Origin of the Factorial Symbol !

Date: 01/14/2002 at 06:44:04
From: Julia Kolb
Subject: Origin of mathematical symbol !

My students would like to know the origin of the mathematical symbol 
for factorial - !.  Furthermore, was the symbol used as an exclamation 
mark in writing before it was used as a mathematical symbol?

Date: 01/14/2002 at 07:19:52
From: Doctor Peterson
Subject: Re: Origin of mathematical symbol !

Hi, Julia.

The Dr. Math FAQ includes a link to 

    Earliest Uses of Mathematical Symbols 
    http://jeff560.tripod.com/mathsym.html   

which is a great site to answer questions about the origin of math 
symbols. If you look up "!" there (under "probability and 
statistics"), you find that the symbol was used in place of an 
earlier notation that was less convenient for printers. The 
exclamation mark was already in use as punctuation, so printers did 
not need to add a special symbol. (It sounds like what we do these 
days using punctuation like "*" and "^" to avoid needing special 
fonts in e-mail.) The article quotes a complaint about this usage 
of symbols that already meant something:

    In his article "Symbols" in the Penny Cyclopaedia (1842) De Morgan
    complained: "Among the worst of barabarisms is that of introducing
    symbols which are quite new in mathematical, but perfectly
    understood in common, language. Writers have borrowed from the
    Germans the abbreviation n! to signify 1.2.3.(n - 1).n, which
    gives their pages the appearance of expressing surprise and
    admiration that 2, 3, 4, &c. should be found in mathematical
    results." 

I have to admit I often feel the same way! (Symbolic pun not 
intended.)

- Doctor Peterson, The Math Forum
  http://mathforum.org/dr.math/