Celebrating 19 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday

Today in Science History - Quickie Quiz
Who said: “God does not care about our mathematical difficulties. He integrates empirically.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index B > Jacob Bernoulli Quotes

Thumbnail of Jacob Bernoulli (source)
Jacob Bernoulli
(27 Dec 1654 - 16 Aug 1705)

Swiss mathematician and astronomer who was the first of the Bernoulli family with generations of eight mathematicians. Jakob's contributions included early work on the calculus of variation. He developed Bernoulli numbers by which he derived the exponential series.


Science Quotes by Jacob Bernoulli (1 quote)

It often happens that men, even of the best understandings and greatest circumspection, are guilty of that fault in reasoning which the writers on logick call the insufficient, or imperfect enumeration of parts, or cases: insomuch that I will venture to assert, that this is the chief, and almost the only, source of the vast number of erroneous opinions, and those too very often in matters of great importance, which we are apt to form on all the subjects we reflect upon, whether they relate to the knowledge of nature, or the merits and motives of human actions. It must therefore be acknowledged, that the art which affords a cure to this weakness, or defect, of our understandings, and teaches us to enumerate all the possible ways in which a given number of things may be mixed and combined together, that we may be certain that we have not omitted anyone arrangement of them that can lead to the object of our inquiry, deserves to be considered as most eminently useful and worthy of our highest esteem and attention. And this is the business of the art, or doctrine of combinations ... It proceeds indeed upon mathematical principles in calculating the number of the combinations of the things proposed: but by the conclusions that are obtained by it, the sagacity of the natural philosopher, the exactness of the historian, the skill and judgement of the physician, and the prudence and foresight of the politician, may be assisted; because the business of all these important professions is but to form reasonable conjectures concerning the several objects which engage their attention, and all wise conjectures are the results of a just and careful examination of the several different effects that may possibly arise from the causes that are capable of producing them.
— Jacob Bernoulli
Ars conjectandi (1713). In F. Maseres, The Doctrine of Permutations and Combinations (1795), 36.
Science quotes on:  |  Action (328)  |  All (4107)  |  Arise (158)  |  Arrangement (91)  |  Art (657)  |  Assert (66)  |  Attention (191)  |  Best (459)  |  Business (149)  |  Call (769)  |  Capable (168)  |  Cause (542)  |  Certain (550)  |  Chief (97)  |  Circumspection (5)  |  Combination (144)  |  Conclusion (255)  |  Conjecture (49)  |  Consider (416)  |  Cure (122)  |  Defect (31)  |  Deserve (65)  |  Different (577)  |  Effect (394)  |  Engage (39)  |  Erroneous (30)  |  Error (321)  |  Exactness (29)  |  Examination (98)  |  Fault (55)  |  Form (960)  |  Great (1575)  |  Greatest (329)  |  Happen (275)  |  Historian (55)  |  Human (1470)  |  Imperfect (45)  |  Importance (287)  |  Indeed (323)  |  Inquiry (79)  |  Knowledge (1536)  |  Lead (385)  |  Mathematics (1333)  |  Matter (801)  |  Merit (50)  |  Most (1729)  |  Motive (59)  |  Must (1526)  |  Natural (796)  |  Nature (1928)  |  Number (701)  |  Object (422)  |  Obtain (163)  |  Opinion (281)  |  Philosopher (259)  |  Physician (273)  |  Politician (38)  |  Possible (554)  |  Possibly (111)  |  Principle (510)  |  Proceed (129)  |  Profession (102)  |  Reasoning (207)  |  Result (678)  |  Sagacity (10)  |  Skill (109)  |  Subject (522)  |  Thing (1915)  |  Together (387)  |  Understanding (514)  |  Useful (250)  |  Vast (178)  |  Way (1216)  |  Weakness (48)  |  Will (2354)  |  Wise (132)  |  Writer (86)



Quotes by others about Jacob Bernoulli (5)

I want to put in something about Bernoulli’s numbers, in one of my Notes, as an example of how the implicit function may be worked out by the engine, without having been worked out by human head & hands first. Give me the necessary data & formulae.
Lovelace Papers, Bodleian Library, Oxford University, 42, folio 12 (6 Feb 1841). As quoted and cited in Dorothy Stein (ed.), 'This First Child of Mine', Ada: A Life and a Legacy (1985), 106-107.
Science quotes on:  |  Analytical Engine (5)  |  Calculate (54)  |  Data (156)  |  Engine (98)  |  Example (94)  |  First (1284)  |  Formula (98)  |  Function (229)  |  Hand (143)  |  Head (81)  |  Human (1470)  |  Implicit (12)  |  Necessary (363)  |  Note (34)  |  Number (701)  |  Something (719)  |  Want (497)  |  Work (1351)

Following the example of Archimedes who wished his tomb decorated with his most beautiful discovery in geometry and ordered it inscribed with a cylinder circumscribed by a sphere, James Bernoulli requested that his tomb be inscribed with his logarithmic spiral together with the words, “Eadem mutata resurgo,” a happy allusion to the hope of the Christians, which is in a way symbolized by the properties of that curve.
From 'Eloge de M. Bernoulli', Oeuvres de Fontenelle, t. 5 (1768), 112. As translated in Robert Édouard Moritz, Memorabilia Mathematica; Or, The Philomath’s Quotation-Book (1914), 143-144. [The Latin phrase, Eadem numero mutata resurgo means as “Though changed, I arise again exactly the same”. —Webmaster]
Science quotes on:  |  Allusion (2)  |  Archimedes (58)  |  Beautiful (259)  |  Christian (44)  |  Circumscribe (2)  |  Curve (49)  |  Cylinder (10)  |  Decorate (2)  |  Discovery (785)  |  Example (94)  |  Follow (379)  |  Geometry (259)  |  Happy (105)  |  Hope (299)  |  Inscribe (4)  |  Logarithmic (5)  |  Mathematicians and Anecdotes (141)  |  Most (1729)  |  Order (632)  |  Property (169)  |  Request (7)  |  Sphere (116)  |  Spiral (18)  |  Symbolize (8)  |  Together (387)  |  Tomb (15)  |  Way (1216)  |  Wish (212)  |  Word (622)

In the year 1692, James Bernoulli, discussing the logarithmic spiral [or equiangular spiral, ρ = αθ] … shows that it reproduces itself in its evolute, its involute, and its caustics of both reflection and refraction, and then adds: “But since this marvellous spiral, by such a singular and wonderful peculiarity, pleases me so much that I can scarce be satisfied with thinking about it, I have thought that it might not be inelegantly used for a symbolic representation of various matters. For since it always produces a spiral similar to itself, indeed precisely the same spiral, however it may be involved or evolved, or reflected or refracted, it may be taken as an emblem of a progeny always in all things like the parent, simillima filia matri. Or, if it is not forbidden to compare a theorem of eternal truth to the mysteries of our faith, it may be taken as an emblem of the eternal generation of the Son, who as an image of the Father, emanating from him, as light from light, remains ὁμοούσιος with him, howsoever overshadowed. Or, if you prefer, since our spira mirabilis remains, amid all changes, most persistently itself, and exactly the same as ever, it may be used as a symbol, either of fortitude and constancy in adversity, or, of the human body, which after all its changes, even after death, will be restored to its exact and perfect self, so that, indeed, if the fashion of Archimedes were allowed in these days, I should gladly have my tombstone bear this spiral, with the motto, ‘Though changed, I arise again exactly the same, Eadem numero mutata resurgo.’”
In 'The Uses of Mathesis', Bibliotheca Sacra, Vol. 32, 516-516. [The Latin phrase “simillima filia matri” roughly translates as “the daughter resembles the mother”. “Spira mirabilis” is Latin for “marvellous spiral”. The Greek word (?µ???s???) translates as “consubstantial”, meaning of the same substance or essence (used especially of the three persons of the Trinity in Christian theology). —Webmaster]
Science quotes on:  |  Add (40)  |  Adversity (3)  |  All (4107)  |  Allow (45)  |  Archimedes (58)  |  Arise (158)  |  Bear (159)  |  Body (537)  |  Both (494)  |  Caustic (2)  |  Change (595)  |  Compare (70)  |  Constancy (12)  |  Death (391)  |  Discuss (23)  |  Emanate (2)  |  Emblem (4)  |  Eternal (111)  |  Evolute (2)  |  Evolution (593)  |  Exact (68)  |  Exactly (13)  |  Faith (203)  |  Fashion (30)  |  Father (110)  |  Forbid (14)  |  Forbidden (18)  |  Fortitude (2)  |  Generation (242)  |  Gladly (2)  |  Human (1470)  |  Human Body (34)  |  Image (96)  |  Indeed (323)  |  Involve (90)  |  Involved (90)  |  James (3)  |  Light (609)  |  Logarithmic (5)  |  Marvellous (25)  |  Mathematicians and Anecdotes (141)  |  Matter (801)  |  Most (1729)  |  Motto (28)  |  Mystery (178)  |  Overshadow (2)  |  Parent (76)  |  Peculiarity (25)  |  Perfect (216)  |  Persistent (18)  |  Please (65)  |  Precisely (92)  |  Prefer (25)  |  Produce (104)  |  Progeny (15)  |  Reflect (32)  |  Reflection (91)  |  Refraction (11)  |  Remain (349)  |  Representation (54)  |  Reproduce (11)  |  Restore (8)  |  Same (157)  |  Satisfied (23)  |  Scarce (10)  |  Self (267)  |  Show (346)  |  Similar (36)  |  Singular (23)  |  Son (24)  |  Spiral (18)  |  Symbol (94)  |  Symbolic (15)  |  Theorem (112)  |  Thing (1915)  |  Think (1086)  |  Thinking (415)  |  Thought (954)  |  Tombstone (2)  |  Truth (1062)  |  Various (200)  |  Will (2354)  |  Wonderful (149)  |  Year (932)

We pass with admiration along the great series of mathematicians, by whom the science of theoretical mechanics has been cultivated, from the time of Newton to our own. There is no group of men of science whose fame is higher or brighter. The great discoveries of Copernicus, Galileo, Newton, had fixed all eyes on those portions of human knowledge on which their successors employed their labors. The certainty belonging to this line of speculation seemed to elevate mathematicians above the students of other subjects; and the beauty of mathematical relations and the subtlety of intellect which may be shown in dealing with them, were fitted to win unbounded applause. The successors of Newton and the Bernoullis, as Euler, Clairaut, D’Alembert, Lagrange, Laplace, not to introduce living names, have been some of the most remarkable men of talent which the world has seen.
In History of the Inductive Sciences, Vol. 1, Bk. 4, chap. 6, sect. 6.
Science quotes on:  |  Admiration (59)  |  All (4107)  |  Applause (9)  |  Beauty (300)  |  Belong (162)  |  Belonging (37)  |  Bright (79)  |  Certainty (174)  |  Alexis Claude Clairaut (2)  |  Nicolaus Copernicus (49)  |  Cultivate (19)  |  Jean le Rond D’Alembert (11)  |  Deal (188)  |  Discovery (785)  |  Elevate (12)  |  Employ (113)  |  Leonhard Euler (35)  |  Eye (423)  |  Fame (50)  |  Fit (134)  |  Fix (25)  |  Galileo Galilei (125)  |  Great (1575)  |  Group (78)  |  High (363)  |  Human (1470)  |  Intellect (233)  |  Introduce (63)  |  Knowledge (1536)  |  Labor (107)  |  Count Joseph-Louis de Lagrange (26)  |  Pierre-Simon Laplace (62)  |  Line (91)  |  Live (629)  |  Living (491)  |  Mathematician (389)  |  Mathematics (1333)  |  Mechanic (119)  |  Mechanics (132)  |  Men Of Science (143)  |  Most (1729)  |  Name (333)  |  Sir Isaac Newton (335)  |  Other (2236)  |  Pass (238)  |  Portion (84)  |  Relation (157)  |  Remarkable (48)  |  Science (3880)  |  See (1082)  |  Seem (145)  |  Series (149)  |  Show (346)  |  Speculation (126)  |  Student (301)  |  Subject (522)  |  Subtlety (19)  |  Successor (14)  |  Talent (96)  |  Theoretical (22)  |  Time (1877)  |  Unbounded (5)  |  Win (52)  |  World (1778)

In my opinion, there is absolutely no trustworthy proof that talents have been improved by their exercise through the course of a long series of generations. The Bach family shows that musical talent, and the Bernoulli family that mathematical power, can be transmitted from generation to generation, but this teaches us nothing as to the origin of such talents. In both families the high-watermark of talent lies, not at the end of the series of generations, as it should do if the results of practice are transmitted, but in the middle. Again, talents frequently appear in some member of a family which has not been previously distinguished.
In 'On Heredity', Essays upon Heredity and Kindred Biological Problems (1889), Vol. 1, 95-96.
Science quotes on:  |  Appear (118)  |  Bach (7)  |  Bach_Johann (2)  |  Both (494)  |  Course (408)  |  Distinguish (160)  |  Distinguished (83)  |  Do (1908)  |  End (590)  |  Exercise (110)  |  Family (95)  |  Frequent (23)  |  Generation (242)  |  High (363)  |  Improve (58)  |  Lie (364)  |  Long (789)  |  Mathematics (1333)  |  Member (41)  |  Middle (16)  |  Musical (10)  |  Nothing (969)  |  Opinion (281)  |  Origin (241)  |  Power (747)  |  Practice (204)  |  Previous (13)  |  Proof (289)  |  Result (678)  |  Series (149)  |  Show (346)  |  Talent (96)  |  Teach (278)  |  Through (849)  |  Transmit (11)  |  Trustworthy (11)


See also:
  • 27 Dec - short biography, births, deaths and events on date of Bernoulli'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 |

- 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



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