"As soon as science has emerged from its initial stages, theoretical advances are no longer achieved merely by a process of arrangement. Guided by empirical data, the investigator rather develops a system of thought which, in general, is built up logically from a small number of fundamental assumptions, the so-called axioms. We call such a system of thought a theory. The theory finds the justification for its existence in the fact that it correlates a large number of single observations, and it is just here that the 'truth' of the theory lies. " (Albert Einstein, "Relativity: The Special and General Theory ", 1916)
"No fairer destiny could be allotted to any physical theory, than that it should of itself point out the way to the introduction of a more comprehensive theory, in which it lives on as a limiting case. " (Albert Einstein, "Relativity, The Special and General Theory ", 1916)
"Since the introduction of the special principle of relativity has been justified, every intellect which strives after generalization must feel the temptation to venture the step towards the general principle of relativity." (Albert Einstein, 1917)
"The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them."(Albert Einstein, "Principles of Research ", 1918)
"Most teachers waste their time by asking questions which are intended to discover what a pupil does not know whereas the true art of questioning has for its purpose to discover what the pupil knows or is capable of knowing." (Albert Einstein, 1920)
"The discovery of Minkowski […] is to be found […] in the fact of his recognition that the four-dimensional space-time continuum of the theory of relativity, in its most essential formal properties, shows a pronounced relationship to the three-dimensional continuum of Euclidean geometrical space. In order to give due prominence to this relationship, however, we must replace the usual time co-ordinate t by an imaginary magnitude, √-1*ct, proportional to it. Under these conditions, the natural laws satisfying the demands of the (special) theory of relativity assume mathematical forms, in which the time co-ordinate plays exactly the same role as the three space-coordinates. Formally, these four co-ordinates correspond exactly to the three space co-ordinates in Euclidean geometry." (Albert Einstein,"Relativity: The Special and General Theory", 1920)
"A geometrical-physical theory as such is incapable of being directly pictured, being merely a system of concepts. But these concepts serve the purpose of bringing a multiplicity of real or imaginary sensory experiences into connection in the mind. To ‘visualise’ a theory, or bring it home to one's mind, therefore means to give a representation to that abundance of experiences for which the theory supplies the schematic arrangement " (Albert Einstein, "Geometry and Experience ", 1921)
"Geometry thus completed is evidently a natural science; we may in fact regard it as the most ancient branch of physics. Its affirmations rest essentially on induction from experience, but not on logical inferences only. We call this 'practical geometry'. [...] The question whether the practical geometry of the universe is Euclidean or not has a clear meaning, and its answer can only be furnished by experience." (Albert Einstein, [lecture] 1921)
"It seems that the human mind has first to construct forms independently, before we can find them in things. Kepler’s marvelous achievement is a particularly fine example of the truth that knowledge cannot spring from experience alone, but only from the comparison of the inventions of the intellect with observed fact." (Albert Einstein, 1930)
"Physics is the attempt at the conceptual construction of a model of the real world and its lawful structure. " (Albert Einstein, [letter to Moritz Schlick] 1931)
"It can scarcely be denied that the supreme goal of all theory is to make the irreducible basic elements as simple and as few as possible without having to surrender the adequate representation of a single datum of experience. " (Albert Einstein, [lecture] 1933)
"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, [Obituary for Emmy Noether], 1935)
"Creating a new theory is not like destroying an old barn and erecting a skyscraper in its place. It is rather like climbing a mountain, gaining new and wider views, discovering unexpected connections between our starting point and its rich environment. But the point from which we started out still exists and can be seen, although it appears smaller and forms a tiny part of our broad view gained by the mastery of the obstacles on our adventurous way up. " (Albert Einstein & Leopold Infeld, "The Evolution of Physics ", 1938)
"Most of the fundamental ideas of science are essentially simple, and may, as a rule, be expressed in a language comprehensible to everyone." (Albert Einstein & Leopold Infeld, "The Evolution of Physics", 1938)
"Physical concepts are free creations of the human mind, and are not, however it may seem, uniquely determined by the external world In our endeavor to understand reality we are somewhat like a man trying to understand the mechanism of a closed watch. He sees the face and the moving hands, even hears its ticking, but he has no way of opening the case. If he is ingenious he may form some picture of a mechanism which could be responsible for all the things he observes, but he may never be quite sure his picture is the only one which could explain his observations. He will never be able to compare his picture with the real mechanism and he cannot even imagine the possibility of the meaning of such a comparison." (Albert Einstein & Leopold Infeld, "The Evolution of Physics ", 1938)
"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 & Leopold Infeld, "The Evolution of Physics", 1938)
"With the help of physical theories we try to find our way through the maze of observed facts, to order and understand the world of our sense impressions. " (Albert Einstein & Leopold Infeld, "The Evolution of Physics ", 1938)
"The development of science and of creative activities of the spirit in general requires still another kind of freedom, which may be characterized as inward freedom. It is this freedom of the spirit which consists in the independence of thought from the restrictions of authoritarian and social prejudices as well as from unphilosophical routinizing and habit in general." (Albert Einstein, "On Freedom", 1940)
"When the number of factors coming into play in a phenomenological complex is too large, scientific method in most cases fails us. One need only think of the weather, in which case prediction even for a few days ahead is impossible. Nevertheless no one doubts that we are confronted with a causal connection whose causal components are in the main known to us.
Occurrences in this domain are beyond the reach of exact prediction because of the variety of factors in operation, not because of any lack of order in nature." (Albert Einstein, "Science and Religion", 1941)
"The words of the language, as they are written or spoken, do not seem to play any role in any mechanism of thought. The physical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be 'voluntarily' reproduced or combined. […] But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought - before there is any connection with logical construction in words or other kinds of signs which can be communicated to others. The above-mentioned elements are, in my case, of visual and some of muscular type. Conventional words or other signs have to be sought for laboriously only in a secondary stage, when the mentioned associative play is sufficiently established and can be reproduced at will. " (Albert Einstein, [letter to Hadamard, in (Jacques Hadamard, "The Psychology of Invention in the Mathematical Field,1945)])
"A theory is the more impressive the greater the simplicity of its premises is, the more different kinds of things it relates, and the more extended its area of applicability." (Albert Einstein, "Autobiographical Notes", 1949)
"In speaking here of ‘comprehensibility’, the expression is used in its most modest sense. It implies: the production being produced by the creation of general concepts, relations between these concepts and sense experience. It is in this sense that the world of our sense experiences is comprehensible. The fact that it is comprehensible is a miracle." (Albert Einstein, "Out of My Later Years", 1950)
"Physics too deals with mathematical concepts; however, these concepts attain physical content only by the clear determination of their relation to the objects of experience." (Albert Einstein, "Out of My Later Years", 1950)
"Science is the attempt to make the chaotic diversity of our sense-experience correspond to a logically uniform system of thought." (Albert Einstein, "Out of My Later Years", 1950)
"Space-time does not claim existence on its own, but only as a structural quality of the field." (Albert Einstein, 1954)
"The important point for us to observe is that all these constructions and the laws connecting them can be arrived at by the principle of looking for the mathematically simplest concepts and the link between them. In the limited number of mathematically existent simple field types, and the simple equations possible between them, lies the theorist’s hope of grasping the real in all its depth." (Albert Einstein, "Ideas and Opinions", 1954)
"The supreme task of the physicist is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can reach them." (Albert Einstein,"Ideas and Opinions", 1954)
"The theory of relativity is a fine example of the fundamental character of the modern development of theoretical science. The initial hypotheses become steadily more abstract and remote from experience. On the other hand, it gets nearer to the grand aim of all science, which is to cover the greatest possible number of empirical facts by logical deduction from the smallest possible number of hypotheses or axioms." (Albert Einstein, 1954)
"We have thus assigned to pure reason and experience their places in a theoretical system of physics. The structure of the system is the work of reason: the empirical contents and their mutual relations must find their representation in the conclusions of the theory. In the possibility of such a representation lie the sole value and justification of the whole system, and especially of the concepts and fundamental principles which underlie it. Apart from that, these latter are free inventions of human intellect, which cannot be justified either by the nature of that intellect or in any other fashion a priori." (Albert Einstein, "Ideas and Opinions", 1954)
"What distinguishes the language of science from language as we ordinarily understand the word? […] What science strives for is an utmost acuteness and clarity of concepts as regards their mutual relation and their correspondence to sensory data." (Albert Einstein, "Ideas and Opinions", 1954)
"When a man after long years of searching chances upon a thought which discloses something of the beauty of this mysterious universe, he should not therefore be personally celebrated. He is already sufficiently paid by his experience of seeking and finding." (Albert Einstein, [The New York Times] 1978)
"All great achievements in science start from intuitive knowledge, namely, in axioms, from which deductions are then made. […] Intuition is the necessary condition for the discovery of such axioms. " (Albert Einstein)
"Equations are more important to me, because politics is for the present, but an equation is something for eternity. " (Albert Einstein)
"How can it be that mathematics, a product of human thought independent of experience, is so admirably adapted to the objects of reality." (Albert Einstein)
"It is a miracle that curiosity survives formal education. " (Albert Einstein)
"It is an outcome of faith that nature - as she is perceptible to our five senses - takes the character of such a well formulated puzzle. " (Albert Einstein)
"It stands to the everlasting credit of science that by acting on the human mind it has overcome man's insecurity before himself and before nature. " (Albert Einstein)
"It’s not that I’m so smart, it’s just that I stay with problems longer." (Albert Einstein)
"Look deep, deep, deep into nature, and then you will understand everything." (Albert Einstein)
"Our experience hitherto justifies us in believing that nature is the realization of the simplest conceivable mathematical ideas. " (Albert Einstein)
"That deep emotional conviction of the presence of a superior reasoning power, which is revealed in the incomprehensible universe, forms my idea of God. " (Albert Einstein)
"The aim [of education] must be the training of independently acting and thinking individuals who, however, see in the service to the community their highest life achievement." (Albert Einstein)
"The supreme task is to arrive at those universal elementary laws from which the cosmos can be built up by pure deduction. There is no logical path to these laws; only intuition, resting on sympathetic understanding of experience, can lead to them." (Albert Einstein)
"The truth of a theory is in your mind, not in your eyes." (Albert Einstein)
"Truth is what stands the test of experience. " (Albert Einstein)
"To raise new questions, new possibilities, to regard old problems from a new angle, requires creative imagination and marks real advance in science." (Albert Einstein)
"We can not solve our problems with the same level of thinking that created them." (Albert Einstein)
"What I’m really interested in is whether God could have made the world in a different way; that is, whether the necessity of logical simplicity leaves any freedom at all. " (Albert Einstein)
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