Math in Computer History

Date: 11/04/2000 at 20:21:45
From: Sarah
Subject: Computer history

I'm doing a major project on the history of computers, focusing on the 
mathematical issues and ideas. I am having difficulty finding any 
comprehensible information. I understand very little of what I have 
read and have found nothing related to the math involved in computing. 
I have thoroughly searched the Internet and looked in several books. 

Basically I need to know how math was involved in the invention of 
computers. Could you please tell me a way I can find this information 
in a format simple enough for a 10th-grade math student to understand? 

Thank you.

Date: 11/06/2000 at 13:22:27
From: Doctor TWE
Subject: Re: Computer history

Hi Sarah - thanks for writing to Dr. Math.

The role mathematics played in the history and development of 
computers is quite an involved subject, and I don't have the time or 
resources to give you a detailed accounting. What I can do, however, 
is give you some math topics and the names of some key mathematicians 
who were involved - looking them up (either using an Internet search 
engine or looking in encyclopedias, etc.) should get you started.

Here are some key mathematical topics in computing:

Binary or base-2: all data in computers is represented in binary.

Octal (base-8) and Hexadecimal (base-16): these number systems are 
often used as a "shorthand notation" for binary.

Boolean Algebra or Boolean Simplification: computer circuits are built 
out of digital logic gates. These gates perform basic logic operations 
that can be mathematically represented by Boolean algebra. Boolean 
algebra is also used in simplifying these circuits (i.e. making the 
circuits with as few electronic components as possible.)

Propositional Calculus or Symbolic Logic: a more broad-based study of 
logic. Boolean algebra is a "subtopic" in this larger field.

Karnaugh Mapping: related to Venn diagrams and Boolean algebra, 
Karnaugh maps are a graphical way to simplify logic circuits.

Coding and cyphering: the study of representing non-numeric data. All 
data in a computer is represented in some form of code or cypher.

Linear Algebra and Vectors: heavily used in video imaging - especially 
in 3D imaging.

Here are some mathematicians who have contributed significantly to 
the math behind computers. This is not a comprehensive list, and I've 
tried to stick primarily to those who have contributed to the 
theoretical underpinnings of computing, rather than the implementation 
of hardware or software.

Leon Battista Alberti (1400's): made a scientific study of perspective 
visualization. His mathematical interpretation of 3D objects as 2D 
images is the foundation of computer graphics.

Gottfried Leibnitz (1600's): described the binary number system.

Blaise Pascal (1600's): developed the first mechanical calculator.

Charles Babbage and Ada Lovelace (1800's): invented the first 
mechanical computer with stored program capabilities, and wrote the 
first algorithmic computer program.

George Boole (1800's): developed an algebraic system for logic 
(Boolean algebra.)

Herman Goldstone (1940's): invented the flowchart.

John W. Mauchly and William F. Schmitt (1940's): developed Short Code, 
the first "high-level" programming language.

Dr. Alan Turing (1950's): developed a "Turing Test" for determining 
machine intelligence.

Diffie-Hellman-Merkle (1970's): developed a key exchange algorithm 
(foundations of public key encryption.)

Fiat Shamir (1980's): developed zero-knowledge-based data encryption.

I hope this helps get you started. If you have any more questions, 
write back.

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