And how Cambridge has helped me see math as an art.
At MIT, it's easy to get caught up in the routine of things. Mindlessly powering through psets is common, and it makes sense when there's always too much work and too little time. An MIT education is known to be like drinking from a firehose, and for good reason: work comes in a constant stream and respite is hard to come by. But MIT, despite the firehose that it is, does have its merits. It relentlessly exposes you to so many concepts that you quickly learn how to learn. If there's anything you can be confident in after graduation, it's your ability to pick up concepts quickly.
But exposure is all it is. Cambridge emphasizes something different: understanding. It mimics graduate school in its emphasis on delving deep, not wide. There's much more time to focus on not only finishing problems, but also fully exploring concepts down the rabbit holes of textbooks and online resources. You get weeks instead of days in between learning concepts and applying them, so there's plenty of time to let the neural networks mature between new ideas and old. The Cambridge learning environment promotes a curiosity to really understand a problem rather than booking it to office hours the night before a pset is due. It's a much more traditional approach, and it puts the responsibility on the students to have the internal motivation to learn. However, I feel that I can only fully appreciate this freedom because I have experienced the other extreme. I value the time to explore topics because I know the rushed dissatisfaction of not having that luxury. Just like how you can't fully appreciate happiness without knowing disappointment, most of the value here lies in the contrast. So it's hard to definitively say that one way of learning is better than the other: students benefit from a balance of the learning types and to help them see how they can complement each other.
After being exposed to Cambridge's focus on understanding, I have a new appreciation for the beauty of how disparate concepts work together. It's a painting of academia, a dance of intertwined ideas. I'm addicted to the mindblowing feeling of finding connections between concepts in seeming disorder. It helps me view the world from a distorted, unique perspective, similar to the way psychoactive drugs work. Johann Hari explains how it is human nature to seek out the high of living, which could translate to an innate craving for understanding just to have a heightened sense of the world.
From photography to music, art tries to preserve the beauty of the world, but in an exaggerated sense, a saturated sense, an abstract sense. Math and science are beautiful in their truthfulness. They define the world in an honest glory, without the excess or frills. Studies show that the same parts of the brain fire when people appreciate art as when mathematicians see beautiful math. So why the constant bickering between the humanities and science? They both exist to fulfill the same goal: represent the world's beauty. There's so much intersection between the goals of the two that if anything, they complement each other more than they oppose.
When I came to Cambridge, I expected to encounter new sights, new smells, a new experience to be appreciated by the senses. However, I've also been introduced to a scholarly beauty that I couldn't have imagined. Thank you Cambridge for being a beautiful place in every way possible. :)
But exposure is all it is. Cambridge emphasizes something different: understanding. It mimics graduate school in its emphasis on delving deep, not wide. There's much more time to focus on not only finishing problems, but also fully exploring concepts down the rabbit holes of textbooks and online resources. You get weeks instead of days in between learning concepts and applying them, so there's plenty of time to let the neural networks mature between new ideas and old. The Cambridge learning environment promotes a curiosity to really understand a problem rather than booking it to office hours the night before a pset is due. It's a much more traditional approach, and it puts the responsibility on the students to have the internal motivation to learn. However, I feel that I can only fully appreciate this freedom because I have experienced the other extreme. I value the time to explore topics because I know the rushed dissatisfaction of not having that luxury. Just like how you can't fully appreciate happiness without knowing disappointment, most of the value here lies in the contrast. So it's hard to definitively say that one way of learning is better than the other: students benefit from a balance of the learning types and to help them see how they can complement each other.
After being exposed to Cambridge's focus on understanding, I have a new appreciation for the beauty of how disparate concepts work together. It's a painting of academia, a dance of intertwined ideas. I'm addicted to the mindblowing feeling of finding connections between concepts in seeming disorder. It helps me view the world from a distorted, unique perspective, similar to the way psychoactive drugs work. Johann Hari explains how it is human nature to seek out the high of living, which could translate to an innate craving for understanding just to have a heightened sense of the world.
From photography to music, art tries to preserve the beauty of the world, but in an exaggerated sense, a saturated sense, an abstract sense. Math and science are beautiful in their truthfulness. They define the world in an honest glory, without the excess or frills. Studies show that the same parts of the brain fire when people appreciate art as when mathematicians see beautiful math. So why the constant bickering between the humanities and science? They both exist to fulfill the same goal: represent the world's beauty. There's so much intersection between the goals of the two that if anything, they complement each other more than they oppose.
When I came to Cambridge, I expected to encounter new sights, new smells, a new experience to be appreciated by the senses. However, I've also been introduced to a scholarly beauty that I couldn't have imagined. Thank you Cambridge for being a beautiful place in every way possible. :)
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