Math—one of the most reviled “four-letter words” ever invented. In fact, I am surprised it made it through the editors into this article. However, this common revulsion need not be a common occurrence. Mathematics should be neither reprehensible nor detestable to any human being and in the Challenge math seminar we particularly endeavor to reconcile mathematics with the humanities, and, thereby, with humanity in general.
The humanities are often described as “studies in words,” while mathematics and geometry are described as “studies in numbers.” In the weekly Challenge math seminar, we reconcile math with mankind through a dual emphasis on both words and numbers. We work toward this reconciliation via three mathematical conversations: inquiry, discovery, and beauty.
Inquiry: The students in the upper Challenge programs know to bring questions from the previous week’s work completed at home. In fact, helping to answer questions is one of the main purposes of our time together on community day. The first portion of the Classical Conversations math seminar is to answer any questions the students have from the previous week. The students ask their questions, hence the first link between words and numbers. They must recognize where their math knowledge ended, formulate a question that seeks to bridge the gap in their knowledge, then offer their inquiry to the director and the class for discussion. When a student asks their own question concerning a math problem there is an implicit link between the concrete and the abstract, between word and number, between the humanities and the sciences. For the student to ask their own math question is necessarily humanizing and will, therefore, be ultimately satisfying when an answer is discovered. Even the search will be more humanizing than simply checking the answer key for the proper value.
This does not mean that the director is the one with all the answers. When a question related to the previous week’s work is asked in seminar , the director then directs the question to the other students for input and suggestions. In order to answer the question, the Challenge class discusses the concepts that they already know which will help them better understand the “unknown” of the problem at hand. We work the problem together and often find several suggestions to help understand the concepts and arrive at a solution. One student asks; another student explains; another student asks; other students elaborate, ask, agree, disagree, and so on. Through this conversation math is embodied by words in the air—sounds made from the lungs, throats, teeth, and tongues, heard by the ears of colleagues in a joint venture toward a solution. A math conversation is humanizing for it can only be undertaken by humans.
Discovery: Another way we humanize math in Challenge is by asking the students to make regular math presentations. They stand; they speak; they describe; they explain; they ask. They both embody and adorn math through their presentation. I ask my students to bring a problem or concept with them that they found especially challenging and eventually overcame. Through their weekly discoveries, they will be able to minister to one another by relating to each other’s struggles. As a human, it is satisfying to be able to share how the struggle was eventually overcome, and in community with other humans it is encouraging to know that others share similar struggles and that they can be overcome. Answers can be discovered. This type of presentation links humans to other humans via words instead of simply allowing math to link humans to numbers.
Beauty: The other type of presentation I ask students to bring involves problems they found distinctively beautiful during the week. Math is elegant. The solutions are orderly, even when accomplished in different orders by different people. The answers are perfect, even when perfectly irrational. The concepts work together in harmony—a symphony of steps, through an orchestra of laws and operations, performed by mathematical musicians. We often think of math as cold and rational, but the elegance of mathematics is seen by employing the human imagination to the problem at hand. The opportunity to rejoice in this elegance is an important step toward making the most of a human’s interaction with math, as well as a habituation of our minds towards objective beauty.
“Math” is not a curse word. As the triune God is forever three and one, He has been forever counting. Created in His image, humanity has been blessed, not cursed, to count. Also, as the triune God created us in His image by the power of His word—as He is a speaking God, He also made us wordsmiths. In the Challenge math seminar we seek to embody both the counting and the speaking of our blessed Creator. We seek to make warm and rational that which is so often relegated to the “cold and rational.” We seek to embody math through our words and humanize math through our community.