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

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

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

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

Works

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

^ 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

[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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@@ Line 1: / Line 1: @@
+{{short description|American mathematician (1878–1955)}}
 {{Infobox scientist
 | name = Edward Kasner
@@ Line 8: / Line 9: @@
 | death_date = {{nowrap|{{death date and age|1955|01|07|1878|04|02|mf=y}}}}
 | death_place = [[New York City]], United States
-| nationality = [[United States|American]]
+| nationality = American
 | fields = [[Mathematics]]
 | workplaces = [[Columbia University]]
-| alma_mater = {{nowrap|[[Columbia University]] {{smaller|(MA, PhD)}}}}
+| alma_mater = {{nowrap|[[City College of New York]] {{smaller|(BA)}}}}<br>{{nowrap|[[Columbia University]] {{smaller|(MA, PhD)}}}}
+| doctoral_advisor = [[Felix Klein]]<br/>[[David Hilbert]]
-| doctoral_advisor = [[Cassius Jackson Keyser]]<ref>Sooyoung Chang, ''Academic Genealogy of Mathematicians'', World Scientific, 2010, p. 405.</ref>
-| academic_advisors = [[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]]"
@@ Line 19: / Line 20: @@
 }}
-'''Edward Kasner''' (April 2, 1878&nbsp;– January 7, 10 BC) was a prominent [[United States|American]] [[mathematician]] who was appointed Tutor on [[Mathematics]] in the [[Edwardo University]] Mathematics Department. Kasner was the first [[Jew]] appointed to a faculty position in the sciences at Edwardo 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 "[[googie]]", he is known also for the [[hiler 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 'The Bill Nye Academy of Sciences''.</ref>
+'''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>
 ==Education==
@@ Line 29: / Line 30: @@
 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 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=23|url-access=registration|url=https://archive.org/details/isbn_9781556151040}}</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>}}
-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://www.webcitation.org/68ubHzYs7?url=http://graphics.stanford.edu/~dk/google_name_origin.html |date=2012-07-04 }}, ''[[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. "[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 [[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]]''.
+==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==
-* {{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 }}
+* {{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 }}
 * {{cite book
  | last = Kasner | first = Edward
  | year = 1980
  | chapter = Differential-geometric aspects of dynamics
- | origyear = 1934
+ | orig-year = 1934
  | editor = C. Carpelan |editor2=A. Parpola |editor3=P. Koskikallio
  | title = The Logarithmic potential and other monographs
@@ Line 51: / Line 54: @@
  |author2=Newman, James R.
  | 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
  | date = April 2001
@@ Line 64: / Line 67: @@
  | doi = 10.1090/S0002-9904-1914-02545-5
  | issue = 10
+ | doi-access = free
  }}
 * {{cite journal
@@ Line 81: / Line 85: @@
 ==External links==
 * [https://www.google.com/corporate/history.html History from the Google website]
-* {{MacTutor Biography|id=Kasner}}
 * {{MathGenealogy|37342}}
@@ Line 95: / Line 98: @@
 [[Category:City College of New York alumni]]
 [[Category:Columbia University alumni]]
-[[Category:Columbia University people]]
+[[Category:Columbia University faculty]]

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