Ever tried so hard to solve a problem that you thought your head would explode? You're not alone. Sometimes our obsession to figure something out gets in the way of finding the answer.
it gets in the way of the soul's progress, as well.
Simone Weil (pronounced "vay") was a French philosopher, Jewish by birth, and Christian by attraction, who died at the age of 34 during World War II. While she never was baptized, and never produced any systematic works, she became a profoundly influential Christian theologian. In her "Reflections on the Right Use of School Studies with a View tot the Love of God", she wrote that "the development of the faculty of attention forms the real object and almost the sole interest of studies." She used the example of a student trying to solve a geometry problem, no doubt influenced by her brother Andre, a prodigy at the subject. Even if no progress is made with the problem itself, if the student applies concentrated attention to it, "this apparently barren effort has brought more light into the soul. The result will one day be discovered in prayer." Each such serious application of the attention in academic studies helps form "the habit of that attention which is the substance of prayer."
In the 2017 film, "Lady Bird", the protagonist meets with her Catholic high school teacher, a nun, to discuss a paper she has written in which she disparages her home city of Sacramento. The nun remarks that Lady Bird must love Sacramento. The teenager is surprised. The nun celebrates how much detail she included in the paper. "I guess I pay attention," Lady Bird replies. "Don't you think maybe they are the same thing? Love, and attention?" asks the nun.
William James, the late 19th/early 20th century psychologist and educator, wrote that “The faculty of voluntarily bringing back a wandering attention, over and over again, is the very root of judgment, character, and will… An education which would improve this faculty would be the education par excellence.” But this attention is not of the sort that bangs itself against its object, trying to beat it into submission. As Simone Weil put it, "most often attention is confused with a kind of muscular effort." But "the intelligence can only be led by desire. For there to be desire, there must be pleasure and joy in the work."
This resonates with the thesis of the widely-read 2002 musing by a Brooklyn high school math teacher, Paul Lockhart: "A Mathematician's Lament". Of students, he reported: "They say, 'math class is stupid and boring,' and they are right." Because math is an art, not a bunch of formulas to memorize. Lockhart compared most math education to "paint-by-numbers" masquerading as art education. One must do math in order to begin to appreciate what it is. Mathematics can be used, but fundamentally it is as "useless" as poetry and music and theater. It is about beauty, not about its applications. "A good problem is something you don’t know how to solve. That’s what makes it a good puzzle, and a good opportunity. A good problem does not just sit there in isolation, but serves as a springboard to other interesting questions. A triangle takes up half its box. What about a pyramid inside its three-dimensional box? Can we handle this problem in a similar way?"
George Polya, a celebrated mathematician who pioneered the field of multi-dimensional geometry, shared Lockhart's concerns about mathematics education. To contribute to better teaching methods, he wrote a "How to Solve It" in 1944. In it, Polya repeated this admonition: "Look at the unknown." Stop trying to solve it, at least for a while. Just look at it, sit with it. Give it your mindful attention, but not in a "muscular" way. Let it sink in. Admire it! Then compare it to other unknowns, other problems. How were those problems solved? How might those solutions apply to this problem? Polya's wisdom generalizes to all forms of problem-solving, within and beyond mathematics.