Keith Devlin knew that his July 2 Distinguished Lecture, “When Mathematics Changed the World,” had an obvious title. Math has always had a hand in changing the world. But Devlin made it clear that he wasn’t at the MAA Carriage House Conference Center to present a lengthy list of mathematical advances. Instead, he focused on the key “times in history when something…happened in mathematics that…changed the way ordinary people think about their lives.”

Devlin posited that three such mathematical events radically reshaped the way we live. The invention of counting, which dates back nearly 35,000 years, was at the top of his list. Devlin described some of the ancient uses of counting, such as keeping track of the moon and the seasons, and the ways counting records were kept, from notches in bones to markings on stones. **Audio **

Devlin noted that abstract numbers did not come into existence until about 8000 B.C., when the Sumerians began using them to keep track of property and goods in their developing society. As Sumerian bankers improved their system of counting, they developed a society built around numbers.

The second historically significant mathematical event occurred when people began to apply numbers to business and trade. One landmark was the publication of *Liber Abaci* by Leonardo de Pisa, better known as Fibonacci. The volume introduced the Hindu-Arabic number system to Europe and showed the value of applying modern arithmetic to the commercial world.

*Liber Abaci *allowed people to run their own businesses by teaching them concepts such as calculating interest, conversion rates, and bookkeeping. Devin conceded that it may be “the dullest book ever written,” but added that it undoubtedly “changed everything.”

Leonardo’s writings had a domino effect all the way to the 16th century and the work of Galileo Galilei, who was able to take number the world beyond commerce. Quantifying things such as temperature, mass, and velocity meant that people could start to determine how one thing would affect another.

The third and final event Devlin touched upon was a series of letters sent in 1654 in which Blaise Pascal and Pierre de Fermat attempted to calculate the odds of a dice game. Devlin described how this correspondence laid the foundation for modern probability theory and helped people begin to predict the future using numbers. **Audio**

The two famous mathematicians were attempting to solve a seemingly simple problem in a world that was devoid of statistics and probability, making the task more difficult than we would now imagine. Their solution to the dice game problem quickly led to advances in the field of probability.

“Once you are able to quantify risk, you can begin to do much more elaborate things,” Devlin concluded.

We may currently be in the midst of a fourth dynamic change, one spearheaded by the mobile phone, Devlin said. Always being connected to our entire community is changing the way we interact with each other.

“When you phone somebody up, you no longer say ‘who is it?’, you ask ‘where are you?’” Devlin said. “And that’s a very different view of space and distance.”

Listen to Keith Devlin's lecture (mp3)

This MAA Distinguished Lecture was funded by the National Security Agency.