Celebrating 20 Years on the Web
TODAY IN SCIENCE HISTORY ®
Find science on or your birthday


Today in Science History - Quickie Quiz
Who said: “A people without children would face a hopeless future; a country without trees is almost as helpless.”
more quiz questions >>
Home > Dictionary of Science Quotations > Scientist Names Index L > Sophus Lie Quotes

Thumbnail of Sophus Lie (source)
Sophus Lie
(17 Dec 1842 - 18 Feb 1899)

Norwegian mathematician.


Science Quotes by Sophus Lie (1 quote)

In our century the conceptions substitution and substitution group, transformation and transformation group, operation and operation group, invariant, differential invariant and differential parameter, appear more and more clearly as the most important conceptions of mathematics.
— Sophus Lie
In Lapziger Berichte, No. 47 (1896), 261.
Science quotes on:  |  Appear (118)  |  Century (310)  |  Clearly (41)  |  Conception (154)  |  Differential (7)  |  Group (78)  |  Important (210)  |  Invariant (10)  |  Mathematics (1333)  |  Modern Mathematics (50)  |  More (2559)  |  Most (1729)  |  Operation (213)  |  Parameter (4)  |  Substitution (13)  |  Transformation (69)



Quotes by others about Sophus Lie (5)

When the late Sophus Lie … was asked to name the characteristic endowment of the mathematician, his answer was the following quaternion: Phantasie, Energie, Selbstvertrauen, Selbstkritik.
In Lectures on Philosophy, Science and Art (1908), 31. [“Quaternion” is used here in its meaning of a set of four people or things. The last four words, given in German, translate as “Imagination, Energy, Self-confidence, Self-criticism.” —Webmaster]
Science quotes on:  |  Answer (366)  |  Ask (411)  |  Characteristic (148)  |  Endowment (16)  |  Follow (379)  |  Late (118)  |  Lie (364)  |  Mathematician (389)  |  Name (333)  |  Quaternion (9)

Sophus Lie, great comparative anatomist of geometric theories.
In Lectures on Science, Philosophy and Art (1908), 31.
Science quotes on:  |  Anatomist (23)  |  Comparative (13)  |  Geometric (5)  |  Great (1575)  |  Lie (364)  |  Mathematicians and Anecdotes (141)  |  Theory (972)

It has been the final aim of Lie from the beginning to make progress in the theory of differential equations; as subsidiary to this may be regarded both his geometrical developments and the theory of continuous groups.
In Lectures on Mathematics (1911), 24.
Science quotes on:  |  Aim (165)  |  Beginning (305)  |  Both (494)  |  Continuous (82)  |  Development (424)  |  Differential Equation (18)  |  Equation (132)  |  Final (119)  |  Geometrical (10)  |  Group (78)  |  Lie (364)  |  Mathematicians and Anecdotes (141)  |  Progress (468)  |  Regard (304)  |  Subsidiary (5)  |  Theory (972)

To fully understand the mathematical genius of Sophus Lie, one must not turn to books recently published by him in collaboration with Dr. Engel, but to his earlier memoirs, written during the first years of his scientific career. There Lie shows himself the true geometer that he is, while in his later publications, finding that he was but imperfectly understood by the mathematicians accustomed to the analytic point of view, he adopted a very general analytic form of treatment that is not always easy to follow.
In Lectures on Mathematics (1911), 9.
Science quotes on:  |  Accustom (52)  |  Accustomed (46)  |  Adopt (19)  |  Analytic (10)  |  Book (394)  |  Career (76)  |  Collaboration (15)  |  Early (186)  |  Easy (204)  |  Ernst Engel (2)  |  Find (999)  |  First (1284)  |  Follow (379)  |  Form (960)  |  Fully (21)  |  General (511)  |  Genius (285)  |  Geometer (24)  |  Himself (461)  |  Imperfect (45)  |  Late (118)  |  Lie (364)  |  Mathematician (389)  |  Mathematicians and Anecdotes (141)  |  Mathematics (1333)  |  Memoir (13)  |  Must (1526)  |  Point (580)  |  Point Of View (82)  |  Publication (102)  |  Publish (36)  |  Recently (3)  |  Scientific (940)  |  Show (346)  |  Treatment (130)  |  True (214)  |  Turn (447)  |  Understand (607)  |  Understood (156)  |  View (488)  |  Write (231)  |  Year (932)

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 (5)  |  Art (657)  |  Artist (90)  |  Baron Augustin-Louis Cauchy (11)  |  Completeness (19)  |  Conformity (14)  |  Constructive (14)  |  Critical (66)  |  Degree (275)  |  Doubt (305)  |  Employment (32)  |  Leonhard Euler (35)  |  Faculty (72)  |  Find (999)  |  Form (960)  |  Great (1575)  |  High (363)  |  Ideal (100)  |  Imagination (328)  |  Individual (404)  |  Kind (557)  |  Count Joseph-Louis de Lagrange (26)  |  Lie (364)  |  Logical (55)  |  Mathematician (389)  |  Perfection (130)  |  Possess (156)  |  Rare (89)  |  Requisite (11)  |  Bernhard Riemann (7)  |  Specially (3)  |  Study (656)  |  Vary (27)  |  Karl Weierstrass (10)  |  Work (1351)


See also:
  • 17 Dec - short biography, births, deaths and events on date of Lie'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 Einstein • Isaac Newton • Lord Kelvin • Charles Darwin • Srinivasa Ramanujan • Carl Sagan • Florence Nightingale • Thomas Edison • Aristotle • Marie Curie • Benjamin Franklin • Winston Churchill • Galileo Galilei • Sigmund Freud • Robert Bunsen • Louis Pasteur • Theodore Roosevelt • Abraham Lincoln • Ronald Reagan • Leonardo DaVinci • Michio Kaku • Karl Popper • Johann Goethe • Robert Oppenheimer • Charles Kettering  ... (more people)

Quotations about: • Atomic  Bomb • Biology • Chemistry • Deforestation • Engineering • Anatomy • Astronomy • Bacteria • Biochemistry • Botany • Conservation • Dinosaur • Environment • Fractal • Genetics • Geology • History of Science • Invention • Jupiter • Knowledge • Love • Mathematics • Measurement • Medicine • Natural Resource • Organic Chemistry • Physics • Physician • Quantum Theory • Research • Science and Art • Teacher • Technology • Universe • Volcano • Virus • Wind Power • Women Scientists • X-Rays • Youth • Zoology  ... (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.