Howard W Eves - Collected Quotes

"A formal manipulator in mathematics often experiences the discomforting feeling that his pencil surpasses him in intelligence." (Howard W Eves, "An introduction to the history of mathematics", 1953)

"An expert problem solver must be endowed with two incompatible qualities, a restless imagination and a patient pertinacity." (Howard Eves, "In Mathematical Circles", 1969)

"Mathematics may be likened to a large rock whose interior composition we wish to examine. The older mathematicians appear as persevering stone cutters slowly attempting to demolish the rock from the outside with hammer and chisel. The later mathematicians resemble expert miners who seek vulnerable veins, drill into these strategic places, and then blast the rock apart with well-placed internal charges."     (Howard W Eves, "In Mathematical Circles", 1969)

"Older mathematics appears static while the newer appears dynamic, so that the older mathematics compares to the still-picture stage of photography while the newer mathematics compares to the moving-picture stage. Again, the older mathematics is to the newer much as anatomy is to physiology, wherein the former studies the dead body and the latter studies the living body. Once more, the older mathematics concerned itself with the fixed and the finite while the newer mathematics embraces the changing and the infinite." (Howard W Eves, "In Mathematical Circles", 1969)

"The development of mathematics over the ages may be viewed as a continent slowly rising from the sea. At first perhaps a single island appears, and, as it grows in size, other islands emerge at varying distances from one another. As the continent continues to rise, some of the islands become joined to others by isthmuses that widen until pairs of islands become single large islands. At length a point is reached where the shape of the continent is essentially defined, and there remain only a number of lakes and inland seas of various sizes. As the continent further rises, these lakes and seas shrink and vanish one by one. The older mathematics compares to the situation when the general shape of the rising continent is still undefined and the land area consists largely of islands of different sizes. The newer mathematics compares to the situation when the general shape of the rising continent has become essentially clear, with most of the former islands now joined by stretches of land." (Howard W Eves, "In Mathematical Circles", 1969)

"A good problem should be more than a mere exercise; it should be challenging and not too easily solved by the student, and it should require some ‘dreaming’ time." (Howard W Eves)

"It is impossible to overstate the importance of problems in mathematics. It is by means of problems that mathematics develops and actually lifts itself by its own bootstraps. […] Every new discovery in mathematics, results from an attempt to solve some problem."   (Howard W Eves)