Math Discovery Lab

Math Discovery Lab (Math 101) is a discovery-based project course in mathematics at Stanford University created by Professor Thomas Church. MDL will next be taught in Winter 2018.

Apply to take Math Discovery Lab in Winter 2018!

There are a few slots left in the class; applications will be considered on a rolling basis while space remains (but please apply or contact Prof. Church ASAP, since groups will be assigned during the break).


Motivated students with any level of mathematical background are encouraged to apply. (Freshmen are eligible, but should see info below.) For questions or more information, interested students can contact Prof. Church at (this will not affect admissions).


Course description

In Math Discovery Lab, students work independently in groups of 3 to explore open-ended mathematical problems and discover original mathematics. Students formulate conjectures and hypotheses; test predictions by computation, simulation, or pure thought; and present their results to classmates. There is no lecture component, other than some introductory workshops in the first few weeks; in-class meetings will be used for group meetings and for student presentations (attendance at these presentations is required).

The three main components of the course are two 5-week projects, each culminating in a written Project Report, and one in-class presentation on your findings (either from the first or second project). These three components contribute equally to the grade (30% each); the remaining 10% is based on in-class participation and comments on other groups' presentations.

Sample projects

Project topics will be selected from a list of pre-chosen topics, designed to give teams room to explore the topic without running into unforeseen roadblocks—although that doesn't mean you won't bump up against unsolved problems! (We're grateful to MIT's Project Lab in Mathematics for sharing their materials, on which many of these topic prompts are based, under a CC BY-NC-SA license.) In rare cases, a team which excels on the first project will have the chance to propose their own topic for the second project. Here are some sample project topics:
  1. Number squares (games)
  2. The shape of stones (simulation / modeling)
  3. Floating bodies (analysis)
  4. Decimal expansions (algebra)

Course schedule

Common questions

Q: Do I have to be a math major to take Math Discovery Lab?
A: No. The point of MDL is to discover mathematics that is new to you; in some sense, the less you know, the easier this is! To benefit from MDL you will need some past exposure to mathematical thinking, but this could come from many places, including courses in other departments and experiences outside school. For example, many projects (such as Sample Project #2 above) are helped by a teammate with experience in coding or simulation.

Q: Is this undergraduate math research?
A: Not really. We have no expectation that your group will prove theorems previously unknown to the world; the goal is to discover mathematics previously unknown to you. So MDL is quite different from a typical undergraduate REU in mathematics. But this is a feature, not a bug: it means that you can tackle problems immediately, without months or years of preparation.

Q: I'm a freshman. Can I take MDL this year?
A: In general, most freshmen will do better to wait and take Math Discovery Lab in a later year. In particular, we don't recommend MDL for freshmen in the Math 41 or Math 51 series. But there have certainly been exceptional freshmen who succeeded in MDL. If you're a freshman, the application gives you a chance to list your past experience in math.