contributed by: Justin Brody
go back to category: Mindfulness, Reading & Writing


In Fall 2014 I taught a first-year seminar on Contemplating Infinity. The goal of the class was to teach shamatha meditation and then use this as a foundation for employing analytical meditation to engage with some difficult mathematical content. Mathematically, we covered Cantor's Theorem and Goedel's First Incompleteness Theorem and also explored the mathematics of Zeno's Paradox.

Class information

The class had 20 students registered, and was conducted at Goucher College, a small liberal college. The course was conducted as part of Goucher's Frontier's program, which aims to acclimate students to college academics. The students were a mix of people drawn by the meditation and those drawn by the infinite.


Meditation was a major part of this course. We spent the first two weeks covering the basic techniques of shamatha (using Kamalashila's Buddhist Meditation: Tranquillity, Imagination and Insight). Afterward, students were expected to practice shamatha on their own according to the following schedule.
Daily Meditation Expectation
Meditation on Friday
Week 3
10 minutes
20 minutes
Week 4
12 minutes
20 minutes
Week 5
15 minutes
25 minutes
Week 6
17 minutes
25 minutes
Week 7
20 minutes
30 minutes
Week 8
25 minutes
50 minutes
Week 9
30 minutes
50 minutes
Week 10
40 minutes
50 minutes
Week 11
40 minutes
50 minutes
Week 12 on
45 minutes
50 minutes
Daily (calm-abiding) meditation was to be recorded in a meditation journal.

Description of activity

The daily meditations were shamatha (calm-abiding) meditation where students were expected to follow their breath and develop good posture (7 points of Vairocana). On Fridays we mixed this with analytical medtiation in which students would repeat a phrase or question silently to themselves, contemplate it, and then rest in the results of their contemplation. For example, when we were studying Cantor, the students might be given the prompt "When is one infinite set smaller than another infinite set". They would be expected to repeat this prompt to themselves for a couple of minutes, then think it through, and then rest their minds. The idea was to enable to students to go deeply into the meaning of mathematical ideas rather than skimming them superficially and moving on.

Students were expected to participate in a one-day retreat at the end of the semester.


I think the course as designed was much too ambitious in the context I was working in. The format was largely inspired by a Tibetan college program (Shedra) which I participated in at Gampo Abbey. I came in already dedicated to meditation practice and academic study. Many of my students were dedicated to neither, so the expectations may have been too high.

In particular, I don't think many students really did the daily meditations. In future iterations of the course, I will require students to come to a designated place to sit together. The focus on sitting in the initial weeks left students with the impression that the class would be easy and they weren't prepared for the difficult reading that followed, and many were not able to switch gears into something more rigorous. I think a shift in the course will be needed to convey that the expectations will be high from day one.

That said, there were a number of students who did engage fully and got a lot out of the course. They learned how to study with a calm and focused mind and engaged in a meditation practice which they found rich and rewarding.


The inspiration for the class came my experiences at Gampo Abbey Shedra ( and Nitartha Institute ( Traditionally, Buddhist practice views shamatha as a preparation for vipashyana. The latter is often translated as "insight", and in many traditions this insight is gained through analytical meditation on philosophical ideas. I personally used this framework in studying for my qualifying exams -- I would summarize an entire math text by writing out the definitions, lemmas, theorems, etc. I would then do analytical meditation on these to get a deep understanding of not just the proofs but how the ideas fit together.

Related Activities


My main goals were:
  1. Introduce students to meditation as a "life" practice
  2. Introduce students to meditation as an "academic" practice
  3. Introduce students to some beautiful mathematics and philosophy


Overall, students enjoyed the course and got a lot from it. There is a lot of work I have to do to improve it though.


The syllabus for the course: . Note that I pared down much of the reading during the semester.