty (180)  |  Chair (25)  |  Civil (26)  |  Classic (13)  |  William Kingdon Clifford (23)  |  Commercial (28)  |  Comparative (14)  |  Compare (76)  |  Constantly (27)  |  Constitution (78)  |  Contemplate (29)  |  Creation (350)  |  Creator (97)  |  Current (122)  |  Baron Georges Cuvier (34)  |  Charles Darwin (322)  |  Deal (192)  |  Degree (277)  |  René Descartes (83)  |  Descriptive (18)  |  Descriptive Geometry (3)  |  Devotee (7)  |  Devotion (37)  |  Direct (228)  |  Dissimilar (6)  |  Distinction (72)  |  Diverse (20)  |  Division (67)  |  Doctrine (81)  |  Due (143)  |  Eminent (20)  |  Empire (17)  |  Endless (60)  |  Engage (41)  |  Enough (341)  |  Exercise (113)  |  Eye (440)  |  Fact (1257)  |  False (105)  |  Fauna (13)  |  Field (378)  |  Finally (26)  |  Find (1014)  |  Flora (9)  |  Flourish (34)  |  Baron Jean-Baptiste-Joseph Fourier (17)  |  Function (235)  |  Carl Friedrich Gauss (79)  |  General (521)  |  Genuinely (4)  |  Geometry (271)  |  Great (1610)  |  Greatest (330)  |  Ground (222)  |  Group (83)  |  Hero (45)  |  Hide (70)  |  High (370)  |  Histology (4)  |  Host (16)  |  Idea (881)  |  Illuminate (26)  |  Illuminating (12)  |  Immortal (35)  |  Industry (159)  |  Infinitesimal (30)  |  Inheritor (2)  |  Interest (416)  |  Intimate (21)  |  Invoke (7)  |  Judgment (140)  |  Kingdom (80)  |  Felix Klein (15)  |  Know (1538)  |  Known (453)  |  Land (131)  |  Large (398)  |  Gottfried Wilhelm Leibniz (51)  |  Letter (117)  |  Logical (57)  |  Major (88)  |  Master (182)  |  Mathematician (407)  |  Mathematics (1395)  |  Matter (821)  |  Microscopic (27)  |  Mind (1377)  |  Minute (129)  |  Monarch (6)  |  Gaspard Monge (2)  |  Most (1728)  |  Sir Isaac Newton (363)  |  Office (71)  |  Operation (221)  |  Operations (107)  |  Opinion (291)  |  Organize (33)  |  Other (2233)  |  Part (235)  |  Blaise Pascal (81)  |  Peace (116)  |  Peer (13)  |  Philosophy (409)  |  Henri Poincaré (99)  |  Jean-Victor Poncelet (2)  |  Position (83)  |  Practical (225)  |  Prepare (44)  |  Probability (135)  |  Projective Geometry (3)  |  Public Service (6)  |  Pure (299)  |  Range (104)  |  Reality (274)  |  Recess (8)  |  Reduce (100)  |  Reducible (2)  |  Reflect (39)  |  Relate (26)  |  Render (96)  |  Require (229)  |  Required (108)  |  Bernhard Riemann (7)  |  Rightful (3)  |  Sagacious (7)  |  Salmon (7)  |  Say (989)  |  Scatter (7)  |  Seldom (68)  |  Service (110)  |  Similarity (32)  |  Single (365)  |  Statesman (20)  |  Structure (365)  |  Surprise (91)  |  Survey (36)  |  Theory (1015)  |  Thing (1914)  |  Tune (20)  |  Unfit (13)  |  Variety (138)  |  View (496)  |  Vision (127)  |  War (233)  |  Wield (10)  |  Work (1402)  |  World (1850)

Objections … inspired Kronecker and others to attack Weierstrass’ “sequential” definition of irrationals. Nevertheless, right or wrong, Weierstrass and his school made the theory work. The most useful results they obtained have not yet been questioned, at least on the ground of their great utility in mathematical analysis and its implications, by any competent judge in his right mind. This does not mean that objections cannot be well taken: it merely calls attention to the fact that in mathematics, as in everything else, this earth is not yet to be confused with the Kingdom of Heaven, that perfection is a chimaera, and that, in the words of Crelle, we can only hope for closer and closer approximations to mathematical truth—whatever that may be, if anything—precisely as in the Weierstrassian theory of convergent sequences of rationals defining irrationals.
In Men of Mathematics (1937), 431-432.
Science quotes on:  |  Analysis (244)  |  Approximation (32)  |  Attack (86)  |  Attention (196)  |  Call (781)  |  Chimera (10)  |  Close (77)  |  Closer (43)  |  Competent (20)  |  Confuse (22)  |  Convergent (3)  |  Define (53)  |  Definition (238)  |  Earth (1076)  |  Everything (489)  |  Fact (1257)  |  Great (1610)  |  Ground (222)  |  Heaven (266)  |  Hope (321)  |  Implication (25)  |  Inspire (58)  |  Irrational (16)  |  Judge (114)  |  Kingdom (80)  |  Kingdom Of Heaven (3)  |  Leopold Kronecker (6)  |  Mathematical Analysis (23)  |  Mathematics (1395)  |  Mean (810)  |  Merely (315)  |  Mind (1377)  |  Most (1728)  |  Nevertheless (90)  |  Objection (34)  |  Obtain (164)  |  Other (2233)  |  Perfection (131)  |  Precise (71)  |  Precisely (93)  |  Question (649)  |  Rational (95)  |  Result (700)  |  Right (473)  |  School (227)  |  Sequence (68)  |  Sequential (2)  |  Theory (1015)  |  Truth (1109)  |  Useful (260)  |  Utility (52)  |  Whatever (234)  |  Word (650)  |  Work (1402)  |  Wrong (246)

The arithmetization of mathematics … which began with Weierstrass … had for its object the separation of purely mathematical concepts, such as number and correspondence and aggregate, from intuitional ideas, which mathematics had acquired from long association with geometry and mechanics. These latter, in the opinion of the formalists, are so firmly entrenched in mathematical thought that in spite of the most careful circumspection in the choice of words, the meaning concealed behind these words, may influence our reasoning. For the trouble with human words is that they possess content, whereas the purpose of mathematics is to construct pure thought. But how can we avoid the use of human language? The … symbol. Only by using a symbolic language not yet usurped by those vague ideas of space, time, continuity which have their origin in intuition and tend to obscure pure reason—only thus may we hope to build mathematics on the solid foundation of logic.
In Tobias Dantzig and Joseph Mazur (ed.), Number: The Language of Science (1930, ed. by Joseph Mazur 2007), 99.
Science quotes on:  |  Acquire (46)  |  Acquired (77)  |  Aggregate (24)  |  Association (49)  |  Avoid (123)  |  Begin (275)  |  Behind (139)  |  Build (211)  |  Careful (28)  |  Choice (114)  |  Circumspection (5)  |  Conceal (19)  |  Concealed (25)  |  Concept (242)  |  Construct (129)  |  Content (75)  |  Continuity (39)  |  Correspondence (24)  |  Entrench (2)  |  Firmly (6)  |  Foundation (177)  |  Geometry (271)  |  Hope (321)  |  Human (1512)  |  Idea (881)  |  Influence (231)  |  Intuition (82)  |  Language (308)  |  Latter (21)  |  Logic (311)  |  Long (778)  |  Mathematics (1395)  |  Mean (810)  |  Meaning (244)  |  Mechanic (120)  |  Mechanics (137)  |  Most (1728)  |  Number (710)  |  Object (438)  |  Obscure (66)  |  Opinion (291)  |  Origin (250)  |  Possess (157)  |  Pure (299)  |  Purely (111)  |  Purpose (336)  |  Reason (766)  |  Reasoning (212)  |  Separation (60)  |  Solid (119)  |  Space (523)  |  Spite (55)  |  Symbol (100)  |  Tend (124)  |  Thought (995)  |  Time (1911)  |  Trouble (117)  |  Use (771)  |  Vague (50)  |  Word (650)

Inspiration plays no less a role in science than it does in the realm of art. It is a childish notion to think that a mathematician attains any scientifically valuable results by sitting at his desk with a ruler, calculating machines or other mechanical means. The mathematical imagination of a Weierstrass is naturally quite differently oriented in meaning and result than is the imagination of an artist, and differs basically in quality. But the psychological processes do not differ. Both are frenzy (in the sense of Plato’s “mania”) and “inspiration.”
Max Weber
From a Speech (1918) presented at Munich University, published in 1919, and collected in 'Wissenschaft als Beruf', Gessammelte Aufsätze zur Wissenschaftslehre (1922), 524-525. As given in H.H. Gerth and C. Wright-Mills (translators and eds.), 'Science as a Vocation', Max Weber: Essays in Sociology (1946), 136.
Science quotes on:  |  Art (680)  |  Artist (97)  |  Attain (126)  |  Basic (144)  |  Both (496)  |  Calculating Machine (3)  |  Childish (20)  |  Desk (13)  |  Differ (88)  |  Differently (4)  |  Do (1905)  |  Frenzy (6)  |  Imagination (349)  |  Inspiration (80)  |  Machine (271)  |  Mania (3)  |  Mathematician (407)  |  Mathematics (1395)  |  Mean (810)  |  Meaning (244)  |  Means (587)  |  Mechanical (145)  |  Naturally (11)  |  Notion (120)  |  Other (2233)  |  Plato (80)  |  Process (439)  |  Psychological (42)  |  Psychology (166)  |  Quality (139)  |  Realm (87)  |  Result (700)  |  Role (86)  |  Ruler (21)  |  Science And Art (195)  |  Sense (785)  |  Sitting (44)  |  Think (1122)  |  Value (393)

One morning a great noise proceeded from one of the classrooms [of the Braunsberger gymnasium] and on investigation it was found that Weierstrass, who was to give the recitation, had not appeared. The director went in person to Weierstrass’ dwelling and on knocking was told to come in. There sat Weierstrass by a glimmering lamp in a darkened room though it was daylight outside. He had worked the night through and had not noticed the approach of daylight. When the director reminded him of the noisy throng of students who were waiting for him, his only reply was that he could impossibly interrupt his work; that he was about to make an important discovery which would attract attention in scientific circles.
In Karl Weierstrass: Jahrbuch der Deutschen Mathematiker Vereinigung (1897), 6), 88-89. As quoted, cited and translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 180.
Science quotes on:  |  Approach (112)  |  Attention (196)  |  Attract (25)  |  Circle (117)  |  Classroom (11)  |  Daylight (23)  |  Discovery (837)  |  Glimmer (5)  |  Glimmering (2)  |  Great (1610)  |  Home (184)  |  Important (229)  |  Impossible (263)  |  Interrupt (6)  |  Investigation (250)  |  Lamp (37)  |  Mathematicians and Anecdotes (141)  |  Morning (98)  |  Night (133)  |  Noise (40)  |  Notice (81)  |  Outside (141)  |  Person (366)  |  Proceed (134)  |  Reply (58)  |  Scientific (955)  |  Student (317)  |  Through (846)  |  Wait (66)  |  Waiting (42)  |  Work (1402)

Weierstrass related … that he followed Sylvester’s papers on the theory of algebraic forms very attentively until Sylvester began to employ Hebrew characters. That was more than he could stand and after that he quit him.
From Naturwissenschaftliche Rundschau (1897), 12 (1897), 361. As cited in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 180.
Science quotes on:  |  Algebra (117)  |  Attentive (15)  |  Character (259)  |  Employ (115)  |  Follow (389)  |  Form (976)  |  Hebrew (10)  |  Mathematicians and Anecdotes (141)  |  More (2558)  |  Paper (192)  |  Quit (10)  |  Stand (284)  |  James Joseph Sylvester (58)  |  Theory (1015)

Who has studied the works of such men as Euler, Lagrange, Cauchy, Riemann, Sophus Lie, and Weierstrass, can doubt that a great mathematician is a great artist? The faculties possessed by such men, varying greatly in kind and degree with the individual, are analogous with those requisite for constructive art. Not every mathematician possesses in a specially high degree that critical faculty which finds its employment in the perfection of form, in conformity with the ideal of logical completeness; but every great mathematician possesses the rarer faculty of constructive imagination.
In Presidential Address British Association for the Advancement of Science, Sheffield, Section A, Nature (1 Sep 1910), 84, 290.
Science quotes on:  |  Analogous (7)  |  Art (680)  |  Artist (97)  |  Baron Augustin-Louis Cauchy (11)  |  Completeness (19)  |  Conformity (15)  |  Constructive (15)  |  Critical (73)  |  Degree (277)  |  Doubt (314)  |  Employment (34)  |  Leonhard Euler (35)  |  Faculty (76)  |  Find (1014)  |  Form (976)  |  Great (1610)  |  High (370)  |  Ideal (110)  |  Imagination (349)  |  Individual (420)  |  Kind (564)  |  Count Joseph-Louis de Lagrange (26)  |  Lie (370)  |  Sophus Lie (6)  |  Logical (57)  |  Mathematician (407)  |  Perfection (131)  |  Possess (157)  |  Rare (94)  |  Requisite (12)  |  Bernhard Riemann (7)  |  Specially (3)  |  Study (701)  |  Vary (27)  |  Work (1402)


See also:
  • 31 Oct - short biography, births, deaths and events on date of Weierstrass's birth.

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
Quotations by:Albert EinsteinIsaac NewtonLord KelvinCharles DarwinSrinivasa RamanujanCarl SaganFlorence NightingaleThomas EdisonAristotleMarie CurieBenjamin FranklinWinston ChurchillGalileo GalileiSigmund FreudRobert BunsenLouis PasteurTheodore RooseveltAbraham LincolnRonald ReaganLeonardo DaVinciMichio KakuKarl PopperJohann GoetheRobert OppenheimerCharles Kettering  ... (more people)

Quotations about:Atomic  BombBiologyChemistryDeforestationEngineeringAnatomyAstronomyBacteriaBiochemistryBotanyConservationDinosaurEnvironmentFractalGeneticsGeologyHistory of ScienceInventionJupiterKnowledgeLoveMathematicsMeasurementMedicineNatural ResourceOrganic ChemistryPhysicsPhysicianQuantum TheoryResearchScience and ArtTeacherTechnologyUniverseVolcanoVirusWind PowerWomen ScientistsX-RaysYouthZoology  ... (more topics)
Sitewide search within all Today In Science History pages:
Visit our Science and Scientist Quotations index for more Science Quotes from archaeologists, biologists, chemists, geologists, inventors and inventions, mathematicians, physicists, pioneers in medicine, science events and technology.

Names index: | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |

Categories index: | 1 | 2 | A | B | C | D | E | F | G | H | I | J | K | L | M | N | O | P | Q | R | S | T | U | V | W | X | Y | Z |
Thank you for sharing.
- 100 -
Sophie Germain
Gertrude Elion
Ernest Rutherford
James Chadwick
Marcel Proust
William Harvey
Johann Goethe
John Keynes
Carl Gauss
Paul Feyerabend
- 90 -
Antoine Lavoisier
Lise Meitner
Charles Babbage
Ibn Khaldun
Euclid
Ralph Emerson
Robert Bunsen
Frederick Banting
Andre Ampere
Winston Churchill
- 80 -
John Locke
Bronislaw Malinowski
Bible
Thomas Huxley
Alessandro Volta
Erwin Schrodinger
Wilhelm Roentgen
Louis Pasteur
Bertrand Russell
Jean Lamarck
- 70 -
Samuel Morse
John Wheeler
Nicolaus Copernicus
Robert Fulton
Pierre Laplace
Humphry Davy
Thomas Edison
Lord Kelvin
Theodore Roosevelt
Carolus Linnaeus
- 60 -
Francis Galton
Linus Pauling
Immanuel Kant
Martin Fischer
Robert Boyle
Karl Popper
Paul Dirac
Avicenna
James Watson
William Shakespeare
- 50 -
Stephen Hawking
Niels Bohr
Nikola Tesla
Rachel Carson
Max Planck
Henry Adams
Richard Dawkins
Werner Heisenberg
Alfred Wegener
John Dalton
- 40 -
Pierre Fermat
Edward Wilson
Johannes Kepler
Gustave Eiffel
Giordano Bruno
JJ Thomson
Thomas Kuhn
Leonardo DaVinci
Archimedes
David Hume
- 30 -
Andreas Vesalius
Rudolf Virchow
Richard Feynman
James Hutton
Alexander Fleming
Emile Durkheim
Benjamin Franklin
Robert Oppenheimer
Robert Hooke
Charles Kettering
- 20 -
Carl Sagan
James Maxwell
Marie Curie
Rene Descartes
Francis Crick
Hippocrates
Michael Faraday
Srinivasa Ramanujan
Francis Bacon
Galileo Galilei
- 10 -
Aristotle
John Watson
Rosalind Franklin
Michio Kaku
Isaac Asimov
Charles Darwin
Sigmund Freud
Albert Einstein
Florence Nightingale
Isaac Newton


by Ian Ellis
who invites your feedback
Thank you for sharing.
Today in Science History
Sign up for Newsletter
with quiz, quotes and more.