We have a beautiful math verse in '24/'25 homeroom. A few weeks ago, we demonstrated the line "reciprocals, a magic trick, flip the numbers quick and slick. One half becomes two, you see..." Students dug into this line and subsequently showed their understanding that one half can gracefully transform into two.
   Last week, we picked another part of the verse to explore: "Half a leaf and quarter pie." First, someone expressed their interpretation through drawing on the board. I then held the chalk up, in silence, scanning the room (signature move to invite someone to the board). A few students raised their hand and added to the board one by one. Many of the additions involved fractions/decimals/percentages, which we had been working on.
   With no volunteers left after about 20 minutes, I prompted "add to it." Students hesitated, eyes flicking between the chalkboard and me trying to think about what they should be adding. Crickets were chirping so I drew a tree on the board. Why? I don't know. Planned? Definitely not. Then, one by one, curiosity took hold. Each student, in turn, approached the board, adding something unexpected... an extension, a shadow, a new thread to the tapestry. What had begun as quiet confusion turned into an unspoken work of art and intellect.
​   At the end of the day, no one could point to the artist. No one could explain it or give it a name. No one knew they created something that day. Many individual hands touched the board, though no more than one person was touching the board at the same time. Did we agree with one another? I don’t know. Did we disagree with one another? I don’t know. I DO know that we respected one another. For 90 minutes, we watched, thought, and worked together. For 90 minutes, we met all classroom expectations. Do you know what we made? I don’t. Yet, with no need for explanation, no final vision in mind, no conclusion being sought, the process itself became the purpose. A river doesn’t rush to reach the ocean—it carves landscapes, nourishes life, and changes course along the way. The movement itself is its purpose, just like how we weren’t racing toward an outcome; we were shaping something together, moment by moment.

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We have learned that Euclid stands out amongst old world Greek philosophers and mathematicians because of the way he PROVED his assumptions. With numbers so infinite, this concept is instinctually impossible! We have seen the connection between philosophy and mathematics; knowing how foundations were laid adds meaning, intrigue, and context to many areas of interest.
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​Below, we explore Fermat's Last Theorem, which was, until recently, one of the few well-known concepts in mathematics that was not officially proven. In the mid-17th century, Pierre de Fermat wrote that "no value of n greater than 2 could satisfy the equation x^n + y^n = z^n, where n, x, y and z are all integers." He claimed that he had a simple proof of this theorem, but no record of it has ever been found.

Ever since that time, countless professional mathematicians have tried to find a valid proof (and wondered whether Fermat really ever had one). In 1994, Andrew Wiles of Princeton University announced that he had discovered a proof while working on a more general problem in geometry.

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