*By Benjamin Braun, Editor-in-Chief*

Two of my favorite pieces of mathematical writing are recent essays: Francis Su’s January 2017 MAA Retiring Presidential Address “Mathematics for Human Flourishing”, and Federico Ardila-Mantilla’s November 2016 *AMS Notices* article “Todos Cuentan: Cultivating Diversity in Combinatorics”. *If you have not yet read these, stop everything you are doing and give them your undivided attention.* In response to the question “Why do mathematics?”, Su argues that mathematics helps people flourish through engagement with five human desires that should influence our teaching: play, beauty, truth, justice, and love. In a similar spirit, Ardila-Mantilla lists the following four axioms upon which his educational work is built:

**Axiom 1.** Mathematical talent is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

**Axiom 2.** Everyone can have joyful, meaningful, and empowering mathematical experiences.

**Axiom 3.** Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

**Axiom 4.** Every student deserves to be treated with dignity and respect.

These essays are two of my favorites because they provide visions of teaching and learning mathematics that are rich with humanity and culture, visions that welcome and invite everyone to join our community.

The ideals and aspirations offered by Su and Ardila-Mantilla are inspiring, emotional, and profound, yet also fragile — for many mathematicians, it can be difficult to balance these with the sometimes harsh reality of our classes. An unfortunate fact is that for many of us, a significant part of teaching mathematics consists of the struggle to support students who are uninterested, frustrated, inattentive, or completely absent. We are regularly faced with the reality that large percentages of our students fail or withdraw from our courses, despite our best efforts, and often despite genuine effort on the part of our students as well. How does a concerned, thoughtful teacher navigate this conflict between the truth of the tremendous potential for our mathematical community and the truth of our honest struggle, our reality?

In my practice of teaching, I have found that the only way to resolve this conflict is to simultaneously accept both truths. This has not been, and still is not, an easy resolution to manage. In this essay, I want to share and discuss some of the mantras that I have found most helpful in my reflections on these truths. Continue reading →