# Edward Kasner

Edward Kasner
Born April 2, 1878
New York City
Died January 7, 1955 (aged 76)
New York City
Nationality American
Fields Mathematics
Institutions Columbia University
Alma mater Columbia University (M.A., Ph.D.)
David Hilbert
Doctoral students John De Cicco
Rufus Isaacs
Joseph Ritt
Jesse Douglas

Edward Kasner (April 2, 1878 – January 7, 1955) was a prominent 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.[1] Subsequently, he became a full professor at the university. In addition to introducing the term "googol", he is known also for the Kasner metric and the Kasner polygon.

Kasner's Ph.D. dissertation 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

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 a hundred zeros. On a walk in the New Jersey Palisades with his nephews, Milton (March 8, 1911 - Feb. 1981)[2] and Edwin Sirotta, Kasner asked for their ideas. Nine-year-old Milton suggested "googol."

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:

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.

[3]

Kasner's number naming legacy includes technology unforeseen in his lifetime. The Internet search engine "Google" originated from a misspelling of "googol",[4][5] which refers to 10100 (the number represented by a 1 followed by 100-zeros).[6]

The "Googleplex" is the Google company headquarters, located at 1600 Amphitheatre Parkway in Mountain View, Santa Clara County, California, near San Jose.

Googleplex is a play on words for googolplex, the name given by Kasner's nephew to a number with that many zeros that you get tired from counting. Kasner assigned it to the large number:

$\mbox{googolplex} = {10}^{\mbox{googol}} = {10}^{({10}^{100})}$

(the number represented by a 1 followed by a googol of zeros).

## References

• 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. JSTOR 1986367.
• Kasner, Edward (1980) [1934]. "Differential-geometric aspects of dynamics". In C.Carpelan, A.Parpola P.Koskikallio (ed.). 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 Am. Math. Soc. 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. (The Johns Hopkins University Press) 43 (4): 217–221. doi:10.2307/2370192. JSTOR 2370192.
• Bialik, Carl (June 14, 2004). "There Could Be No Google Without Edward Kasner". The Wall Street Journal Online.
• Douglas, Jesse (1958) Edward Kasner, A Biographical Memoir prepared for the National Academy of Sciences.

## Footnotes

1. ^ Columbia and the "Jewish Problem” http://beatl.barnard.columbia.edu/stand_columbia/TimelineCUJew.html
2. ^ [1] Milton Sirotta in the Social Security Death Index
3. ^ Edward Kasner and James R. Newman, Mathematics and the Imagination, Tempus Books of Microsoft Press, 1989, p. 23.
4. ^ Koller, David. "Origin of the name, "Google", Stanford University January 2004.
5. ^ Hanley, Rachael. "From Googol to Google: Co-founder returns", The Stanford Daily February 12, 2003 (retrieved July 14, 2006).
6. ^ Bylund, Anders. "To Google or Not to Google", The Motley Fool via MSNBC. July 5, 2006 (retrieved July 7, 2006).