H Marston Morse - Collected Quotes

"It is possible that analysis in the large may eventually reduce to topology, but not until topology has been greatly broadened. It is equally conceivable that the apparently less general situations which arise with such frequency in problems in analysis in the large may form the canonical cases about which the topology of the future can be built." (Marston Morse, "What is Analysis in the Large?", The American Mathematical Monthly Vol. 49 (6), 1942) 

"A definition is topological if it makes no use of mathematical elements other than those defined in terms of continuous deformations or transformations. Such deformations or transformations take the straightness out of planes and alter lengths and areas." (Marston Morse, "Equilibria in Nature: Stable and Unstable", Proceedings of the American Philosophical Society Vol. 93 (3), 1949)

"Mathematicians are led to new problems not only by way of contact with the world of physical experience but also by introspective study of the methods which they have elected to use. The trend of classical analysis has been to break up the object of study into finer and finer elements without end." (Marston Morse, "Equilibria in Nature: Stable and Unstable", Proceedings of the American Philosophical Society Vol. 93 (3), 1949)

"The concepts of an equilibrium theory are not put forward as a practical method of attaining an economic Utopia. Lack of economic data, knowledge, political and psychological understanding, are too obvious to permit this. Perhaps the greatest value which these considerations have is qualitative in nature. The implications are negative in the sense that the general mathematical theory of equilibria, points to the high a priori probability that any given state of equilibrium is unstable in character." (Marston Morse, "Equilibria in Nature: Stable and Unstable", Proceedings of the American Philosophical Society Vol. 93 (3), 1949)

"There is no conflict between science, philosophy and theology. What conflict there may be is due to a failure of agreement as to the implications of the word 'science'." (Marston Morse, "Science in the Modern World", Mathematics Magazine Vol. 28 (4), 1955)

"This continuity of effort is particularly important in mathematics. It is needed to realize the promise of unity which modern mathematics holds. In no science does it appear truer than- in mathematics that the relatively unexplained universe of known facts can be unified by theories of a general character, built of the bricks of current techniques, if only there could rise enough men of talent with a sense of values that would hold them to their task to the very end." (Marston Morse, "Science in the Modern World", Mathematics Magazine Vol. 28 (4), 1955)

"Mathematics are the result of mysterious powers which no one understands, and which the unconscious recognition of beauty must play an important part. Out of an infinity of designs a mathematician chooses one pattern for beauty's sake and pulls it down to earth." (Marston Morse, 1959)

"From its beginning critical point theory has been concerned with mutual relations between topology and geometric analysis, including differential geometry. Although it may have seemed to many to have been directed in its initial years toward applications of topology to analysis, one now sees that the road from topology to geometric analysis is a two-way street. Today the methods of critical point theory enter into the foundations of almost all studies of analysis or geometry 'in the large'." (Marston Morse & Stewart S Cairns, "Critical Point Theory in Global Analysis and Differential Topology: An Introduction", 1969)

"Mathematicians are finding that the study of global analysis or differential topology requires a knowledge not only of the separate techniques of analysis, differential geometry, topology, and algebra, but also a deeper understanding of how these fields can join forces." (Marston Morse & Stewart S Cairns, "Critical Point Theory in Global Analysis and Differential Topology: An Introduction", 1969)

"But mathematics is the sister, as well as the servant, of the arts and is touched with the same madness and genius." (Marston Morse)

"Discovery in mathematics is not a matter of logic. It is rather the result of mysterious powers which no one understands, and in which unconscious recognition of beauty must play an important part. Out of an infinity of designs, a mathematician chooses one pattern for beauty's sake and pulls it down to earth." (Marston Morse)

"Mathematicians of today are perhaps too exuberant in their desire to build new logical foundations for everything. Forever the foundation and never the cathedral." (Marston Morse)

"Most convincing to me of the spiritual relations between mathematics and music, is my own very personal experience. Composing in an amateurish way, I get exactly the same elevation from a prelude that has come to me at the piano, as I do from a new idea that has come to me in mathematics." (Marston Morse)

"The creative scientist lives in a 'wildness of logic,' where reason is the handmaiden and not the master." (Marston Morse)