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Albert Einstein
(14 Mar 1879 - 18 Apr 1955)
German-American physicist who developed the special and general theories of relativity. He was awarded the 1921 Nobel Prize for Physics for his explanation of the photoelectric effect.
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Albert Einstein Quotes on Mathematics (25 quotes)
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… how the real proof should run. The main thing is the content, not the mathematics. With mathematics one can prove anything.
— Albert Einstein
Commenting on a mistake in some work from Planck, for which “the result is correct but the proof is faulty.” As quoted in Denis Brian, Einstein—A Life (1996), 76.
[Kepler] had to realize clearly that logical-mathematical theoretizing, no matter how lucid, could not guarantee truth by itself; that the most beautiful logical theory means nothing in natural science without comparison with the exactest experience. Without this philosophic attitude, his work would not have been possible.
— Albert Einstein
From Introduction that Einstein wrote for Carola Baumgardt and Jamie Callan, Johannes Kepler Life and Letters (1953), 13.
As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.
— Albert Einstein
Sidelights on Relativity (1920), 28.
But the creative principle resides in mathematics. In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
— Albert Einstein
From Herbert Spencer Lecture, at University of Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed in Philosophy of Science, (Apr 1934), 1, No. 2. Quoted and cited in epigraph, A. H. Louie, More Than Life Itself: A Synthetic Continuation in Relational Biology (2013), 81.
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.
— Albert Einstein
In letter (7 Jan 1943) to Barbara Wilson, a junior high school student, who had difficulties in school with mathematics. In Einstein Archives, 42-606. Quoted in Alice Calaprice, Dear Professor Einstein: Albert Einstein's Letters to and from Children (2002), 140.
Do not worry about your problems in mathematics. I assure you, my problems with mathematics are much greater than yours.
— Albert Einstein
…...
God does not care about our mathematical difficulties. He integrates empirically.
— Albert Einstein
Quoted, without citation, by Léopold Infeld in Quest (1942, 1980), 279. If you know the primary source, please contact Webmaster.
Here arises a puzzle that has disturbed scientists of all periods. How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality? Is human reason, then, without experience, merely by taking thought, able to fathom the properties of real things?
— Albert Einstein
From 'Geometry and Experience', an expanded form of an Address by Albert Einstein to the Prussian Academy of Sciences in Berlin (27 Jan 1921). In Albert Einstein, translated by G. B. Jeffery and W. Perrett, Sidelights on Relativity (1923).
I don’t believe in mathematics.
— Albert Einstein
A offhand remark when discussing the rigid rules of mathematics in a café conversation with engineer Gustave Ferrière. As quoted in Denis Brian, Einstein—A Life (1996), 76.
In the beginning (if there was such a thing), God created Newton’s laws of motion together with the necessary masses and forces. This is all; everything beyond this follows from the development of appropriate mathematical methods by means of deduction.
— Albert Einstein
Autobiographical Notes (1946), 19. In Albert Einstein, Alice Calaprice, Freeman Dyson , The Ultimate Quotable Einstein (2011), 397.
In the judgment of the most competent living mathematicians, Fraulein Noether was the most significant mathematical genius thus far produced since the higher education of women began.
— Albert Einstein
In letter (1 May 1935), Letters to the Editor, 'The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician', New York Times (4 May 1935), 12.
Insofar as mathematics is about reality, it is not certain, and insofar as it is certain, it is not about reality.
— Albert Einstein
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It is difficult even to attach a precise meaning to the term “scientific truth.” So different is the meaning of the word “truth” according to whether we are dealing with a fact of experience, a mathematical proposition or a scientific theory. “Religious truth” conveys nothing clear to me at all.
— Albert Einstein
From 'Scientific Truth' in Essays in Science (1934, 2004), 11.
It is mathematics that offers the exact natural sciences a certain measure of security which, without mathematics, they could not attain.
— Albert Einstein
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One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.
— Albert Einstein
In Albert Einstein, translated by G.B. Jeffery and W. Perrett, 'Geometry and Experience',Sidelights on Relativity (1922), 27.
Our experience up to date justifies us in feeling sure that in Nature is actualized the ideal of mathematical simplicity. It is my conviction that pure mathematical construction enables us to discover the concepts and the laws connecting them, which gives us the key to understanding nature… In a certain sense, therefore, I hold it true that pure thought can grasp reality, as the ancients dreamed.
— Albert Einstein
In Herbert Spencer Lecture at Oxford (10 Jun 1933), 'On the Methods of Theoretical Physics'. Printed in Discovery (Jul 1933), 14, 227. Also quoted in Stefano Zambelli and Donald A. R. George, Nonlinearity, Complexity and Randomness in Economics (2012).
Pure mathematics is, in its way, the poetry of logical ideas. One seeks the most general ideas of operation which will bring together in simple, logical and unified form the largest possible circle of formal relationships. In this effort toward logical beauty spiritual formulas are discovered necessary for the deeper penetration into the laws of nature.
— Albert Einstein
In letter (1 May 1935), Letters to the Editor, 'The Late Emmy Noether: Professor Einstein Writes in Appreciation of a Fellow-Mathematician', New York Times (4 May 1935), 12.
Since the mathematicians have invaded the theory of relativity, I do not understand it myself anymore.
— Albert Einstein
Quoted as “Einstein once joked”, in Carl Seelig, Albert Einstein: A Documentary Biography (1956), 28.
The formulation of a problem is often more essential than its solution, which may be merely a matter of mathematical or experimental skill. To raise new questions, new possibilities, to regard old problems from a new angle requires creative imagination and marks real advances in science.
— Albert Einstein
In Albert Einstein and Léopold Infeld, The Evolution of Physics: The Growth of Ideas from Early Concepts to Relativity and Quanta (1938, 1966), 92.
The importance of C.F. Gauss for the development of modern physical theory and especially for the mathematical fundament of the theory of relativity is overwhelming indeed; also his achievement of the system of absolute measurement in the field of electromagnetism. In my opinion it is impossible to achieve a coherent objective picture of the world on the basis of concepts which are taken more or less from inner psychological experience.
— Albert Einstein
Quoted in G. Waldo Dunnington, Carl Friedrich Gauss: Titan of Science (2004), 350.
The physicists say that I am a mathematician, and the mathematicians say that I am a physicist. I am a completely isolated man and though everybody knows me, there are very few people who really know me.
— Albert Einstein
…...
The present theory of relativity is based on a division of physical reality into a metric field (gravitation) on the one hand and into an electromagnetic field and matter on the other hand. In reality space will probably be of a uniform character and the present theory will be valid only as a limiting case. For large densities of field and of matter, the field equations and even the field variables which enter into them will have no real significance. One may not therefore assume the validity of the equations for very high density of field and matter, and one may not conclude that the 'beginning of the expansion' must mean a singularity in the mathematical sense. All we have to realise is that the equations may not be continued over such regions.
— Albert Einstein
In O. Nathan and H. Norden (eds.), Einstein on Peace (1960), 640.
There exists a passion for comprehension, just as there exists a passion for music. That passion is rather common in children but gets lost in most people later on. Without this passion, there would be neither mathematics nor natural science.
— Albert Einstein
'On the Generalized Theory of Gravitation', Scientific American (Apr 1950). Collected in David H. Levy (ed.), The Scientific American Book of the Cosmos (2000), 13.
What is this frog and mouse battle among the mathematicians?
— Albert Einstein
As quoted in an anecdote, without citation, in Howard W. Eves Mathematical Circles Squared (1972), 133. The comment applied to editorial disagreements between L.E.J. Brouwer and David Hilbert while on the staff of Mathematische Annalen. Einstein was “so disturbed by the controversy that he resigned” his position as one of the principal editors.
Yes, we have to divide up our time like that, between our politics and our equations. But to me our equations are far more important, for politics are only a matter of present concern. A mathematical equation stands forever.
— Albert Einstein
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See also:
- 14 Mar - short biography, births, deaths and events on date of Einstein's birth.
- Albert Einstein - Context of “God … integrates empirically” quote - Medium image (500 x 350 px)
- Albert Einstein - Context of “Laws of mathematics refer to reality” quote
- Albert Einstein - Context of “Laws of mathematics refer to reality” quote - with Large image (800 x 600 px).
- Albert Einstein - Context of “God … integrates empirically” quote - Large image (800 x 600 px)
- Albert Einstein - context of quote Mathematics…a product of human thought - Medium image (500 x 350 px)
- Albert Einstein - context of quote Mathematics…a product of human thought - Large image (800 x 600 px)
- Large color picture of Albert Einstein (850 x 1000 px).
- Albert Einstein - context of quote “Politics is more difficult than physics” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “Politics is more difficult than physics” - Large image (800 x 600 px)
- Albert Einstein - context of quote “Science without religion is lame; religion without science is blind.” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “Science without religion is lame; religion without science is blind.” - Large image (800 x 600 px)
- Albert Einstein - My Theory - The Times (1919).
- Geometry and Experience - Address by Albert Einstein to the Prussian Academy of Sciences (27 Jan 1921).
- Even Einstein's Little Universe Is Big Enough - New York Times article (2 Feb 1921).
- Albert Einstein - context of quote The Lord God is subtle - Medium image (500 x 350 px)
- Albert Einstein - context of quote The Lord God is subtle - Large image (800 x 600 px)
- Albert Einstein - context of quote Imagination is more important than knowledge - Medium image (500 x 350 px)
- Albert Einstein - context of quote Imagination is more important than knowledge - Large image (800 x 600 px)
- Albert Einstein - context of quote A theory can be proved by experiment - Medium image (500 x 350 px)
- Albert Einstein - context of quote A theory can be proved by experiment - Large image (800 x 600 px)
- Albert Einstein - context of quote Falling in love is not at all the most stupid thing - Medium image (500 x 350 px)
- Albert Einstein - context of quote Falling in love is not at all the most stupid thing - Large image (800 x 600 px)
- Albert Einstein - context of quote That is relativity - Medium image (500 x 350 px)
- Albert Einstein - context of quote That is relativity - Large image (800 x 600 px)
- Albert Einstein - context of quote “One thing I have learned in a long life” - Medium image (500 x 350 px)
- Albert Einstein - context of quote One thing I have learned in a long life - Large image (800 x 600 px)
- Albert Einstein - context of quote “Why is the electron negative?” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “Why is the electron negative?” - Large image (800 x 600 px)
- Albert Einstein - context of quote “The formulation of a problem is often far more essential than its solution” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “The formulation of a problem is often far more essential than its solution” - Large image (800 x 600 px)
- Albert Einstein - context of quote “Our exalted technological progress” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “Our exalted technological progress” - Large image (800 x 600 px)
- Albert Einstein - context of quote “There exists a passion for comprehension” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “There exists a passion for comprehension” - Large image (800 x 600 px)
- Albert Einstein - context of quote “An equation is for eternity” - Medium image (500 x 350 px)
- Albert Einstein - context of quote “An equation is for eternity” - Large image (800 x 600 px)
- Subtle Is the Lord: The Science and the Life of Albert Einstein, by Abraham Pais. - book suggestion.
- Booklist for Albert Einstein.
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) -- 
