Compassionate math sprung out of my journey of learning category theory and writing my PhD thesis. In 2022, I was at a small-scale, nice maths conference where the speaker was at the board explaining some maths concept. I was struggling to keep up and had mostly given up at that point. I looked to my side and saw my colleague who was also a masters student at that time, utterly lost and mildly in distress. When I came out that room, I told people "I want compassionate math".
Hailing from an engineering background, it was an incredibly hard, humbling, and self-questioning journey for me to learn Category Theory, to make sense of it and to finally be able to view its beauty. After getting to the other end of the tunnel, I realized that the journey need not have been this hard. The problem was not me! It was the way in which mathematics was communicated to me!
Compassionate math seem to resonate well with anyone who I have discussed with -- from my professors and colleagues to my parents and friends. My PhD advisor Robin Cockett encouraged me to write about compassionate math in my website, hence this post! Even though learning maths is a lot about discipline and hard-work, it is also about joy and wonder! And I want every child to experience this joy!
Compassionate math has begun to grow. Thanks to Brandon Baylor and Esteban Montero for the initial spark! Thanks to Brendan Fong for the amazing mentorship, my NIST colleagues for their encouragement and to every listening ear so far! Here are a few projects I am involved in -- Stringed, a non-math math game based on string diagrams and graphical linear algebra, in collaboration with Pawel Sobocinski, Niels Voorneveld and Namista Tabassum; An Artictionary, exploring the fundamental principles of abstract mathematics through art, in colloboration with Ted Theodosopoulous and Paul Dancstep. Watch out for the fireworks!
If you are wondering what is compassionate math, I have left it deliberately undefined. Compassionate math is what these words mean to you!
For me personally, compassionate math is about communicating mathematics (in education or in research) in way that the learners feel included in the learning experience and their thought processes validated. After all, as said by Henri Poincare, mathematics is the art of giving the same name to different things!
Here are a few lovely materials out there that are exemplars of compassionate math:
https://www.math3ma.com — A blog site 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”
https://graphicallinearalgebra.net - A blog site by Prof. Pawel Sobocinski rewriting linear algebra using string diagrams while explaining the intuition behind these mathematical ideas and what they represent.
https://johncarlosbaez.wordpress.com - A blog site by Prof. John Baez on physics, information theory etc explained through category theory
Coecke, Bob. "Kindergarten quantum mechanics: Lecture notes." AIP Conference Proceedings. Vol. 810. No. 1. American Institute of Physics, 2006.
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.
Fong, Brendan, and David I. Spivak. "Seven sketches in compositionality: An invitation to applied category theory." arXiv preprint arXiv:1803.05316 (2018).
My slides on compassionate math presented at the NIST-hosted "Compositional Structures for Systems Engineering and Design" Workshop in Nov 2022.