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Thumbnail of Albert Einstein (source)
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.


Albert Einstein Quote
“Mathematics and Reality”

Illustrated Quote - Large Image (800 x 600 px)


“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
Addresss to Prussian Academy of Sciences (1921)

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Albert Einstein, Lecturing in Vienna, 1921.
Albert Einstein, Lecturing in Vienna, 1921. (source)
The Context of Albert Einstein's “Laws of mathematics refer to reality” Quote

When Albert Einstein delivered his lecture “Geometry and Experience” at the Prussian Academy of Science in Berlin on 27 January 1921, he spoke in German. An English translation was published, in which the quotes as we know them can be found. He began:

One reason why mathematics enjoys special esteem, above all other sciences, is that its laws are absolutely certain and indisputable, while those of all other sciences are to some extent debatable and in constant danger of being overthrown by newly discovered facts.

In spite of this, the investigator in another department of science would not need to envy the mathematician if the laws of mathematics referred to objects of our mere imagination, and not to objects of reality. For it cannot occasion surprise that different persons should arrive at the same logical conclusions when they have already agreed upon the fundamental laws (axioms), as well as the methods by which other laws are to be deduced therefrom. But there is another reason for the high repute of mathematics, in that it is mathematics which affords the exact natural sciences a certain measure of security, to which without mathematics they could not attain.

At this point an enigma presents itself which in all ages has agitated inquiring minds. 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.

In my opinion the answer to this question is, briefly, this:- 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.

Einstein then continued with the greater part of his talk, speaking about the nature of axioms in geometry, and he distinguished “practical geometry” from “purely axiomatic geometry.” From there Einstein moved on to consider the non-Euclidian three-dimensional universe which is finite, yet unbounded, and how he used that concept in his theory of relativity.

Text of complete lecture, “Geometry and Experience” >>


Context by Webmaster, including quoted section from “Geometry and Experience.” (source)


See also:
  • Science Quotes by Albert Einstein.
  • 14 Mar - short biography, births, deaths and events on date of Einstein's birth.
  • 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).
  • Large color picture of Albert Einstein (850 x 1000 px).
  • 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 “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)
  • 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 - 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.

Nature bears long with those who wrong her. She is patient under abuse. But when abuse has gone too far, when the time of reckoning finally comes, she is equally slow to be appeased and to turn away her wrath. (1882) -- Nathaniel Egleston, who was writing then about deforestation, but speaks equally well about the danger of climate change today.
Carl Sagan Thumbnail Carl Sagan: 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) ...(more by Sagan)

Albert Einstein: I used to wonder how it comes about that the electron is negative. Negative-positive—these are perfectly symmetric in physics. There is no reason whatever to prefer one to the other. Then why is the electron negative? I thought about this for a long time and at last all I could think was “It won the fight!” ...(more by Einstein)

Richard Feynman: It is the facts that matter, not the proofs. Physics can progress without the proofs, but we can't go on without the facts ... if the facts are right, then the proofs are a matter of playing around with the algebra correctly. ...(more by Feynman)
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