# 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
Known for Kasner metric
Kasner polygon
googol

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 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.

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.

## 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 a hundred zeros. On a walk in the New Jersey Palisades with his nephews, Milton (born about 1929) 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: Milton Sirotta) 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.

[2]

Kasner's number naming legacy includes technology unforeseen in his lifetime. The Internet search engine "Google" originated from a misspelling of "googol",[3][4] which refers to 10100 (the number represented by a 1 followed by 100 zeros).[5]

The "Googleplex", the Google company headquarters in Mountain View, California, is a play on words for googolplex, the name given by Kasner's nephew to a number with so many zeros that one gets 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).