MAT336: History of Mathematics

Spring 2026

Study Guide: Quiz 1

Sources and the Beginnings of Counting and Numbers

Note: This is a study guide. The quiz will consist of approximately four questions covering the material below. If you understand the ideas and facts in the non-computational questions and can work through the computational problems, you will be well prepared.

Quiz Questions

  1. Define primary source and secondary source. What is the key difference between them?
  2. Invent a plausible example of a primary source in math history. Explain why it is plausible. (Note: plausible here means that it could pass for real)
  3. Invent a plausible example of a secondary source in math history. Explain why it is plausible.
  4. Give a concrete example or invent a plausible one of a document that can be a primary source for one question and a secondary source for another. Explain your reasoning.
  5. What does it mean to say that counting is based on one-to-one correspondence? Give a concrete example.
  6. The Ishango Bone: Approximately how old is the Ishango bone, and on which continent was it found?
  7. Is the following statement true or false? "There is scholarly consensus that the Ishango bone represents a base-10 counting system." Explain your answer.
  8. If you found a 9th-century Arabic translation of Apollonius's Conics (written in 3rd century BCE), would this be a primary source for studying: (a) Apollonius's mathematical ideas? (b) 9th-century Arabic translation practices? Explain your reasoning.
  9. The website storyofmathematics.com contains mathematical history information but includes advertisements and lacks citations. Can we trust the information of this website? Can this website be used as a source in academic writing? Why or why not?
  10. Why is "contains information" or "states facts" not the same as "is a reliable source"?
  11. What role do body parts (fingers, toes) play in early counting systems?
  12. Why do we require peer-reviewed secondary sources in this course and in academia? Are peer-reviewed sources perfect? Explain.

Reflection Questions (For Study)

These questions will not appear on the quiz. Use them to deepen your understanding of course themes.

  1. Why did the lecture emphasize the quote "We do not see things as they are, we see them as we are" when discussing the Ishango bone interpretations? What does this suggest about doing math history?
  2. Choose one interpretation of the Ishango bone presented in the lecture. What assumptions does that interpretation make about prehistoric peoples? How might those assumptions reflect the interpreter's own time period or culture?
  3. The lecture showed multiple AI-generated images of someone carving the Ishango bone, highlighting differences in how the person was depicted. What lesson about sources and interpretation can we draw from this exercise?
  4. Why did the lecture include Russell's paradox when discussing "what is a number"? What does this tell us about seemingly simple mathematical concepts?
  5. Explain the hypothesis about the evolutionary link between fingers and counting. What evidence from the lecture supports this connection.
Quiz Rubric - Canvas Format

Quiz Problem Rubric

Points Criteria
3 Correct answer with reasoning/work shown
2 Partially correct with some reasoning shown
1 Correct answer without reasoning/work OR significant attempt with some understanding
0 Incorrect or blank

Notes