June 2024, Berkeley
Compassionate math enables diverse thought processes to reach the same mathematical truth in their own way. Indeed this is the nature of mathematics — mathematics is compassionate!
Not long after I graduated from my PhD, I was at a small math conference which still happens to be my favorite. By that time, I was used to math talks flying over my head where, at times, the only words that I had followed were "is", "was", "of" and so on. That day, at this conference, I was listening (or at least was trying to listen) to a speaker at the board. However, every word the speaker uttered was flying over my head. I looked to my side, and I saw my colleague who was also a Master’s student at that time, in distress and looking outside the window. When the session ended, I came out of the room and told my PhD advisor, Robin Cockett, "I want compassionate math".
Even though I was not aware of it at the time I uttered it, the term compassionate math had appeared in the Scholarship of Teaching and Learning decades ago [1].
Surprisingly (or unsurprisingly) the words "compassionate math" seemed to speak to anyone who was hearing it. My PhD advisor told me a few days later that what I was saying had teeth to it and that I must at least make a little webpage on it in my website. That was a bit surprising since to hear such a thing from Robin was quite rare.
So I set out on a mission trying to say in words what compassionate math(ematics) is. However, it was easier to experience it than to put it in words.
I was quite inspired at that time by the blog series on graphical linear algebra by Pawel Sobocinski. Based on my conversations with Pawel and feedback from Robin, the best I could say was this:
Compassionate math is about acknowledging that different learners take different roads to understanding the same mathematical idea and to consider this inherent plurality of thought patterns when communicating mathematics.
Well, this explanation did emphasize that compassionate math is about communication and presentation, be it writing, talking, or teaching. Hence, it includes research as well as teaching and education. However, there seemed to be a better way to say it, which I did not know how!
Since then, over the last two years, I have been discussing and working on compassionate math with wonderful people from different walks of life --- engineers, teachers, researchers, friends outside science. Something surprising and significant I learnt early on in this journey, was that "compassionate math" spoke quite differently to different people based on their experience. A few understood it as a school education, for me and my colleagues it was how we will communicate our passion for mathematics, and to a school-going niece of mine, the words "compassion" and "math" do not go together! You may have thought of something that is different from any of these. Compassionate math belongs to everyone!
Since this realization, I stopped trying to assert what compassionate math MUST BE! Rather I have started to listen with curiosity and amazement how each one perceives and expresses it. But, I have also never stopped asking myself what compassionate math is to me in words! Finally, I think I have the clarity I was seeking for! What I was looking for was in the source which inspired these words for me!
Compassionate mathematics is the mathematics that accepts who I am.
So I feel accepted and adequate to work out the math, to have fun, to be creative and to experience the joy of it. It is the mathematics that speaks to me and to any interested learner. Hence, it is intimately connected to communication, thereby including the learner, the communicator and the common ground of their connection --- the mathematical truth. The communication could be between a teacher and a student, a presenter giving a talk at a conference, a researcher writing an article for a journal, or even a casual conversation.
Compassionate math enables diverse thought processes to reach the same mathematical truth in their own way. Indeed this is the nature of mathematics --- mathematics is compassionate. Compassionate math is being aware that mathematics does not have one rigid form, but each of its different forms --- symbols, diagrams, and other modes --- have value in making the mathematical truth apparent to the learner. The same content comes in different containers.
I liked what David Spivak said in one of his talks - "What is mathematics? It is a crystallized thought pattern". To me, compassionate math says that it is a pattern that can take different forms and the mathematics is apart from its forms.
My dream is that there will be a day where mathematics is more like music. One will not need a professional degree or the so-called smartness to experience mathematics at some level. Everyone will get to experience the joy of mathematics in one form or another.
Acknowledgements. This article would not be here but for the initial push from Brandon and Esteban to consider compassionate math seriously, and the unwavering support and trust of Brendan! Thanks to the Compassionate math club for all the thought-provoking discussions over the last one year. Thank you all!
References.
1. Eisenberg, Marilyn. "Compassionate math." The Journal of Humanistic Education and Development 30.4 (1992): 157-166.
Further reading. Here are a few lovely materials out there that are exemplars of compassionate math:
1. www.math3ma.com --- A blog by Dr. Tai-Danae Bradley on various topics from various areas of Mathematics. This blog is a result of Bradley’s own experience on try to clearly see ideas and concepts “hidden behind dense fog of formalities and technical jargon”
2. graphicallinearalgebra.net --- A blog by Prof. Pawel Sobocinski rewriting linear algebra using string diagrams while explaining the intuition behind these mathematical ideas and what they represent.
3. johncarlosbaez.wordpress.com --- A blog by Prof. John Baez on physics, information theory etc explained through category theory
4. Coecke, Bob. "Kindergarten quantum mechanics: Lecture notes." AIP Conference Proceedings. Vol. 810. No. 1. American Institute of Physics, 2006.
5. Cheng, Eugenia. "How to bake pi: An edible exploration of the mathematics of mathematics" Basic Books, 2015 and her sequel book "The Joy of abstraction: An exploration of math, category theory, and life" Cambridge University Press, 2022.
6. Fong, Brendan, and David I. Spivak. "Seven sketches in compositionality: An invitation to applied category theory." arXiv preprint arXiv:1803.05316 (2018).
7. My slide deck on compassionate mathematics presented at "Compositional Structures for Systems Engineering and Design" Workshop in Nov 2022.