§CQ.1 THE FIRST GREAT ADVANCE in algebra after the Middle Ages was the general solution of the cubic equation, immediately followed by a solution for the quartic. I tell the full story in the next ...

In his book The Mathematical Universe, mathematician William Dunham wrote of John Venn’s namesake legacy, the Venn diagram, “No one in the long history of mathematics ever became better known for less ...

Would students take a stronger interest in math if they knew that an ancient African bone (from 20,000 B.C.) might be one of the world’s oldest known counting tools? Or that the work of Muslim ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...

A tablet that dates back some 3700 years has been found to be the oldest example of applied geometry in the history of mathematics. Australian mathematician Dr. Daniel Mansfield from UNSW Science's ...

Do you recall your high school geometry? Given isosceles triangle ABC, where side AB is equal to side BC, then angle A is also equal to angle C. That’s not something your math teacher invented—it’s a ...

Visit NAP.edu/10766 to get more information about this book, to buy it in print, or to download it as a free PDF. §14.2 Algebraic Topology. Topology is generally introduced as I described it in §AG.6, ...