The stories in Living Proof are intended to provide support and inspiration for mathematics students experiencing struggle and despair. If students keep working, if they keep seeking, they’ll be rewarded by serendipity, which is really just, as these stories remind us, the habit of mind to be engaged and to notice when something good has happened.

This powerful collection should also illuminate for faculty the potential damage of debilitating struggle to our students and our discipline and reveal strategies to lessen that harm. Teachers of mathematics can, often unintentionally, wreak profound damage on students by explicitly, or implicitly, conveying an expectation of non-success. The flip side of this is that teachers can also, again often unintentionally, have a profound positive impact with a simple, kindly encouraging remark.