History of mathematics: pre-syllabus

This is a “pre-syllabus” for the Fall 2026 version of Math 160, History of Mathematics, intended to give you an idea of what the class will be like before deciding to take it. A full syllabus (with more detailed policies and topics, grading scheme, readings, etc.) will be made available before the start of the class, likely over the summer.

Material

We will trace the history and development of mathematical ideas from antiquity through the middle ages, the Renaissance, and into the modern era. Focuses may include the mathematics of ancient Greece, Egypt, Babylon, India, and China, the Arab world, the rise of calculus in Europe, and more modern developments. (The above is a non-exhaustive list—for example, although the above are the main “canonical” mathematical cultures typically studied in this sort of course, a wide variety of mathematical cultures have of course existed across (e.g.) the Americas, Africa, Oceania, and northern Asia, whose history is often less well documented by no less interesting.)

In addition to giving an introduction to the history itself, we will also aim to give an introduction to “history of mathematics” as a discipline: the methods used, the academic issues involved, etc. We will study some of the historiography of the subject, various approaches and philosophies, and consider critically some common narratives.

Structure

The most common assignment for this class will be readings, either books (selections or in full), academic articles, or primary sources. These readings will be required and necessary to follow the class; you may also be asked to write answers to questions pertaining to the reading, though these will be intended to provoke additional thought rather than to check factual understanding.

Beyond readings, the main assignment for the class will be a final project in the form of a research paper on a topic of your choice. (Alternate formats will be possible, within reason, but should have essentially analogous content.) There will also be at least one smaller paper due earlier in the semester, possibly two or three but no more. Parts of the class will focus on research and writing methods for these papers.

Prerequisites and expectations

The prerequisites for this class are Math 53, 54, and 113. In practice, I do not expect to enforce these, except possibly as a way of filtering the waitlist.

However, in practice there will be some expected background, both mathematical and otherwise. This is not a technical class: by its nature it involves both mathematics and history, but is closer to a history class than a typical math class. However, since the topics we will study are mathematical, you will need to be comfortable with the associated technical background. For most of the class, the actual mathematics involved should be generally familiar to you; from the point of view of a modern university curriculum, the most “advanced” topic we cover in depth will be calculus, except possibly in the most “modern” portion of the class (in which we will introduce new mathematical concepts as necessary). However the guise in which we encounter these concepts may be unfamiliar, and if you are not generally comfortable with algebra, geometry, and calculus you may find this difficult.

Beyond the mathematical aspects, you will be expected to be able to read and process academic material at a reasonable pace; to write at a college level—although we will study research methods particular to our subject, the general process of writing a well-structured and coherent research paper should be familiar to you; and to have a healthy intellectual curiosity.

With all that said, I hope for the class to be accessible and engaging, and hope you choose to take it!