Primary Sources: Routes to Math

Ralph Pantozzi, a 2024-2025 Albert Einstein Distinguished Educator Fellow at the Library of Congress, wrote this post. 

“Where did they come up with this stuff?” In mathematics classes, students sometimes wonder how humans create the math that they are learning.  

This post explores the question through primary sources at the Library of Congress by focusing on the roots of math and routes to learning it. Everything in mathematics – all its words, symbols, and equations – can be traced back to actions such as:

• moving, sizing, locating
• naming, counting, timing
• sorting, grouping, comparing
• designing, drawing, playing
• touching, gesturing, explaining 

Ask students to consider the image of a machine shop at the Tuskegee Institute. Ask: Which mathematical actions from the list above are evident? What other everyday actions might also be going on before, during, and after the image was created? 

Next, examine this commencement day parade, also at the Tuskegee Institute. Use an observe, reflect and question routine to answer the following questions: 

• What do you observe in this photo?  
• What hypotheses can you make? 
• What do you wonder? 

In addition to these three questions, think again about everyday human actions might you associate with this parade. Record your thoughts before reading the possibilities that follow. 

Examining a primary source can spark questions about quantity, distance, measurement, motion, and repetition that can lead in multiple directions. Students may ask questions about the size of the group, the length of the procession, the timing of the marchers’ motion, the beats of the music, and the planning that went into the parade. All these are roots of mathematics.   

Humans have organized themselves into parades, caravans, and expeditions for millennia. In these or similar settings, keeping time, judging distances, or keeping a beat may be involved. All these actions are sources of the mathematics we have today, from arithmetic progressions to linear equations and coordinate systems to principles of geometry.   

Examining a primary source for information about any topic – from history to science – is a process that takes practice. We hope this post helps you and your students observe, reflect, and question the many roots and routes of mathematics.