... affection and loyalty [for his family] over the years formed one of the cornerstones of his character.

Finding elementary school arithmetic an insufficient challenge to his ability, the boy Kasner obtained an algebra text and would often occupy himself during the arithmetic lesson by solving simultaneous quadratics on his slate ...

Kasner's principal mathematical contributions were in the field of geometry, chiefly differential geometry. His basic mental outlook and equipment, imaginative, intuitive, concrete, visual, fitted him most naturally for work in this branch of mathematics. He observed that many propositions in mathematical physics, in analysis, in algebra, had an essence that was purely geometrical, and could be stated entirely in terms of spatial relations without reference to other concepts peculiar to the special subject, such as force, mass, time, or number. His program was then to distill this geometric essence, and to analyze it from various points of view, particularly with regard to any interesting problems that might be suggested in this way. A rough subdivision of Kasner's scientific career might be made into four periods according to his dominant interest at the time: Differential-Geometric Aspects of Dynamics (1905-1920), Geometric Aspects of the Einstein Theory of Relativity (1920-1927), Polygenic Functions (1927-1940), Horn Angles (1940-1955).

We ... would meet Kasner at the Fort Lee ferry and take the ride to the Jersey shore, then the trolley car to the top of the Palisades. On the way to the woods we might stop to buy some cookies; these were to consume with the tea which Kasner brewed in a pot, dug up from its hiding place under a log, where it had been left at the end of the previous excursion. It was amusing that Kasner could direct us unerringly to this cache in spite of the absence of any markers that we could notice. Water was obtained by Kasner from a nearby stream, and heated over a fire built from dead branches and leaves which we had gathered. Around this we would then sit through the afternoon, conversing about our teaching at Columbia, about mathematical research, and about random topics of interest. As the sun faded and darkness began to fall, Kasner would arise at the psychological moment signalled by a halt in the conversation, and carefully extinguish the fire with some water kept in reserve - we then knew it was time to start for home.

Words of wisdom are spoken by children as least as often by scientists. The name "googol" was invented by a child (Dr Kasner's nine-year-old nephew) who was asked to think up a name for a very big number, namely, 1 with a hundred zeros after it. He was very certain that this number was not infinite, and therefore equally certain that it had to have a name. At the same time that he suggested "googol" he gave a name for a still larger number: "Googolplex." A googolplex is much larger than a googol, but is still finite, as the inventor of the name was quick to point out. It was suggested that a googolplex should be 1, followed by writing zeros until you get tired. This is a description of what would happen if one actually tried to write a googolplex, but different people get tired at different times and it would never do to have Carnera a better mathematician than Dr Einstein, simply because he had more endurance. The googolplex then, is a specific finite number, with so many zeros after the 1 that the number is a googol. A googolplex is much bigger than a googol. You will get some idea of the size of this very large but finite number from the fact that there would not be enough room to write it, if you went to the farthest star, touring all the nebulae and putting down zeros every inch of the way.

... to show by its very diversity something of the character of mathematics, of its bold, untrammeled spirit, of how, as both an art and a science, it has continued to lead the creative faculties beyond even imagination and intuition.

It is packed with information and deals with all the elementary ingredients of mathematics, number, shape, line, series, pattern, infinity, paradox, chance, change, with copious and entertaining visual aids: and the treatment is refreshing. The book is at once a collection of mathematical puzzles and surprises, a pleasantly written history of mathematical thought, and a real attempt to bring before the interested but unprofessional reader the characteristic findings of mathematicians.

... it is the best account of modern mathematics that we have. It is written in a graceful style, combining clarity of exposition with good humour

This volume has already taken its place among the current best sellers. Apparently it has succeeded in communicating to the layman something of the pleasure experienced by the creative mathematician in difficult problem solving.

This is a highly successful popular presentation of certain ideas of modern mathematics. It departs from the usual trite popularizations of mathematics ... we trust that it will have a long and prosperous career. It is something new, of its own kind, in the popularization of mathematics.

... he was not in any sense careless in his scientific work or its presentation; he simply believed in such a degree of accuracy as was sufficient for the clear comprehension of the theory or problem at hand. Anything more than this he regarded as affectation, positively harmful in its tendency to block the road to that clear insight into essentials, and view of related problems, which he considered paramount.

I think it may truly be said that nearly every mathematician who arose in the New York area during the first half of this century - whether his main interest was differential geometry or not - attended this seminar at some time during his course of study, and derived from it illumination and inspiration.

... a most impressive ceremony in the Cathedral of St John the Divine, near the campus.

... began his mathematical career at the turn of the century, America occupied a minor position in world mathematics. If today this position is patently a leading one, then some significant portion of the credit must be assigned to the work and influence of Edward Kasner.