Undergraduate / 'my foremost passion' - Stanford's Intellectual Vitality, "What is math?" [6]

Any comments/revisions on quality/thoroughness of my response, better ways to word some phrases, and grammar would be greatly appreciated! Thanks everyone!

Stanford students possess an intellectual vitality. Reflect on an idea or experience that has been important to your intellectual development (250 words)

What is math? Before middle school, I thought it was the tedious, tiresome task of 'finding x' - nothing beyond a set of repetitive, meaningless problems. This entire notion, however, drastically changed when I entered middle school.

The bell rang as I stepped into my first math class. I wasn't very excited for another year of boring problems. However, the writing on the board immediately grabbed my attention. "Prove: Any number times zero equals zero". My immediate thoughts were 'what did it mean to 'prove', and why would anyone need to prove such an obvious statement?' This certainly did not seem like the previous math classes I took.

A lanky Russian teacher stepped forward and asked if anyone knew the 'proof'. When no one raised their hands, he took the task upon himself. He wrote:

1. 0 = 0 + 0.
2. Multiply 'n' to both sides: n*0 = n(0 + 0) = n*0 + n*0
3. Subtract n*0 from both sides: 0 = n*0

When he finished writing, he had not only proved that 'n*0 = 0.' He had also proved to me that math wasn't about 'finding x'. Rather, math was a wonderful process of using acquired knowledge to unveil further truths. I had finally discovered the true beauty of mathematics. As we delved into more complicated and exciting proofs, my passion for mathematics continued to rise, and until today, it remains my foremost passion.

Undergraduate / 'meaningful activities' Princeton - How I Spent My Last Two Summers [4]

Any comments on the quality/ thoroughness of my response, better ways to word some phrases, and grammar would be very appreciated! Thanks!

PROMPT: Please tell us how you have spent the last two summers (or vacations between school years), including any jobs you have held. (About 150 words)

My last two summers were full of meaningful activities. During the summer of 2012, I participated in multiple church and service retreats, widening my horizons and interacting with other teenagers for a few days in the countryside. My family trip was also memorable, as I visited some of Korea's landmarks for the first time. Journeying through the beauties of Pyeongchang, I couldn't help but feel joyful to see my mom smiling after a long period of hospitalization. The next summer, we continued our trip as we visited Busan and the south, although I was busier with test preps, research at Seoul National University, and an internship at the National Assembly. In addition, I had a chance to represent Germany in the Leadership Conference, whereby I improved my public speaking and debate skills. Despite hectic schedule, I managed to squeeze some time to catch up with some old friends.

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