## Introduction

Mathematics has been vital to the development of civilization; from ancient to
modern times it has been fundamental to advances in science, engineering, and philosophy.
As a result, the history of mathematics has become an important study; hundreds of books, papers, and web pages have addressed the
subject in a variety of different ways.

The purpose of this site is to present a small portion of the
history of mathematics through an investigation of some of the great problems that have
inspired mathematicians
throughout the ages. Included are problems that are suitable for middle school
and high school math students, with links to solutions, as well as links to
mathematicians' biographies and other math history sites.

*WARNING:*Some of the links on the page in this site lead to other math history sites. In particular, whenever
a mathematician's name is highlighted, you can follow it to link to his biography in the MacTutor
archives.

## Table of Contents

**The Bridges of Konigsberg** - This problem inspired
the great Swiss mathematician Leonhard Euler to create graph theory, which led to the development
of topology.
**The Value of Pi** - Throughout the history of civilization
various mathematicians have been concerned with discovering the value of and different expressions
for the ratio of the circumference of a circle to its diameter.

**Puzzling Primes** - To fully comprehend our number system,
mathematicians need to understand the properties of the prime numbers. Finding them isn't so easy,
either.

**Famous Paradoxes** - In the history of mathematical thought,
several paradoxes have challenged the notion that mathematics is a self-consistent system of knowledge. Presented here are Zeno's Paradox and Cantor's Infinities.

**The Problem of Points** - An age-old gambling problem led to the development of probability by French mathematicians Pascal and Fermat in the seventeenth century.

**A Proof of the Pythagorean Theorem** - One of the most
famous theorems in mathematics, the Pythagorean theorem has many proofs. Presented here is one
that relies on Euclidean algebraic geometry and is thus beautifully simple.

**A Proof that ***e* is irrational - A proof by contradiction that relies on the expression of e as a power series.

**
Book Reviews**

References

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**- by Isaac Reed**