Edward Kasner: Difference between revisions

Edward Kasner
Edward Kasner
	Photograph of Kasner dated 1907.
Born	April 2, 1878; New York City, United States
Died	January 7, 1955 (aged 76); New York City, United States
Nationality	American
Alma mater	City College of New York (BA); Columbia University (MA, PhD)
Known for	Kasner metric; Kasner polygon; "googol"
	Scientific career
Fields	Mathematics
Institutions	Columbia University
Doctoral advisor	Felix Klein; David Hilbert
Doctoral students	Rufus Isaacs; Joseph Ritt; Jesse Douglas ; Edna Kramer

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Edward Kasner (April 2, 1878 – January 7, 1955) was an American mathematician who was appointed Tutor on Mathematics in the Columbia University Mathematics Department. Kasner was the first Jewish person appointed to a faculty position in the sciences at Columbia University.^[1] Subsequently, he became an adjunct professor in 1906, and a full professor in 1910, at the university. Differential geometry was his main field of study. In addition to introducing the term "googol", he is known also for the Kasner metric and the Kasner polygon.^[2]

Education[edit]

Kasner's 1899 PhD dissertation at Columbia University was titled The Invariant Theory of the Inversion Group: Geometry upon a Quadric Surface; it was published by the American Mathematical Society in 1900 in their Transactions.

Googol and googolplex[edit]

Kasner is perhaps best remembered today for introducing the term "googol." In order to pique the interest of children, Kasner sought a name for a very large number: one followed by 100 zeros. On a walk in the New Jersey Palisades with his nephews, Milton (1911–1981)^[3] and Edwin Sirotta, Kasner asked for their ideas. Nine-year-old Milton suggested "googol".^[4]

In 1940, with James R. Newman, Kasner co-wrote a non-technical book surveying the field of mathematics, called Mathematics and the Imagination (ISBN 0-486-41703-4). It was in this book that the term "googol" was first popularized:

Words of wisdom are spoken by children at least as often as 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.
— ^[5]

The Internet search engine "Google" originated from a misspelling of "googol",^[6]^[7]^[8] and the "Googleplex" (the Google company headquarters in Mountain View, California) is similarly derived from googolplex.

Personal life[edit]

Kasner was Jewish and was the son of Austrian immigrants.^[9]

Works[edit]

Kasner, E. (1900). "The Invariant Theory of the Inversion Group: Geometry Upon a Quadric Surface". Transactions of the American Mathematical Society. 1 (4): 430–498. doi:10.1090/S0002-9947-1900-1500550-1. hdl:2027/miun.abv0510.0001.001. JSTOR 1986367.
Kasner, Edward (1980) [1934]. "Differential-geometric aspects of dynamics". In C. Carpelan; A. Parpola; P. Koskikallio (eds.). The Logarithmic potential and other monographs. New York: Chelsea. pp. 235–263. ISBN 0-8284-0305-8.
Kasner, Edward; Newman, James R. (April 2001) [London: Penguin, 1940; New York: Simon and Schuster, 1967]. Mathematics and the Imagination. Dover Pubns. ISBN 0-486-41703-4.
Edward Kasner and James R. Newman, Mathematics and the Imagination, Tempus Books of Microsoft Press, 1989. ISBN 1-55615-104-7
Kasner, Edward (July 1914). "The Ratio of the Arc to the Chord of an Analytic Curve Need Not Be Unity". Bulletin of the American Mathematical Society. 20 (10): 524–31. doi:10.1090/S0002-9904-1914-02545-5.
Kasner, Edward (1921). "Geometrical theorems on Einstein's cosmological equations". Amer. J. Math. 43 (4). The Johns Hopkins University Press: 217–221. Bibcode:1921AmJM...43..217K. doi:10.2307/2370192. JSTOR 2370192.

References[edit]

^ Columbia and the "Jewish Problem”
^ Douglas, Jesse (1958) Edward Kasner, A Biographical Memoir prepared for the National Academy of Sciences.
^ There have been several dates reported in the literature, ranging from 1911 to 1929, but only 1911 is consistent with family records (Bialik).
^ Bialik, Carl (June 14, 2004). "There Could Be No Google Without Edward Kasner". The Wall Street Journal Online. (retrieved March 17, 2015)
^ Kasner, Edward; Newman, James R. (1989), Mathematics and the Imagination, Tempus Books of Microsoft Press, p. 23, ISBN 1-55615-104-7
^ Koller, David. "Origin of the name, "Google" Archived 2012-06-27 at the Wayback Machine, Stanford University January 2004.
^ Hanley, Rachael. "From Googol to Google: Co-founder returns Archived 2006-12-14 at the Wayback Machine", The Stanford Daily February 12, 2003 (retrieved July 14, 2006).
^ Bylund, Anders. "To Google or Not to Google", The Motley Fool via MSNBC. July 5, 2006 (retrieved July 7, 2006).
^ "Edward Kasner". MacTutor.

External links[edit]

[1] Columbia and the "Jewish Problem”

[2] Douglas, Jesse (1958) Edward Kasner, A Biographical Memoir prepared for the National Academy of Sciences.

[3] There have been several dates reported in the literature, ranging from 1911 to 1929, but only 1911 is consistent with family records (Bialik).

[4] Bialik, Carl (June 14, 2004). "There Could Be No Google Without Edward Kasner". The Wall Street Journal Online. (retrieved March 17, 2015)

[5] Kasner, Edward; Newman, James R. (1989), Mathematics and the Imagination, Tempus Books of Microsoft Press, p. 23, ISBN 1-55615-104-7

[6] Koller, David. "Origin of the name, "Google" Archived 2012-06-27 at the Wayback Machine, Stanford University January 2004.

[7] Hanley, Rachael. "From Googol to Google: Co-founder returns Archived 2006-12-14 at the Wayback Machine", The Stanford Daily February 12, 2003 (retrieved July 14, 2006).

[8] Bylund, Anders. "To Google or Not to Google", The Motley Fool via MSNBC. July 5, 2006 (retrieved July 7, 2006).

[9] "Edward Kasner". MacTutor.

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+{{short description|American mathematician (1878–1955)}}
-'''Edward Kasner''' (1878&ndash;1955), ([[City College of New York]] 1897; [[Columbia University]] M.A., 1897; Columbia University [[Doctor of Philosophy|Ph.D.]], 1900), who studied  under [[Cassius Jackson Keyser]], was a prominent [[Jewish]] [[United States|American]] [[mathematician]] who was appointed Tutor on [[Mathematics]] in the Columbia University Mathematics Department. Kasner was the first [[Jew]] appointed to a faculty position in the sciences at Columbia University.<ref>Columbia and the "Jewish Problem” http://beatl.barnard.columbia.edu/stand_columbia/TimelineCUJew.html</ref>
+{{Infobox scientist
+| name = Edward Kasner
+| image = PSM V70 D187 Edward Kasner.jpg
+| image_size = | alt =
+| caption = Photograph of Kasner dated 1907.
+| birth_date = {{birth date|1878|04|02|mf=y}}
+| birth_place = [[New York City]], United States
+| death_date = {{nowrap|{{death date and age|1955|01|07|1878|04|02|mf=y}}}}
+| death_place = [[New York City]], United States
+| nationality = American
+| fields = [[Mathematics]]
+| workplaces = [[Columbia University]]
+| alma_mater = {{nowrap|[[City College of New York]] {{smaller|(BA)}}}}<br>{{nowrap|[[Columbia University]] {{smaller|(MA, PhD)}}}}
+| doctoral_advisor = [[Felix Klein]]<br/>[[David Hilbert]]
+| academic_advisors =
+| doctoral_students =[[Rufus Isaacs (game theorist)|Rufus Isaacs]]<br/>[[Joseph Ritt]]<br/>[[Jesse Douglas]] <br/> [[Edna Kramer]]
+| known_for = [[Kasner metric]]<br/>[[Kasner polygon]]<br/>"[[googol]]"
+| awards =
+}}
+'''Edward Kasner''' (April 2, 1878&nbsp;– January 7, 1955) was an American [[mathematician]] who was appointed Tutor on [[Mathematics]] in the [[Columbia University]] Mathematics Department. Kasner was the first [[Jewish]] person appointed to a faculty position in the sciences at Columbia University.<ref>[https://web.archive.org/web/20121221005651/http://beatl.barnard.columbia.edu/stand_columbia/TimelineCUJew.html Columbia and the "Jewish Problem”]</ref> Subsequently, he became an adjunct professor in 1906, and a full professor in 1910, at the university. [[Differential geometry]] was his main field of study. In addition to introducing the term "[[googol]]", he is known also for the [[Kasner metric]] and the [[Kasner polygon]].<ref>Douglas, Jesse (1958) [http://www.nasonline.org/publications/biographical-memoirs/memoir-pdfs/kasner-edward.pdf Edward Kasner, A Biographical Memoir] prepared for the ''National Academy of Sciences''.</ref>
-Kasner's Ph.D. [[dissertation]] was titled ''The Invariant Theory of the Inversion Group''.
-== Googol ==
+==Education==
+Kasner's 1899 PhD [[dissertation]] at Columbia University was titled ''The Invariant Theory of the Inversion Group: Geometry upon a Quadric Surface''; it was published by the [[American Mathematical Society]] in 1900 in their ''Transactions''.
-Kasner is perhaps best remembered today for introducing the term "[[googol]]".  In or about 1920, in order to pique the interest of children, Kasner sought a name for a very large number: one followed by a hundred zeros.  On a walk in the [[New Jersey Palisades]] with his nephews, Milton (1911&ndash;1980) and Edwin Sirotta, Kasner asked for their ideas. Nine-year-old Milton suggested "googol".
+== Googol and googolplex ==
-In 1940, with [[James R. Newman]], Kasner co-wrote a non-technical book surveying the field of mathematics, called ''[[Mathematics and the Imagination]]'' (ISBN 0-486-41703-4). It was in this book that the term "googol" was first introduced:
+Kasner is perhaps best remembered today for introducing the term "googol." In order to pique the interest of children, Kasner sought a name for a very large number: one followed by 100 zeros.  On a walk in the [[New Jersey Palisades]] with his nephews, Milton (1911–1981)<ref>There have been several dates reported in the literature, ranging from 1911 to 1929, but only 1911 is consistent with family records (Bialik).</ref> and Edwin Sirotta, Kasner asked for their ideas. Nine-year-old Milton suggested "googol".<ref>{{cite journal  | title = There Could Be No Google Without Edward Kasner  | first = Carl | last = Bialik  | journal = The Wall Street Journal Online  | date = June 14, 2004 |url=https://www.wsj.com/articles/SB108575924921724042 }} (retrieved March 17, 2015)</ref>
+In 1940, with [[James R. Newman]], Kasner co-wrote a non-technical book surveying the field of mathematics, called ''[[Mathematics and the Imagination]]'' ({{ISBN|0-486-41703-4}}). It was in this book that the term "googol" was first popularized:
-{{quotation|Words of wisdom are spoken by children as least as often by scientists. The name "[[googol]]" was invented by a child (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 [[Primo Carnera|Carnera]]  a better mathematician than [[Albert Einstein|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, much bigger even than a googol times a googol. A googol times a googol would be 1 with 200 zeros, whereas a googolplex is one with a googol of zeros. 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.|<ref>Edward Kasner and James R. Newman, ''Mathematics and the Imagination'',Tempus Books of [[Microsoft Press]], 1989, p. 23.</ref>}}
+{{quotation|Words of wisdom are spoken by children at least as often as 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 [[Primo Carnera|Carnera]]  a better mathematician than [[Albert Einstein|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.|<ref>{{citation|first1=Edward|last1=Kasner|first2=James R.|last2=Newman|title=Mathematics and the Imagination|publisher=Tempus Books of [[Microsoft Press]]|year=1989|isbn=1-55615-104-7|page=[https://archive.org/details/isbn_9781556151040/page/23 23]|url-access=registration|url=https://archive.org/details/isbn_9781556151040/page/23}}</ref>}}
-== Google ==
-Kasner's number naming legacy includes technology unforeseen in his lifetime. The [[Internet]] search engine "[[Google]]" originated from a misspelling of "[[googol]]",<ref>Koller, David. "[http://graphics.stanford.edu/~dk/google_name_origin.html Origin of the name, "Google"], ''[[Stanford University]]'' January 2004.</ref><ref>Hanley, Rachael. "[http://daily.stanford.org/article/2003/2/12/fromGoogolToGoogle From Googol to Google: Co-founder returns]", ''[[The Stanford Daily]]'' [[February 12]] [[2003]] (retrieved [[July 14]] [[2006]]).</ref> which refers to 10<sup>100</sup> (the number represented by a 1 followed by 100-zeros).<ref>Bylund, Anders. "[http://msnbc.msn.com/id/13720643/ To Google or Not to Google]", ''[[The Motley Fool]] via [[MSNBC]]''. [[July 5]] [[2006]] (retrieved [[July 7]] [[2006]]).</ref>
+The [[Internet]] search engine "[[Google]]" originated from a misspelling of "[[googol]]",<ref>Koller, David. "[http://graphics.stanford.edu/~dk/google_name_origin.html Origin of the name, "Google"] {{webarchive |url=https://web.archive.org/web/20120627081942/http://graphics.stanford.edu/~dk/google_name_origin.html |date=2012-06-27 }}, ''[[Stanford University]]'' January 2004.</ref><ref>Hanley, Rachael. "[http://daily.stanford.org/article/2003/2/12/fromGoogolToGoogle From Googol to Google: Co-founder returns] {{Webarchive|url=https://web.archive.org/web/20061214223016/http://daily.stanford.org/article/2003/2/12/fromGoogolToGoogle |date=2006-12-14 }}", ''[[The Stanford Daily]]'' February 12, 2003 (retrieved July 14, 2006).</ref><ref>Bylund, Anders. "[https://web.archive.org/web/20060707062623/http://msnbc.msn.com/id/13720643/ To Google or Not to Google]", ''[[The Motley Fool]] via [[MSNBC]]''. July 5, 2006 (retrieved July 7, 2006).</ref> and the "[[Googleplex]]" (the Google company headquarters in [[Mountain View, Santa Clara County, California|Mountain View]], [[California]]) is similarly derived from ''[[googolplex]]''.
-The "[[Googleplex]]" is the Google company headquarters, located at 1600 Amphitheatre Parkway in [[Mountain View, Santa Clara County, California|Mountain View]], [[Santa Clara County, California|Santa Clara County]], [[California]], near [[San Jose, California|San Jose]].
+==Personal life==
+Kasner was [[Jew]]ish and was the son of [[Austria]]n [[immigrant]]s.<ref>{{Cite web|url=https://mathshistory.st-andrews.ac.uk/Biographies/Kasner/#reference-4|title=Edward Kasner|work=MacTutor}}</ref>
+==Works==
-Googleplex is a play on words for ''[[googolplex]]'', the name given by Kasner's nephew to the large number:
+* {{cite journal | jstor = 1986367 | pages = 430–498 | last1 = Kasner | first1 = E. | title = The Invariant Theory of the Inversion Group: Geometry Upon a Quadric Surface | volume = 1 | issue = 4 | journal = [[Transactions of the American Mathematical Society]] | year = 1900 | doi = 10.1090/S0002-9947-1900-1500550-1 | hdl = 2027/miun.abv0510.0001.001 | url = http://name.umdl.umich.edu/ABV0510.0001.001 | hdl-access = free }}
-::::::::: <math>\mbox{googolplex} = {10}^{\mbox{googol}} = {10}^{({10}^{100})} </math>
-(the number represented by a 1 followed by a googol of zeros).
-==References==
 * {{cite book
  | last = Kasner | first = Edward
  | year = 1980
  | chapter = Differential-geometric aspects of dynamics
- | origyear = 1934
+ | orig-year = 1934
- | editor = C.Carpelan, A.Parpola P.Koskikallio (ed.)
+ | editor = C. Carpelan |editor2=A. Parpola |editor3=P. Koskikallio
  | title = The Logarithmic potential and other monographs
- | pages = pp. 235-263
+ | pages = 235–263
  | location = New York
  | publisher = Chelsea
- | id = ISBN 0-8284-0305-8
+ | isbn = 0-8284-0305-8
  }}
 * {{cite book
  | last = Kasner | first = Edward
- | coauthors = Newman, James R.
+ |author2=Newman, James R.
- | title = Mathematics and the Imagination
+ | title = [[Mathematics and the Imagination]]
- | origyear = London: Penguin, [[1940]]; New York: Simon and Schuster, [[1967]]
+ | orig-year = London: Penguin, 1940; New York: Simon and Schuster, 1967
  | publisher = Dover Pubns
- | year = April [[2001]]
+ | date = April 2001
- | id = ISBN 0-486-41703-4
+ | isbn = 0-486-41703-4
+ }}
+* Edward Kasner and James R. Newman, ''[[Mathematics and the Imagination]]'', Tempus Books of [[Microsoft Press]], 1989. {{ISBN|1-55615-104-7}}
+* {{cite journal
+ | last = Kasner | first = Edward
+ | title = The Ratio of the Arc to the Chord of an Analytic Curve Need Not Be Unity
+ | journal = Bulletin of the American Mathematical Society
+ | date = July 1914 | volume = 20 | pages = 524–31
+ | doi = 10.1090/S0002-9904-1914-02545-5
+ | issue = 10
+ | doi-access = free
  }}
-* Edward Kasner and James R. Newman, ''Mathematics and the Imagination'', Tempus Books of [[Microsoft Press]], 1989. ISBN 1556151047
 * {{cite journal
  | last = Kasner | first = Edward
  | title = Geometrical theorems on Einstein's cosmological equations
  | journal = Amer. J. Math.
- | year = 1921 | volume = 43 | pages = 217
+ | year = 1921 | volume = 43 | pages = 217–221
+ | doi = 10.2307/2370192
- }}
+ | issue = 4
-* {{cite journal
+ | publisher = The Johns Hopkins University Press
- | title = There Could Be No Google Without Edward Kasner
+ | jstor = 2370192
- | first = Carl | last = Bialik
+ | bibcode = 1921AmJM...43..217K}}
- | journal = The Wall Street Journal Online
- | date = [[June 14]] [[2004]]
- }}
-== Footnotes ==
+==References==
+{{Reflist}}
-<references/>
 ==External links==
-* [http://www.google.com/corporate/history.html History from the Google website]
+* [https://www.google.com/corporate/history.html History from the Google website]
+* {{MathGenealogy|37342}}
+{{Authority control}}
-[[Category:American Jews|Kasner, Edward]]
-[[Category:Jews|Kasner, Edward]]
-[[Category:Jewish scientists|Kasner, Edward]]
-[[Category:American mathematicians|Kasner, Edward]]
-[[Category:American scientists|Kasner, Edward]]
-[[Category:1878 births|Kasner, Edward]]
-[[Category:1955 deaths|Kasner, Edward]]
-[[Category:Differential geometers|Kasner, Edward]]
-[[Category:19th century mathematicians|Kasner, Edward]]
-[[Category:20th century mathematicians|Kasner, Edward]]
+{{DEFAULTSORT:Kasner, Edward}}
-[[de:Edward Kasner]]
-[[eu:Edward Kasner]]
+[[Category:1878 births]]
-[[fr:Edward Kasner]]
+[[Category:1955 deaths]]
+[[Category:Jewish American scientists]]
-[[it:Edward Kasner]]
+[[Category:Differential geometers]]
-[[lv:Edvards Kāzners]]
+[[Category:19th-century American mathematicians]]
-[[lb:Edward Kasner]]
+[[Category:20th-century American mathematicians]]
-[[nl:Edward Kasner]]
+[[Category:City College of New York alumni]]
-[[ja:エドワード・カスナー]]
+[[Category:Columbia University alumni]]
-[[simple:Edward Kasner]]
+[[Category:Columbia University faculty]]
+[[Category:American people of German-Jewish descent]]
+[[Category:American Jews]]

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