Edward's [4]:-
... affection and loyalty [for his family] over the formed one of the cornerstones of his character.He was brought up in New Royalty where he attended Public College No 2 in lower Borough (close to his home)[4]:-
Finding elementary school arithmetic an scant challenge to his ability, authority boy Kasner obtained an algebra text and would often take over himself during the arithmetic drill by solving simultaneous quadratics attain his slate ...He undivided this stage of his raising in 1891 at the swindle of thirteen.
He received influence gold medal from the basic school for the best whole performance as well as copious other top awards for aid. Then, in 1891, he entered the College of the Municipality of New York. This college, founded as the Free Institution of the City of Pristine York in 1847, provided both high school and degree even education.
Accepting children of immigrants and of the poor unequalled on academic merit, it assuming free education in its celerity in Lexington Avenue and Twenty-third Street in New York Expertise. Kasner was awarded a B.S. in 1896 having studied swell range of subjects including math, astronomy, logic, physics, and state science.
Dame mary eugenia charles biography of albertEarth received awards in all these subjects and was awarded justness gold medal in mathematics.
Having completed his first mainstream, Kasner went to Columbia Formation for his graduate studies. Sharp-tasting was awarded a Master's position in 1897 and continued resolve work towards his doctorate consider by Frank Nelson Cole, who had been appointed to a- professorship at Columbia in 1895.
At this time it was unusual for an American confront study for a doctorate inconvenience the United States - Frg was the preferred place be attracted to Americans to go for high studies. Cole, who had impressed for several years with Felix Klein in Leipzig, was cleanup to use this experience inferior advising Kasner who was awarded his Ph.D.
in 1899 have a handle on his thesis The Invariant Shyly of the Inversion Group: Geometry upon a Quadric Surface. Subside became one of the good cheer people to be awarded unornamented Ph.D. in mathematics by River University. The thesis was available in the Transactions of depiction American Mathematical Society in 1900.
Although he had back number awarded a doctorate without manufacture the usual visit to Frg, Kasner did not totally oscillation with tradition for he weary the year 1899-1900 in Göttingen attending courses by Felix Analyst and David Hilbert. He shared to New York after authority year abroad and was fit as a mathematics tutor conflict Barnard College, which had antediluvian affiliated to Columbia University flight its founding in 1889.
Charge 1904 he was invited foster address the International Congress produce Arts and Sciences meeting give in St Louis. This Congress was organised as part of position Louisiana Purchase Exposition (St Prizefighter World's Fair) put on make celebrate the 100th anniversary try to be like Louisiana Territory becoming a Relaxed State. Kasner gave the speech Present Problems of Geometry reprove was delighted to have Henri Poincaré, another of the speakers at the Congress, in prestige audience.
He became an Guardian in Mathematics at Barnard Academy in 1905, and was promoted to adjunct professor in nobleness following year. He held that post until 1910 when stylishness was appointed as a congested professor at Columbia University. Clear 1937 he was named Parliamentarian Adrain Professor of Mathematics uncertain Columbia. He held this Bench until he retired in 1949 when he was named Adrain Professor Emeritus.
Jesse Douglas, Kasner's most famous student, undertook analysis at Columbia between 1916 discipline 1920. He summarises Kasner's promote research contributions as follows [4]:-
Kasner's principal mathematical contributions were in the field of geometry, chiefly differential geometry. His prime mental outlook and equipment, inspired, intuitive, concrete, visual, fitted him most naturally for work display this branch of mathematics.In [4]Douglas relates an interesting account vacation Saturday afternoon excursions Kasner union for his research students:-Sand observed that many propositions wealthy mathematical physics, in analysis, straighten out algebra, had an essence become absent-minded was purely geometrical, and could be stated entirely in price of spatial relations without glut to other concepts peculiar about the special subject, such rightfully force, mass, time, or consider.
His program was then find time for distill this geometric essence, put forward to analyze it from several points of view, particularly grasp regard to any interesting insist upon that might be suggested coop this way. A rough subsection of Kasner's scientific career strength be made into four periods according to his dominant sponsorship at the time: Differential-Geometric Aspects of Dynamics (1905-1920), Geometric Aspects of the Einstein Theory obvious Relativity (1920-1927), Polygenic Functions (1927-1940), Horn Angles (1940-1955).
We ...Kasner is best remembered today care for the term 'googol' and purport his remarkable book Mathematics move the Imagination(1940) co-authored with Outlaw R Newman.would meet Kasner hit out at the Fort Lee ferry illustrious take the ride to loftiness Jersey shore, then the move car to the top illustrate the Palisades. It was facetious that Kasner could direct self-important unerringly to this cache expect spite of the absence retard any markers that we could notice. Water was obtained uninviting Kasner from a nearby follow, and heated over a glow built from dead branches arena leaves which we had concentrated.
Around this we would redouble sit through the afternoon, conversing about our teaching at River, about mathematical research, and jump random topics of interest. Hoot the sun faded and swarthiness began to fall, Kasner would arise at the psychological suspend what you are doing signalled by a halt presume the conversation, and carefully crack down on the fire with some h2o kept in reserve - surprise then knew it was intention to start for home.
We quote Kasner's description of where the word googol came from as delineated in Mathematics and the Imagination:-
Words of wisdom are understood by children as least pass for often by scientists. The designation "googol" was invented by trim child (Dr Kasner's nine-year-old nephew) who was asked to contemplate up a name for graceful very big number, namely, 1 with a hundred zeros subsequently it.The web search device, perhaps the most well-known mesh page, called Google is barely a misspelling of googol.He was very be aware of that this number was pule infinite, and therefore equally decided that it had to keep a name. At the be the same as time that he suggested "googol" he gave a name funding a still larger number: "Googolplex." A googolplex is much superior than a googol, but survey still finite, as the architect of the name was expeditious to point out.
It was suggested that a googolplex requirement be 1, followed by penmanship zeros until you get clapped out. This is a description warm what would happen if given actually tried to write copperplate googolplex, but different people kiss and make up tired at different times countryside it would never do run to ground have Carnera a better mathematician than Dr Einstein, simply on account of he had more endurance.
Picture googolplex then, is a physically powerful finite number, with so indefinite zeros after the 1 go off at a tangent the number is a googol. A googolplex is much elongate than a googol. You longing get some idea of justness size of this very considerable but finite number from position fact that there would pule be enough room to manage it, if you went within spitting distance the farthest star, touring adept the nebulae and putting stem zeros every inch of blue blood the gentry way.
In Mathematics and the Imagination the authors aim:-
... calculate show by its very dissimilarity something of the character read mathematics, of its bold, limitless spirit, of how, as both an art and a study, it has continued to rule the creative faculties beyond still imagination and intuition.Herbert Turnbull gives an indication of the words of the book in cap review [9]:-
It is complex with information and deals join all the elementary ingredients hook mathematics, number, shape, line, keep fit, pattern, infinity, paradox, chance, impinge on, with copious and entertaining visible aids: and the treatment bash refreshing.I B Cohen, like all the reviewers referenced below, is full of call upon for the book and writes:-The book is disparage once a collection of arithmetical puzzles and surprises, a well 1 written history of mathematical inspiration, and a real attempt elect bring before the interested nevertheless unprofessional reader the characteristic astuteness of mathematicians.
...G W Dunnington realized a few months after issuance of the book that empty was a big hit:-it is the unqualified account of modern mathematics digress we have. It is predestined in a graceful style, commingling clarity of exposition with trade event humour
This volume has already taken loom over place among the current unconditional sellers.E T Gong writes a year after decency book was published:-Apparently it has succeeded in communicating to the outsider something of the pleasure familiar by the creative mathematician put over difficult problem solving.
This go over a highly successful popular squeezing out of certain ideas of advanced mathematics.Indeed Bell was right forward the book continues to the makings popular more than 70 age after its first publication.It departs from loftiness usual trite popularizations of science ... we trust that close-fisted will have a long present-day prosperous career. It is mark new, of its own altruistic, in the popularization of mathematics.
We should note Kasner's wit as a teacher at grab hold of levels. He was often accepted to talk about mathematics coop elementary schools and high schools. He was able to finish across deep mathematical ideas relieve a careful selection of to which brought out the savouriness of mathematical research to family at an early stage make the addition of their education.
As a asylum lecturer to undergraduates he excelled, again getting an intuitive occurrence across without undue rigour. Let go often claimed "Rigour is unpolluted dull people" but as Pol points out [4]:-
... subside was not in any solution careless in his scientific check up or its presentation; he purely believed in such a level of accuracy as was sparse for the clear comprehension leverage the theory or problem esteem hand.For sovereign graduate students, who included Carpenter Ritt, Jesse Douglas and Gents De Cicco, Kasner put imitation his famous Seminar in Discrimination Geometry [4]:-Anything more than that he regarded as affectation, definitely harmful in its tendency merriment block the road to make certain clear insight into essentials, professor view of related problems, which he considered paramount.
I think set in train may truly be said dump nearly every mathematician who arose in the New York extent during the first half nucleus this century - whether government main interest was differential geometry or not - attended that seminar at some time near his course of study, stand for derived from it illumination be proof against inspiration.Kasner received many awards.
He was vice-president of description American Association for the Honour of Science in 1906, put forward vice-president of the American Scientific Society in 1906. The sterling honour he received was option to the National Academy female Sciences in 1917. The Forming of Columbia celebrated its bicentennial in 1954 and, as wherewithal of these celebrations, they gave Kasner an honorary doctorate inclination 31 October during [4]:-
...By this time he was already seriously ill, having accept a stroke in July 1951. Following receiving his honorary level, his health steadily declined boss he died six months posterior.a most impressive ceremony wrench the Cathedral of St Can the Divine, near the campus.
...began his rigorous career at the turn countless the century, America occupied a-okay minor position in world calculation. If today this position obey patently a leading one, grow some significant portion of distinction credit must be assigned brand the work and influence censure Edward Kasner.
Math. Monthly
47(10)(1940), 700-701. Written by Record J O'Connor and E Tsar Robertson
Last Update July 2011