Grace Hopper, Augustus De Morgan, John von Neumann, John Backus

The last three sketches in the book " Math Through the Ages: A Gentle History for Teachers and Others" are on "electronic computers," "logic and boolean algebra," and "infinity and the theory of sets," respectively. These sketches reference mathematicians such as Charles Babbage, Ada Lovelace, George Boole, Augustus De Morgan, John von Neumann, Herman Hollerith and Claude Shannon; however, they do not acknowledge Grace Murray Hopper.

About Grace Murray Hopper

A few years ago SCC's math department received a collection of math posters. The faculty took turns selecting a poster for their classroom and GDT selected a poster titled "Historic Women of Mathematics." ( Eton Press poster)

         Historic Women of Mathematics
     Talent realized through perseverance
   Hypatia of Alexandria (c. 370-416, Egypt)
      Sophie Germain (1776-1831, France)
     Sonya Kovalevsky (1850-1891, Russia)
   Amalie "Emmy" Noether (1882-1935, Germany)
      Grace Murray Hopper (1906-1992, USA)

GDT selected the poster because Grace Hopper is a member of his Computing DeadTeam.

Just like the book "Math Through the Ages," a couple of mathematical quotation resources fail to honor Grace Hopper. Furman University provides a Mathematical Quotation Server; however, it has no Grace Hopper quotes. The School of Mathematics and Statistics at the University of St Andrews Scotland has an extensive collection of mathematician quotes, but their collection is void of Grace Hopper quotes.

Grace Murray Hopper is considered the "mother" of computing. She was one of the first programmers of IBM's Automatic Sequence Controlled Calculator (the Harvard Mark I, 1944, sketch 23, page 179); during the late-1940s and early-1950s, Grace worked on the team that developed the first UNIVersal Automatic Computer (the UNIVAC I, sketch 23, page 180); Hopper created FLOW-MATIC (1st English-like data processing language) and its respective compiler during the mid-1950s (end of sketch 24, page 184); COBOL was strongly influenced by Hopper's work; and, Hopper is connected with the term computer bug. In 1969 Grace Hopper won the first "man of the year" award from the Data Processing Management Association; in 1986 she received the Defense Distinguished Service Medal; and in 1991 she received the National Medal of Technology. In the 21st century, the Grace Hopper Celebration of Women in Computing is held annually.

According to, Rear Admiral Grace Murray Hopper, USN, died on "1 January 1992 in Alexandria, Virginia; buried in Arlington Cemetery."

About Augustus De Morgan

The book "Math Through the Ages" (sketch 24) introduced readers to Augustus De Morgan, an Indian-born British mathematician and logician. De Morgan was born in 1806 and he died in 1871.

Mathematical quotation collections have found De Morgan quote-worthy.

The GDT::Computing DeadTeam, which list names in death date order, starts with Ada Lovelace, George Boole and Charles Babbage. Alexander Graham Bell was fourth followed by Herman Hollerith. Augustus De Morgan was not on the DeadTeam prior to reading "Math Through the Ages," but he is now taking over fourth place from Bell.

With respect to the logical operators AND, OR and NOT, De Morgan's Laws state the following.

   NOT (a or B) = NOT a AND NOT b
   NOT (a and B) = NOT a OR NOT b

De Morgan's laws are typically covered in introductory computer programming courses to help learn about logical expressions. The last time GDT did CSC100 (spring 2006), De Morgan's Laws were discussed in the Lecture Note for Day 11.

From John von Neumann to John Backus

Sketch 23 from the book "Math Through the Ages" referenced John von Neumann and his computer architecture idea of "stored programs." (In sketch 7 on page 92, the book mentioned that in 1949 von Neumann used the ENIAC to compute Pi to 2035 decimal digits.) John von Neumann died in 1957. John Backus, who is not mentioned in "Math Through the Ages," died on 17 March 2007. Backus led the team that invented the programming language Fortran. The first Fortran compiler was released in 1957. In 1954, Backus discussed Fortran with von Neumann prompting von Neumann to ask "why would you want more than machine language?" [Note: Fortran's life-span has been extended thanks to supercomputing.]

Nanosecond: Connecting Grace Hopper with ASU

Grace Hopper was quoted using the term nanosecond. (She also taught others about the microsecond and the picosecond.) GDT turned Hopper's nanosecond quote into a Basic Arithmetic Bit (BAB).

A couple of weeks after GDT discovered Hopper's use of the term nanosecond, the Chair of the Sun Angel Foundation used the term nanosecond when discussing how long it will take ASU to find a new athletic director. GDT turned this nanomoment into a Computing Bit. A few months later, ASU president Michael Crow started blogging and his first blog posting contained the term nanosecond.

Miscellaneous Grace Hopper Stuff
Related and External Hyperlinks

As a side-effect of working on this document, the Learning About Mathgurus (past and present) resource was instantiated.

Creator: Gerald D. Thurman []
Created: 27 April 2007

Creative Commons License
This work is licensed under a Creative Commons License.
How Hopper Taught About Micro- Nano- and Pico-seconds

The following was copied from the Wikipedia webpage on Grace Hopper.

   "Grace Hopper is famous for her nanoseconds visual aid. People 
    (such as generals and admirals) used to ask her why satellite 
    communication took so long. She started handing out pieces of 
    wire which were just under one foot long, which is the distance 
    that light travels in one nanosecond. She gave these pieces of 
    wire the metonym "nanoseconds." Later she used the same pieces 
    of wire to illustrate why computers had to be small to be fast. 
    At many of her talks and visits, she handed out "nanoseconds" 
    to everyone in the audience, contrasting them with a coil of 
    wire nearly a thousand feet long, representing a microsecond. 
    Later, while giving these lectures while working for DEC, she 
    passed out packets of pepper which she called picoseconds.