We are perhaps too near the age of transition to see clearly the interplay of all that made for progress. Each of us has had his own peculiar training, his own personal contact with the mighty ones of the immediate past; and this forms as it were a telescopic tube determining limits to our field of vision. No doubt we may range the whole horizon; but after all we look from our own point of vantage.
cargill gilston knottMarcel Duchamp, one of this century’s pioneers, moved his work through the retinal boundaries which had been established with Impressionism into a field where language, thought and vision act upon one another. There it changed form through a complex interplay of new mental and physical materials, heralding many of the technical, mental and visual details to be found in more recent art.. ..He declared that he wanted to kill art (“for myself”) but his persistent attempts to destroy frames of reference altered our thinking, established new units of thought, a “new thought for that object”.
jasper johnsMusic is a means capable of expressing dark dramatism and pure rapture, suffering and ecstasy, fiery and cold fury, melancholy and wild merriment – and the subtlest nuances and interplay of these feelings which words are powerless to express and which are unattainable in painting and sculpture.
dmitri shostakovichMarcel Duchamp, one of this century’s pioneers, moved his work through the retinal boundaries which had been established with Impressionism into a field where language, thought and vision act upon one another. There it changed form through a complex interplay of new mental and physical materials, heralding many of the technical, mental and visual details to be found in more recent art.. ..He declared that he wanted to kill art (“for myself”) but his persistent attempts to destroy frames of reference altered our thinking, established new units of thought, a “new thought for that object”.
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.