#### Dan Henderson, Millington, MD, *danielhenderson@cpm.org*

Tony Jones, Mahomet, IL *anthonyjones@cpm.org*

How confident are you in your knowledge of the history of mathematics? Try your hand at answering the following without the help of Google.

- In which culture did fractions originate?
- Why are there 360 degrees in a circle, 60 minutes in an hour, and 12 hours in each half of the day?
- Both the words Algebra and algorithm originate from which culture?
- Evidence of special right triangles can be found dating back to what century and which culture?
*Hint: It’s not the dude with his name attached to them.* - Where and why did the game Mancala originate?
- Which ancient civilization had the most accurate astronomical observations, including the length of a year and the moon’s cycle?
- There is evidence that Pascal’s Triangle was known for over 500 years before Pascal was born. In which century and which culture was this evidence found?
- The number series 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … are known today as the Fibonacci numbers. But, where did they originate?
*Hint: Not with the dude from Pisa.*

This is just the tip of the iceberg. Much of mathematics was born out of a desire to quantify, understand, and predict the world around us. It has a fascinating and incredible history that includes thousands of years and dozens of different cultures. Think of mathematics as the intellectual version of the Pando Tree, also known as the trembling giant, in southern Utah. It is a clonal colony of an individual male quaking aspen. It is determined to be a single living organism by identical genetic markers and assumed to have one massive underground root system. Similarly, the roots of mathematics may stretch deep and wide, but they are all part of the same system.

Unfortunately, very few of our students know the cultural background where many of our mathematical concepts originated. How many of our students have heard of the stories of the incredible accuracy and efficacy of mathematics from thousands of years ago? How many of our students, particularly students of color, have been able to identify with this rich history?

The recent release of the movie *Bill and Ted Face the Music* harkens back to our younger days and the original release when Bill and Ted’s history project was full of a bunch of “dead, white dudes.” If you have paid attention to mathematics and its history as taught in the United States, you have undoubtedly heard the names of Pythagoras, Euclid, Pascal, Fibonacci, Leibnitz, Euler and a plethora of others. Do you notice what all these mathematicians have in common? They all have a common cultural background, or in the words of Bill and Ted, they are a bunch of “dead, white dudes.”

Yet, the history of our mathematics is far more diverse and multicultural than what many of us have been led to believe. Sunil Singh, author, blogger, and editor of Q.E.D, writes that mathematics “is rich and complex.” To help students feel a sense of inclusion in the mathematics within our classrooms, they must be able to see themselves in the story. Telling the true, historical context of mathematics is a crucial piece that is often missing. Singh states it this way: “much of its roots [have been] hidden, ignored, and marginalized.” (Singh, 2020).

When we capitalize on the opportunity to talk, discuss, and interject these histories within our classrooms, we open up potential spaces for connection, belonging, identity, and self-actualization for our students. This necessitates that we be intentional in creating those opportunities. Take time to highlight a mathematical concept or a specific mathematician once a week, perhaps as you begin the week. Seek specific, explicit connections between the math in a lesson and the history of that concept. Assign a research project where students read, research, and report on specific mathematical concepts through the ages. There are a multitude of ways to do this without losing valuable class time while also making your class more culturally responsive as you share this rich history.

There is an entire history of mathematics outside of San Dimas*. And “dead, white dudes” represent merely a portion of that history. We owe it to ourselves and our students to share a truly global understanding of the entire scope of mathematics through the ages.

For more on the amazing history of mathematics, here are a few resources to get you started:

- The Story of Mathematics
- The Crest of the Peacock: Non-European Roots of Mathematics (Third Edition) by George Gheverghese Joseph
- African Mathematics: History, Textbook and Classroom Lessons by Robin Walker and John Matthews.
- Rethinking Mathematics: Teaching Social Justice by the Numbers by Eric (Rico) Gutstein.
- High School Mathematics Lessons to Explore, Understand, and Respond to Social Injustice by Robert Q. Berry, et al.

*San Dimas: home to Bill and Ted.

**References:**

Singh, S. (2020, June 1). 10 Questions to Begin Decolonizing Mathematics In Your Classroom. *Medium*. Retrieved from 10 Questions To Begin Decolonizing Mathematics In Your Classroom.

**Answers to the quiz:**

- Ancient Egypt, around 1800 BCE, developed the system we use for fractions. The Egyptians developed their system using unit fractions.
- The Babylonians borrowed from the ancient Sumerians, who used the sexagesimal number system (base 60). This may have been due to the rotation of the earth around the sun in about 360 days. 60 and 12 are both divisible by more numbers than 10 and 100.
- The word Algebra originated from the Arabic word
*al-jabr*, literally “the restoring of broken parts.” It was part of the title of the 9th century book by the Persian mathematician and astronomer al Khwarizimi. Interestingly enough, it is the name of the man who invented the system of balancing equations that is the namesake for the procedures we use to solve mathematical problems. - Historians of Mesopotamian mathematics have concluded that the Pythagorean rule was in widespread use during the Old Babylonian period (20th to 16th centuries BCE), over a thousand years before Pythagoras was born
*.* - Mancala is so old its precise origins are unknown, but the most reliable evidence exists for Mancala having been played 3,600 years ago in Ancient Sudan or Ghana. It has been found in some ancient temples, so there may have been some spiritual ritual associated with this game.
- The ancient Mayans in the first century BCE had calculations that were far more accurate than any in Europe into the 20th century. Their math produced 365.242 days for a calendar year and 29.5308 days for the lunar cycle. These are almost identical to the computer-generated numbers we know today.
- Yang Hui’s triangle was developed by Jia Xian in the 12th century in China.
- This sequence can be found in Sanskrit poetry. Examining how different kinds of poems can be made with long (guru) and short (laghu) vowels, the “Fibonacci” numbers appear here long before Fibonacci was born. The work can be traced back to Pingala around 200 to 300 CE.