“Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that govern phenomena.”

—  Albert Einstein

From Lettre à Maurice Solvine, by A. Einstein (Gauthier-Villars: Paris 1956)
Attributed in posthumous publications, Albert Einstein: A guide for the perplexed (1979)

Adopted from Wikiquote. Last update Sept. 14, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "Physics is essentially an intuitive and concrete science. Mathematics is only a means for expressing the laws that gove…" by Albert Einstein?
Albert Einstein photo
Albert Einstein702
German-born physicist and founder of the theory of relativi… 1879–1955

Related quotes

William John Macquorn Rankine photo

“An essential distinction exists between two stages in the process of advancing our knowledge of the laws of physical phenomena; the first stage consists in observing the relations of phenomena, whether of such as occur in the ordinary course of nature, or of such as are artificially produced in experimental investigations, and in expressing the relations so observed by propositions called formal laws. The second stage consists in reducing the formal laws of an entire class of phenomena to the form of a science; that is to say, in discovering the most simple system of principles, from which all the formal laws of the class of phenomena can be deduced as consequences.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: "Outlines of the Science of Energetics," (1855), p. 121; Lead paragraph: Section "What Constitutes A Physical Theory"

Fritjof Capra photo

“If physics leads us today to a world view which is essentially mystical, it returns, in a way, to its beginning, 2,500 years ago. […] This time, however, it is not only based on intuition, but also on experiments of great precision and sophistication, and on a rigorous and consistent mathematical formalism.”

Fritjof Capra book The Tao of Physics

Source: The Tao of Physics (1975), Ch. 1, Modern Physics, p. 19.

“The assumptions and definitions of mathematics and science come from our intuition”

Richard Hamming (1915–1998) American mathematician and information theorist

Methods of Mathematics Applied to Calculus, Probability, and Statistics (1985)
Context: The assumptions and definitions of mathematics and science come from our intuition, which is based ultimately on experience. They then get shaped by further experience in using them and are occasionally revised. They are not fixed for all eternity.

E. W. Hobson photo

“The opinion appears to be gaining ground that this very general conception of functionality, born on mathematical ground, is destined to supersede the narrower notion of causation, traditional in connection with the natural sciences. As an abstract formulation of the idea of determination in its most general sense, the notion of functionality includes and transcends the more special notion of causation as a one-sided determination of future phenomena by means of present conditions; it can be used to express the fact of the subsumption under a general law of past, present, and future alike, in a sequence of phenomena. From this point of view the remark of Huxley that Mathematics "knows nothing of causation" could only be taken to express the whole truth, if by the term "causation" is understood "efficient causation." The latter notion has, however, in recent times been to an increasing extent regarded as just as irrelevant in the natural sciences as it is in Mathematics; the idea of thorough-going determinancy, in accordance with formal law, being thought to be alone significant in either domain.”

E. W. Hobson (1856–1933) British mathematician

Source: Presidential Address British Association for the Advancement of Science, Section A (1910), p. 290 ; Cited in: Moritz (1914, 29): The Nature of Mathematics.

Kim Stanley Robinson photo

“The world operates by number, by physical laws, expressed mathematically. If you know these, you will have a better grasp of things. And some possible job skills.”

Kim Stanley Robinson book The Years of Rice and Salt

Book 9: "Nsara", § 5
The Years of Rice and Salt (2002)

William John Macquorn Rankine photo

“Science Of Energetics. Although the mechanical hypothesis just mentioned may be useful and interesting as a means of anticipating laws, and connecting the science of thermodynamics with that of ordinary mechanics, still it is to be remembered that the science of thermodynamics is by no means dependent for its certainty on that or any other hypothesis, having been now reduced, to a system of principles, or general facts, expressing strictly the results of experiment as to the relations between heat and motive power. In this point of view the laws of thermodynamics may be regarded as particular cases of more general laws, applicable to all such states of matter as constitute Energy, or the capacity to perform work, which more general laws form the basis of the science of energetics, — a science comprehending, as special branches, the theories of motion, heat, light, electricity, and all other physical phenomena.”

William John Macquorn Rankine (1820–1872) civil engineer

Source: A Manual of the Steam Engine and Other Prime Movers (1859), p. 31

Kurt Lewin photo

“[Progress in psychology depends] upon keeping in mind that general validity of the law and concreteness of the individual case are not antitheses, and that reference to the totality of the concrete whole situation must take the place of reference to the largest possible historical collection of frequent repetitions. This means methodologically that the importance of a case, and its validity as proof, cannot be evaluated by the frequency of its occurrence. Finally, it means for psychology, as it did for physics, a transition from an abstract classificatory procedure to an essentially concrete constructive method.”

Kurt Lewin (1890–1947) German-American psychologist

Source: 1930s, A Dynamic Theory of Personality, 1935, p. 42 as cited in: Anthony C. Westerhof (1938) Representative psychologists. p. 48.

Richard Courant photo

“Mathematics as an expression of the human mind reflects the active will, the contemplative reason, and the desire for aesthetic perfection. Its basic elements are logic and intuition, analysis and construction, generality and individuality. Though different traditions may emphasize different aspects, it is only the interplay of these antithetic forces and the struggle for their synthesis that constitute the life, usefulness, and supreme value of mathematical science.”

Richard Courant (1888–1972) German American mathematician (1888-1972)

Richard Courant in: The Australian Mathematics Teacher, Volumes 39-40 http://books.google.co.in/books?id=CofxAAAAMAAJ, Australian Association of Mathematics Teachers, 1983, p. 3

“Science doesn’t give authentically access to the Real in the ontological meaning of the word, but only to the links between phenomena.”

Bernard d'Espagnat (1921–2015) French physicist and philosopher

in Une réouverture des chemins du sens, edited by [Jean Staune, Science et quête de sens, Presses de la Renaissance, 2005, 2750901251, 26]

Bernard Le Bovier de Fontenelle photo

“The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there… If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little.”

Bernard Le Bovier de Fontenelle (1657–1757) French writer, satirist and philosopher of enlightenment

Elements de la géométrie de l'infini (1727) as quoted by Amir R. Alexander, Geometrical Landscapes: The Voyages of Discovery and the Transformation of Mathematical Practice (2002) citing Michael S. Mahoney, "Infinitesimals and Transcendent Relations: The Mathematics of Motion in the Late Seventeenth Century" in Reappraisals of the Scientific Revolution, ed. David C. Lindberg, Robert S. Westman (1990)

Related topics