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April 10, 2026
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"Young Prokofiev was attentive to new musical trends. We can find traces of various influences in his early compositions. Some of the piano works from the set Visions fugitives,op. 22 (1915–17), are reminiscent of Debussy; the Andante assai section of the First Piano Concerto, op. 10 (1911–12), sounds like Rachmaninov; and the harmonies of the symphonic poem Osen neye(Autumnor Autumnal Sketch), op. 8 (1910), harken back to Scriabin. These, however, were rather passing influences. Others proved to be more enduring. One of them was the fairy-tale streak in Russian music. Russians have always been fond of fairy tales, which to this day continue to be an important part of every child’s upbringing. ... Another significant influence was the Classical style."
"Prokofiev had a lifelong love of the sonata form. Ever since learning the basic rules during his childhood years, he strove to master them; … In 1941, describing his Sonatinas op. 54 (1931), he remarked, “I liked the idea of writing a simple work in such a superior form as sonata.” One can learn a lot about the composer’s growth by tracing his progress from the early sonatas, which cautiously dare to bend the textbook rules, to the masterful treatment of the form in his late works."
"A fellow student of Rachmaninoff's at the Moscow Conservatory, Lhevinne studied with Safonoff and made his debut in the Emperor Concerto with Anton Rubinstein conducting. As early as 1906 he made his American debut. (That was the year a young man named Arthur Rubinstein came over for the first time.) Lhevinne's remarkable powers were quickly recognized. His tone was like the morning stars singing together, his technique was flawless even measured against the fingers of Hofmann and Rachmaninoff, and his musicianship was sensitive. He was one of the modern romantics who did not have to pull music apart to get its message across. Even when he played Chopin's Etude in thirds and the octave Etude in B minor―his double notes and octaves were fabulous―he never tried to make a stunt of the music. One of his little tricks, the utmost he would permit himself in the way of outward panache, was to take the octave glissandos of the Brahms Paganini Variations prestissimo, staccato and pianissimo. He accomplished this, one guesses, with a rigidly tight wrist that was propelled by sheer nervous impulses. It provided a quasi-glissando that sounds impossible of achievement; but Lhevinne did it, to the amazement of pianists who heard him, and to the utter disbelief of those who didn't."
"Such axioms, together with other unmotivated definitions, serve mathematicians mainly by making it difficult for the uninitiated to master their subject, thereby elevating its authority."
"At the beginning of this century a self-destructive democratic principle was advanced in mathematics (especially by Hilbert), according to which all axiom systems have equal right to be analyzed, and the value of a mathematical achievement is determined, not by its significance and usefulness as in other sciences, but by its difficulty alone, as in mountaineering. This principle quickly led mathematicians to break from physics and to separate from all other sciences. In the eyes of all normal people, they were transformed into a sinister priestly caste . . . Bizarre questions like Fermat's problem or problems on sums of prime numbers were elevated to supposedly central problems of mathematics."
"In the middle of the twentieth century it was attempted to divide physics and mathematics. The consequences turned out to be catastrophic. Whole generations of mathematicians grew up without knowing half of their science and, of course, in total ignorance of any other sciences. They first began teaching their ugly scholastic pseudo-mathematics to their students, then to schoolchildren (forgetting Hardy's warning that ugly mathematics has no permanent place under the Sun)."
"It is almost impossible for me to read contemporary mathematicians who, instead of saying “Petya washed his hands,” write simply: “There is a t_1<0 such that the image of t_1 under the natural mapping t_1 \mapsto {\rm Petya}(t_1) belongs to the set of dirty hands, and a t_2, t_1, such that the image of t_2 under the above-mentioned mapping belongs to the complement of the set defined in the preceding sentence.”"
"A person, who had not mastered the art of the proofs in high school, is as a rule unable to distinguish correct reasoning from that which is misleading. Such people can be easily manipulated by the irresponsible politicians."
"In the last 30 years, the prestige of mathematics has declined in all countries. I think that mathematicians are partially to be blamed as well—foremost, Hilbert and Bourbaki—the ones who proclaimed that the goal of their science was investigation of all corollaries of arbitrary systems of axioms."
"All mathematics is divided into three parts: cryptography (paid for by CIA, KGB and the like), hydrodynamics (supported by manufacturers of atomic submarines) and celestial mechanics (financed by military and by other institutions dealing with missiles, such as NASA.)."
""In almost all textbooks, even the best, this principle is presented so that it is impossible to understand." (K. Jacobi, Lectures on Dynamics, 1842-1843). I have not chosen to break with tradition."
"When you are collecting mushrooms, you only see the mushroom itself. But if you are a mycologist, you know that the real mushroom is in the earth. There’s an enormous thing down there, and you just see the fruit, the body that you eat. In mathematics, the upper part of the mushroom corresponds to theorems that you see. But you don’t see the things which are below, namely problems, conjectures, mistakes, ideas, and so on. You might have several apparently unrelated mushrooms and are unable to see what their connection is unless you know what is behind."
"Mathematics is the part of physics where experiments are cheap."
"The axiomization and algebraization of mathematics, after more than 50 years, has led to the illegibility so such a large number of mathematical texts that the threat of complete loss of contact with physics and the natural sciences has been realized."
"Let me just say that Arnold was a geometer in the widest possible sense of the word, and that he was very fast to make connections between different fields."
"Science looks and observes and art see and foresees. Every great scientist has experienced a moment when the artist in him saved the scientist."
"I realized that the image I had been given by my teachers, the scientists.. ..by their way of looking at Nature, was just another stage setting with all the magnificence and ingenuity that the genius of any artist produces in a work of art. I realized that in my scientific journey I had been under the power of a magic spell of a work of art whose reality was just as true as the verity of the image in an artist's vision."
"From the very beginning of the Constructivist Movement it was clear to me that a constructed sculpture, by its very method and technique brings sculpture very near to architecture.. .My works of this time up to 1924.. ..are all in the search for an image which would fuse the sculptural element with the architectural element in one unit. I consider this Column the culmination of that search."
"What we cannot express by the art of thinking, by the art of Science or philosophy or logic, we can and should express by the poetic, visual, or some other arts. It is for that reason that I consider morals and aesthetics one and the same; for they cover only one impulse, one drive inherent in our consciousness - to bring our life and all our actions into a satisfactory relationship with the events of the world, as our consciousness want it to be, in harmony with our life and according to the laws of consciousness itself - Naum Gabo"
"The true artist always refuses to conform to any standards others than his own. That’s why the attacks in Russia against Shostakovitch and Prokofiev are identical to the attacks that have been made here against American pioneers of abstract painting like Davis, Holty, or Morris. In Russia it was Malevich and Gabo, in this country at the moment it is people like Rothko, Baziotes, Pollock, my self and many others who are being attacked. The names may vary, but the methods, the motives; the objects of attack are essentially the same. Only meritocracy is forever immune, because it is forever ready to conform. (his comment on the attacks on artistic freedom in 1948."
"The point they (Lissitzky, Rodchenko, Tatlin, Gabo, the neo-Plasticists, and so on) all had in common was to be inside and outside at the same time... For me, to be inside and outside is to be in an unheated studio with broken windows in the winter, or taking a nap on somebody’s porch in the summer."
"[The Constructive idea..] has revealed a universal law that the elements of a visual art such as lines, colours, shapes, possess their own forces of expression independent of any association with the external aspects of the world; that their life and action are self-conditioned psychological phenomena rooted in human nature; that those elements are not chosen by convention by any utilitarian or other reason as words and figures are, they are not merely abstract signs, but they are immediately and organically bound up with human emotions. The revelation of this fundamental law has opened up a vast field in art giving the possibility of expression to those human impulses and emotions which have been neglected."
"It needs a poet like Schwitters to show us that unobserved elements of beauty are strewn and spread all around us and we can find them everywhere in the portentous as well as in the insignificant, if only we care to look, to choose and to fit them into a comely order."
"There is no indication of success up to now in the bringing together of art and science. To achieve success the artist must be spiritually at home in the field of science so he can think and feel in the same way as the scientist. A spiritual union, not a technical one, is requested."
"He (Piet Mondrian) couldn't look after himself properly. He was terrible [sic] thin, and seemed to live mostly on currants and vegetable stew, because he followed the Haye diet."
"More often than not, [people] expect a painting to speak to them in terms other than visual, preferably in words, whereas when a painting or a sculpture needs to be supplemented and explained by words it means either that it has not fulfilled its function or that the public is deprived of vision,"
"Art and Science are two different streams which rise from the same creative force and flow into the same ocean of the common culture, but the currents of these two streams flow in different directions."
"If I were an academician.. ..or a believer in a higher reality outside me, as most people are (lucky creatures!), I would have no need for any justification for painting landscapes, or portraits, or social realism. I would rely on my so-called common sense, on which I see and feel, and I would enjoy it. Or I would fix one point in the distant haze of that unknown reality, would try to approach it as nearly as I could, and would find solace in the fanatical belief that I am the only one who is portraying that reality which is the only truth."
"We know only what we do, what we make, what we construct; and all that we make, all that we construct, are realities. I call them images, not in Plato's sense (namely that they are only reflections of reality), but I hold that these images are the reality itself and that there is no reality beyond this reality except when in our creative process we change the images: then we have created new realities."
"I have come to the conclusion that a work of art restricted to what the artist has put in it is only a part of itself. It only attains full stature with what people and time make of it. It involves the whole complex of human relation to life. It is a mode of thinking, acting, perceiving and living."
"No new artistic system will withstand the pressure of a growing new culture until the very foundation of Art will be erected on the real laws of life. Until all artists will say with us... All is a fiction... only life and its laws are authentic and in life only the active is beautiful and wise and strong and right, for life does not know beauty as an aesthetic measure... efficacious existence is the highest beauty. Life knows neither good nor bad nor justice as a measure of morals... need is the highest and most just of all morals. Life does not know rationally abstracted truths as a measure of cognizance, deed is the highest and surest of truths. Those are the laws of life. Can art withstand these laws if it is built on an abstraction, on mirage, and fiction?..."
"Space and time are the only forms on which life is built and hence art must be constructed... The realisation of our perceptions of the world in the forms of space and time is the only aim of our pictorial and plastic art... We renounce the thousand-year-old delusion in art that held the static rhythms as the only elements of the plastic and pictorial arts. We affirm in these arts a new element, the kinetic rhythms as the basic forms of our perception of real time."
"We take four planes and we construct with them the same volume as of four tons of mass."
"Either build functional houses and bridges or create pure art or both. Don't confuse one with the other. Such art is not pure constructive art, but merely an imitation of the machine."
"Up to now sculptors have preferred the mass and neglected or paid little attention to such an important component of mass as space.. ..we consider it as an absolute sculptural element. I do not hesitate to affirm that the perception of space is a primary natural sense which belongs to the basic senses of our psychology"
"The growth of new ideas is more difficult and lengthy the deeper they are rotted in life. Resistance to them is the more obsitnate and exasperated the more persistent their growth is."
"..adding Space perception to the perception of Masses, emphasizing it and forming it, we enrich the expression of Mass.. ..through the contrast between them whereby Mass retains its solidity and Space its extension."
"[ Constructivism is] not as a tool or even a specific method, but rather as a perfect union of the coming state and the movement's 'spiritual' aims."
"The shapes we are creating are not abstract, they are absolute."
"My intellect has been shaped under the sign of Spinoza's words, and it has tried not to be astounded, not to laugh, not to cry, but to understand."
"...In a few words, we can define the true relation of Spinozist teaching on passions to explanatory and descriptive psychology of emotions, saying that, practically speaking, this teaching on solving the one and only problem, the problem of a deterministic, causal explanation of what is higher in the life of human passions, also partially contains explanatory psychology, retaining the idea of causal explanation but rejecting the problem of the higher in human passions, and descriptive psychology, rejecting the idea of a causal explanation and retaining the problem of the higher in the life of human passions. Thus, forming its deepest and most internal nucleus, Spinoza's teaching contains specifically what is in neither of the two parts into which contemporary psychology of emotions has disintegrated: the unity of the causal explanation and the problem of the vital significance of human passions, the unity of descriptive and explanatory psychology of feelings. For this reason, Spinoza is closely connected with the most vital, the most critical news of the day for contemporary psychology of emotions, news of the day which prevails in it, determining the paroxysm of crisis that envelops it. The problems of Spinoza await their solution, without which tomorrow’s day in our psychology is impossible."
"The philosophical perspective opens before is at this point of our study. For the first time in the process of psychological studies we can resolve essentially purely philosophical problems by means of a psychological experiment and demonstrate empirically the origin of the freedom of human will. We cannot trace in all its completeness the philosophical perspective opening before us here. We expect to do this in another work devotes to philosophy. Now we shall try only to note this perspective in order to see most clearly the place we have reached. We cannot help but note that we have come to the same understanding of freedom and self-control that Spinoza developed in his “Ethics.”"
"From the great creations of Spinoza, as from distant stars, light takes several centuries to reach us. Only the psychology of the future will be able to realize the ideas of Spinoza."
"As in the focus of a magnifying glass, play contains all developmental tendencies in a condensed form and is itself a major source of development."
"Through others, we become ourselves."
"Our relationships as experimentalists with theoretical physicists should be like those with a beautiful woman – we should accept with gratitude any favours she offers, but we should not expect too much nor believe all that is said."
"There can be no doubt that our descendants will learn to exploit the energy of fusion for peaceful purposes even before its use becomes necessary for the preservation of human civilization."
"Science is a way to pursue one's sense of inquiry at the expense of the State."
"It would be interesting to use high temperatures - in the billions, which develop during atomic bomb explosions, for conducting synthetic reactions (for example, the formation of helium from hydrogen), which are the source of energy of stars and which could raise the energy liberated during the explosion of basic matter (uranium, bismuth, lead) even higher."
"One has to stress once again, that the mechanical world view and psychophysical interpretation accompanying it are based not on the instructions of the philosophizing mind, but on the clear and accurate facts discovered by experiment and observation; and in the cases of non-correspondence (very rare, fortunately) between the requirements of the mind and the facts, reason must adjust to the facts, and not vice versa."